Bullish or Bearish. Note Quote.

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The term spread refers to the difference in premiums between the purchase and sale of options. An option spread is the simultaneous purchase of one or more options contracts and sale of the equivalent number of options contracts, in a different series of the class of options. A spread could involve the same underlying: 

  •  Buying and selling calls, or 
  •  Buying and selling puts.

Combining puts and calls into groups of two or more makes it feasible to design derivatives with interesting payoff profiles. The profit and loss outcomes depend on the options used (puts or calls); positions taken (long or short); whether their strike prices are identical or different; and the similarity or difference of their exercise dates. Among directional positions are bullish vertical call spreads, bullish vertical put spreads, bearish vertical spreads, and bearish vertical put spreads. 

If the long position has a higher premium than the short position, this is known as a debit spread, and the investor will be required to deposit the difference in premiums. If the long position has a lower premium than the short position, this is a credit spread, and the investor will be allowed to withdraw the difference in premiums. The spread will be even if the premiums on each side results are the same. 

A potential loss in an option spread is determined by two factors: 

  • Strike price 
  • Expiration date 

If the strike price of the long call is greater than the strike price of the short call, or if the strike price of the long put is less than the strike price of the short put, a margin is required because adverse market moves can cause the short option to suffer a loss before the long option can show a profit.

A margin is also required if the long option expires before the short option. The reason is that once the long option expires, the trader holds an unhedged short position. A good way of looking at margin requirements is that they foretell potential loss. Here are, in a nutshell, the main option spreadings.

A calendar, horizontal, or time spread is the simultaneous purchase and sale of options of the same class with the same exercise prices but with different expiration dates. A vertical, or price or money, spread is the simultaneous purchase and sale of options of the same class with the same expiration date but with different exercise prices. A bull, or call, spread is a type of vertical spread that involves the purchase of the call option with the lower exercise price while selling the call option with the higher exercise price. The result is a debit transaction because the lower exercise price will have the higher premium.

  • The maximum risk is the net debit: the long option premium minus the short option premium. 
  • The maximum profit potential is the difference in the strike prices minus the net debit. 
  • The breakeven is equal to the lower strike price plus the net debit. 

A trader will typically buy a vertical bull call spread when he is mildly bullish. Essentially, he gives up unlimited profit potential in return for reducing his risk. In a vertical bull call spread, the trader is expecting the spread premium to widen because the lower strike price call comes into the money first. 

Vertical spreads are the more common of the direction strategies, and they may be bullish or bearish to reflect the holder’s view of market’s anticipated direction. Bullish vertical put spreads are a combination of a long put with a low strike, and a short put with a higher strike. Because the short position is struck closer to-the-money, this generates a premium credit. 

Bearish vertical call spreads are the inverse of bullish vertical call spreads. They are created by combining a short call with a low strike and a long call with a higher strike. Bearish vertical put spreads are the inverse of bullish vertical put spreads, generated by combining a short put with a low strike and a long put with a higher strike. This is a bearish position taken when a trader or investor expects the market to fall. 

The bull or sell put spread is a type of vertical spread involving the purchase of a put option with the lower exercise price and sale of a put option with the higher exercise price. Theoretically, this is the same action that a bull call spreader would take. The difference between a call spread and a put spread is that the net result will be a credit transaction because the higher exercise price will have the higher premium. 

  • The maximum risk is the difference in the strike prices minus the net credit. 
  • The maximum profit potential equals the net credit. 
  • The breakeven equals the higher strike price minus the net credit. 

The bear or sell call spread involves selling the call option with the lower exercise price and buying the call option with the higher exercise price. The net result is a credit transaction because the lower exercise price will have the higher premium.

A bear put spread (or buy spread) involves selling some of the put option with the lower exercise price and buying the put option with the higher exercise price. This is the same action that a bear call spreader would take. The difference between a call spread and a put spread, however, is that the net result will be a debit transaction because the higher exercise price will have the higher premium. 

  • The maximum risk is equal to the net debit. 
  • The maximum profit potential is the difference in the strike
    prices minus the net debit. 
  • The breakeven equals the higher strike price minus the net debit.

An investor or trader would buy a vertical bear put spread because he or she is mildly bearish, giving up an unlimited profit potential in return for a reduction in risk. In a vertical bear put spread, the trader is expecting the spread premium to widen because the higher strike price put comes into the money first. 

In conclusion, investors and traders who are bullish on the market will either buy a bull call spread or sell a bull put spread. But those who are bearish on the market will either buy a bear put spread or sell a bear call spread. When the investor pays more for the long option than she receives in premium for the short option, then the spread is a debit transaction. In contrast, when she receives more than she pays, the spread is a credit transaction. Credit spreads typically require a margin deposit. 

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Option Spread. Drunken Risibility.

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The term spread refers to the difference in premiums between the purchase and sale of options. An option spread is the simultaneous purchase of one or more options contracts and sale of the equivalent number of options contracts, in a different series of the class of options. A spread could involve the same underlying:

  •  Buying and selling calls, or
  •  Buying and selling puts.

Combining puts and calls into groups of two or more makes it feasible to design derivatives with interesting payoff profiles. The profit and loss outcomes depend on the options used (puts or calls); positions taken (long or short); whether their strike prices are identical or different; and the similarity or difference of their exercise dates. Among directional positions are bullish vertical call spreads, bullish vertical put spreads, bearish vertical spreads, and bearish vertical put spreads.

If the long position has a higher premium than the short position, this is known as a debit spread, and the investor will be required to deposit the difference in premiums. If the long position has a lower premium than the short position, this is a credit spread, and the investor will be allowed to withdraw the difference in premiums. The spread will be even if the premiums on each side results are the same.

A potential loss in an option spread is determined by two factors:

  • Strike price
  • Expiration date

If the strike price of the long call is greater than the strike price of the short call, or if the strike price of the long put is less than the strike price of the short put, a margin is required because adverse market moves can cause the short option to suffer a loss before the long option can show a profit.

A margin is also required if the long option expires before the short option. The reason is that once the long option expires, the trader holds an unhedged short position. A good way of looking at margin requirements is that they foretell potential loss. Here are, in a nutshell, the main option spreadings.

A calendar, horizontal, or time spread is the simultaneous purchase and sale of options of the same class with the same exercise prices but with different expiration dates. A vertical, or price or money, spread is the simultaneous purchase and sale of options of the same class with the same expiration date but with different exercise prices. A bull, or call, spread is a type of vertical spread that involves the purchase of the call option with the lower exercise price while selling the call option with the higher exercise price. The result is a debit transaction because the lower exercise price will have the higher premium.

  • The maximum risk is the net debit: the long option premium minus the short option premium.
  • The maximum profit potential is the difference in the strike prices minus the net debit.
  • The breakeven is equal to the lower strike price plus the net debit.

A trader will typically buy a vertical bull call spread when he is mildly bullish. Essentially, he gives up unlimited profit potential in return for reducing his risk. In a vertical bull call spread, the trader is expecting the spread premium to widen because the lower strike price call comes into the money first.

Vertical spreads are the more common of the direction strategies, and they may be bullish or bearish to reflect the holder’s view of market’s anticipated direction. Bullish vertical put spreads are a combination of a long put with a low strike, and a short put with a higher strike. Because the short position is struck closer to-the-money, this generates a premium credit.

Bearish vertical call spreads are the inverse of bullish vertical call spreads. They are created by combining a short call with a low strike and a long call with a higher strike. Bearish vertical put spreads are the inverse of bullish vertical put spreads, generated by combining a short put with a low strike and a long put with a higher strike. This is a bearish position taken when a trader or investor expects the market to fall.

The bull or sell put spread is a type of vertical spread involving the purchase of a put option with the lower exercise price and sale of a put option with the higher exercise price. Theoretically, this is the same action that a bull call spreader would take. The difference between a call spread and a put spread is that the net result will be a credit transaction because the higher exercise price will have the higher premium.

  • The maximum risk is the difference in the strike prices minus the net credit.
  • The maximum profit potential equals the net credit.
  • The breakeven equals the higher strike price minus the net credit.

The bear or sell call spread involves selling the call option with the lower exercise price and buying the call option with the higher exercise price. The net result is a credit transaction because the lower exercise price will have the higher premium.

A bear put spread (or buy spread) involves selling some of the put option with the lower exercise price and buying the put option with the higher exercise price. This is the same action that a bear call spreader would take. The difference between a call spread and a put spread, however, is that the net result will be a debit transaction because the higher exercise price will have the higher premium.

  • The maximum risk is equal to the net debit.
  • The maximum profit potential is the difference in the strike
    prices minus the net debit.
  • The breakeven equals the higher strike price minus the net debit.

An investor or trader would buy a vertical bear put spread because he or she is mildly bearish, giving up an unlimited profit potential in return for a reduction in risk. In a vertical bear put spread, the trader is expecting the spread premium to widen because the higher strike price put comes into the money first.

So, investors and traders who are bullish on the market will either buy a bull call spread or sell a bull put spread. But those who are bearish on the market will either buy a bear put spread or sell a bear call spread. When the investor pays more for the long option than she receives in premium for the short option, then the spread is a debit transaction. In contrast, when she receives more than she pays, the spread is a credit transaction. Credit spreads typically require a margin deposit.

Velocity of Money

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The most basic difference between the demand theory of money and exchange theory of money lies in the understanding of quantity equation

M . v = P . Y —– (1)

Here M is money supply, P is price and Y is real output; in addition, v is constant velocity of money. The demand theory understands that (1) reflects the needs of the economic individual for money, not only the meaning of exchange. Under the assumption of liquidity preference, the demand theory introduces nominal interest rate into demand function of money, thus exhibiting more economic pictures than traditional quantity theory does. Let us, however concentrate on the economic movement through linearization of exchange theory emphasizing exchange medium function of money.

Let us assume that the central bank provides a very small supply M of money, which implies that the value PY of products manufactured by the producer will be unable to be realized only through one transaction. The producer has to suspend the transaction until the purchasers possess money at hand again, which will elevate the transaction costs and even result in the bankruptcy of the producer. Then, will the producer do nothing and wait for the bankruptcy?

In reality, producers would rather adjust sales value through raising or lowering the price or amount of product to attempt the realization of a maximal sales value M than reserve the stock of products to subject the sale to the limit of velocity of money. In other words, producer would adjust price or real output to control the velocity of money, since the velocity of money can influence the realization of the product value.

Every time money changes hands, a transaction is completed; thus numerous turnovers of money for an individual during a given period of time constitute a macroeconomic exchange ∑ipiYi if the prices pi can be replaced by an average price P, then we can rewrite the value of exchange as ∑ipiYi = P . Y. In a real economy, the producer will manage to make P . Y close the money supply M as much as possible through adjusting the real output or its price.

For example, when a retailer comes to a strange community to sell her commodities, she always prefers to make a price through trial and error. If she finds that higher price can still promote the sales amount, then she will choose to continue raising the price until the sales amount less changes; on the other hand, if she confirms that lower price can create the more sales amount, then she will decrease the price of the commodity. Her strategy of pricing depends on price elasticity of demand for the commodity. However, the maximal value of the sales amount is determined by how much money the community can supply, thus the pricing of the retailer will make her sales close this maximal sale value, namely money for consumption of the community. This explains why the same commodity can always be sold at a higher price in the rich area.

Equation (1) is not an identical equation but an equilibrium state of exchange process in an economic system. Evidently, the difference M –  P . Y  between the supply of money and present sales value provides a vacancy for elevating sales value, in other words, the supply of money acts as the role of a carrying capacity for sales value. We assume that the vacancy is in direct proportion to velocity of increase of the sales value, and then derive a dynamical quantity equation

M(t) - P(t) . Y(t)  =  k . d[P(t) . Y(t)]/d(t) —– (2)

Here k is a positive constant and expresses a characteristic time with which the vacancy is filled. This is a speculated basic dynamical quantity equation of exchange by money. In reality, the money supply M(t) can usually be given; (2) is actually an evolution equation of sales value P(t)Y(t) , which can uniquely determine an evolving path of the price.

The role of money in (2) can be seen that money is only a medium of commodity exchange, just like the chopsticks for eating and the soap for washing. All needs for money are or will be order to carry out the commodity exchange. The behavior of holding money of the economic individuals implies a potential exchange in the future, whether for speculation or for the preservation of wealth, but it cannot directly determine the present price because every realistic price always comes from the commodity exchange, and no exchange and no price. In other words, what we are concerned with is not the reason of money generation, but form of money generation, namely we are concerned about money generation as a function of time rather than it as a function of income or interest rate. The potential needs for money which you can use various reasons to explain cannot contribute to price as long as the money does not participate in the exchange, thus the money supply not used to exchange will not occur in (2).

On the other hand, the change in money supply would result in a temporary vacancy of sales value, although sales value will also be achieved through exchanging with the new money supply at the next moment, since the price or sales volume may change. For example, a group of residents spend M(t) to buy houses of P(t)Y(t) through the loan at time t, evidently M(t) = P(t)Y(t). At time t+1, another group of residents spend M(t+1) to buy houses of P(t+1)Y(t+1) through the loan, and M(t+1) = P(t+1)Y(t+1). Thus, we can consider M(t+1) – M(t) as increase in money supply, and this increase can cause a temporary vacancy of sales value M(t+1) – P(t)Y(t). It is this vacancy that encourages sellers to try to maximize sales through adjusting the price by trial and error and also real estate developers to increase or decrease their housing production. Ultimately, new prices and production are produced and the exchange is completed at the level of M(t+1) = P(t+1)Y(t+1). In reality, the gap between M(t+1) and M(t) is often much smaller than the vacancy M(t+1) – P(t)Y(t), therefore we can approximately consider M(t+1) as M(t) if the money supply function M(t) is continuous and smooth.

However, it is necessary to emphasize that (2) is not a generation equation of demand function P(Y), which means (2) is a unique equation of determination of price (path), since, from the perspective of monetary exchange theory, the evolution of price depends only on money supply and production and arises from commodity exchange rather than relationship between supply and demand of products in the traditional economics where the meaning of the exchange is not obvious. In addition, velocity of money is not contained in this dynamical quantity equation, but its significance PY/M will be endogenously exhibited by the system.

Fundamental Theorem of Asset Pricing: Tautological Meeting of Mathematical Martingale and Financial Arbitrage by the Measure of Probability.

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The Fundamental Theorem of Asset Pricing (FTAP hereafter) has two broad tenets, viz.

1. A market admits no arbitrage, if and only if, the market has a martingale measure.

2. Every contingent claim can be hedged, if and only if, the martingale measure is unique.

The FTAP is a theorem of mathematics, and the use of the term ‘measure’ in its statement places the FTAP within the theory of probability formulated by Andrei Kolmogorov (Foundations of the Theory of Probability) in 1933. Kolmogorov’s work took place in a context captured by Bertrand Russell, who observed that

It is important to realise the fundamental position of probability in science. . . . As to what is meant by probability, opinions differ.

In the 1920s the idea of randomness, as distinct from a lack of information, was becoming substantive in the physical sciences because of the emergence of the Copenhagen Interpretation of quantum mechanics. In the social sciences, Frank Knight argued that uncertainty was the only source of profit and the concept was pervading John Maynard Keynes’ economics (Robert Skidelsky Keynes the return of the master).

Two mathematical theories of probability had become ascendant by the late 1920s. Richard von Mises (brother of the Austrian economist Ludwig) attempted to lay down the axioms of classical probability within a framework of Empiricism, the ‘frequentist’ or ‘objective’ approach. To counter–balance von Mises, the Italian actuary Bruno de Finetti presented a more Pragmatic approach, characterised by his claim that “Probability does not exist” because it was only an expression of the observer’s view of the world. This ‘subjectivist’ approach was closely related to the less well-known position taken by the Pragmatist Frank Ramsey who developed an argument against Keynes’ Realist interpretation of probability presented in the Treatise on Probability.

Kolmogorov addressed the trichotomy of mathematical probability by generalising so that Realist, Empiricist and Pragmatist probabilities were all examples of ‘measures’ satisfying certain axioms. In doing this, a random variable became a function while an expectation was an integral: probability became a branch of Analysis, not Statistics. Von Mises criticised Kolmogorov’s generalised framework as un-necessarily complex. About a decade and a half back, the physicist Edwin Jaynes (Probability Theory The Logic Of Science) champions Leonard Savage’s subjectivist Bayesianism as having a “deeper conceptual foundation which allows it to be extended to a wider class of applications, required by current problems of science”.

The objections to measure theoretic probability for empirical scientists can be accounted for as a lack of physicality. Frequentist probability is based on the act of counting; subjectivist probability is based on a flow of information, which, following Claude Shannon, is now an observable entity in Empirical science. Measure theoretic probability is based on abstract mathematical objects unrelated to sensible phenomena. However, the generality of Kolmogorov’s approach made it flexible enough to handle problems that emerged in physics and engineering during the Second World War and his approach became widely accepted after 1950 because it was practically more useful.

In the context of the first statement of the FTAP, a ‘martingale measure’ is a probability measure, usually labelled Q, such that the (real, rather than nominal) price of an asset today, X0, is the expectation, using the martingale measure, of its (real) price in the future, XT. Formally,

X0 = EQ XT

The abstract probability distribution Q is defined so that this equality exists, not on any empirical information of historical prices or subjective judgement of future prices. The only condition placed on the relationship that the martingale measure has with the ‘natural’, or ‘physical’, probability measures usually assigned the label P, is that they agree on what is possible.

The term ‘martingale’ in this context derives from doubling strategies in gambling and it was introduced into mathematics by Jean Ville in a development of von Mises’ work. The idea that asset prices have the martingale property was first proposed by Benoit Mandelbrot in response to an early formulation of Eugene Fama’s Efficient Market Hypothesis (EMH), the two concepts being combined by Fama. For Mandelbrot and Fama the key consequence of prices being martingales was that the current price was independent of the future price and technical analysis would not prove profitable in the long run. In developing the EMH there was no discussion on the nature of the probability under which assets are martingales, and it is often assumed that the expectation is calculated under the natural measure. While the FTAP employs modern terminology in the context of value-neutrality, the idea of equating a current price with a future, uncertain, has ethical ramifications.

The other technical term in the first statement of the FTAP, arbitrage, has long been used in financial mathematics. Liber Abaci Fibonacci (Laurence Sigler Fibonaccis Liber Abaci) discusses ‘Barter of Merchandise and Similar Things’, 20 arms of cloth are worth 3 Pisan pounds and 42 rolls of cotton are similarly worth 5 Pisan pounds; it is sought how many rolls of cotton will be had for 50 arms of cloth. In this case there are three commodities, arms of cloth, rolls of cotton and Pisan pounds, and Fibonacci solves the problem by having Pisan pounds ‘arbitrate’, or ‘mediate’ as Aristotle might say, between the other two commodities.

Within neo-classical economics, the Law of One Price was developed in a series of papers between 1954 and 1964 by Kenneth Arrow, Gérard Debreu and Lionel MacKenzie in the context of general equilibrium, in particular the introduction of the Arrow Security, which, employing the Law of One Price, could be used to price any asset. It was on this principle that Black and Scholes believed the value of the warrants could be deduced by employing a hedging portfolio, in introducing their work with the statement that “it should not be possible to make sure profits” they were invoking the arbitrage argument, which had an eight hundred year history. In the context of the FTAP, ‘an arbitrage’ has developed into the ability to formulate a trading strategy such that the probability, under a natural or martingale measure, of a loss is zero, but the probability of a positive profit is not.

To understand the connection between the financial concept of arbitrage and the mathematical idea of a martingale measure, consider the most basic case of a single asset whose current price, X0, can take on one of two (present) values, XTD < XTU, at time T > 0, in the future. In this case an arbitrage would exist if X0 ≤ XTD < XTU: buying the asset now, at a price that is less than or equal to the future pay-offs, would lead to a possible profit at the end of the period, with the guarantee of no loss. Similarly, if XTD < XTU ≤ X0, short selling the asset now, and buying it back would also lead to an arbitrage. So, for there to be no arbitrage opportunities we require that

XTD < X0 < XTU

This implies that there is a number, 0 < q < 1, such that

X0 = XTD + q(XTU − XTD)

= qXTU + (1−q)XTD

The price now, X0, lies between the future prices, XTU and XTD, in the ratio q : (1 − q) and represents some sort of ‘average’. The first statement of the FTAP can be interpreted simply as “the price of an asset must lie between its maximum and minimum possible (real) future price”.

If X0 < XTD ≤ XTU we have that q < 0 whereas if XTD ≤ XTU < X0 then q > 1, and in both cases q does not represent a probability measure which by Kolmogorov’s axioms, must lie between 0 and 1. In either of these cases an arbitrage exists and a trader can make a riskless profit, the market involves ‘turpe lucrum’. This account gives an insight as to why James Bernoulli, in his moral approach to probability, considered situations where probabilities did not sum to 1, he was considering problems that were pathological not because they failed the rules of arithmetic but because they were unfair. It follows that if there are no arbitrage opportunities then quantity q can be seen as representing the ‘probability’ that the XTU price will materialise in the future. Formally

X0 = qXTU + (1−q) XTD ≡ EQ XT

The connection between the financial concept of arbitrage and the mathematical object of a martingale is essentially a tautology: both statements mean that the price today of an asset must lie between its future minimum and maximum possible value. This first statement of the FTAP was anticipated by Frank Ramsey when he defined ‘probability’ in the Pragmatic sense of ‘a degree of belief’ and argues that measuring ‘degrees of belief’ is through betting odds. On this basis he formulates some axioms of probability, including that a probability must lie between 0 and 1. He then goes on to say that

These are the laws of probability, …If anyone’s mental condition violated these laws, his choice would depend on the precise form in which the options were offered him, which would be absurd. He could have a book made against him by a cunning better and would then stand to lose in any event.

This is a Pragmatic argument that identifies the absence of the martingale measure with the existence of arbitrage and today this forms the basis of the standard argument as to why arbitrages do not exist: if they did the, other market participants would bankrupt the agent who was mis-pricing the asset. This has become known in philosophy as the ‘Dutch Book’ argument and as a consequence of the fact/value dichotomy this is often presented as a ‘matter of fact’. However, ignoring the fact/value dichotomy, the Dutch book argument is an alternative of the ‘Golden Rule’– “Do to others as you would have them do to you.”– it is infused with the moral concepts of fairness and reciprocity (Jeffrey Wattles The Golden Rule).

FTAP is the ethical concept of Justice, capturing the social norms of reciprocity and fairness. This is significant in the context of Granovetter’s discussion of embeddedness in economics. It is conventional to assume that mainstream economic theory is ‘undersocialised’: agents are rational calculators seeking to maximise an objective function. The argument presented here is that a central theorem in contemporary economics, the FTAP, is deeply embedded in social norms, despite being presented as an undersocialised mathematical object. This embeddedness is a consequence of the origins of mathematical probability being in the ethical analysis of commercial contracts: the feudal shackles are still binding this most modern of economic theories.

Ramsey goes on to make an important point

Having any definite degree of belief implies a certain measure of consistency, namely willingness to bet on a given proposition at the same odds for any stake, the stakes being measured in terms of ultimate values. Having degrees of belief obeying the laws of probability implies a further measure of consistency, namely such a consistency between the odds acceptable on different propositions as shall prevent a book being made against you.

Ramsey is arguing that an agent needs to employ the same measure in pricing all assets in a market, and this is the key result in contemporary derivative pricing. Having identified the martingale measure on the basis of a ‘primal’ asset, it is then applied across the market, in particular to derivatives on the primal asset but the well-known result that if two assets offer different ‘market prices of risk’, an arbitrage exists. This explains why the market-price of risk appears in the Radon-Nikodym derivative and the Capital Market Line, it enforces Ramsey’s consistency in pricing. The second statement of the FTAP is concerned with incomplete markets, which appear in relation to Arrow-Debreu prices. In mathematics, in the special case that there are as many, or more, assets in a market as there are possible future, uncertain, states, a unique pricing vector can be deduced for the market because of Cramer’s Rule. If the elements of the pricing vector satisfy the axioms of probability, specifically each element is positive and they all sum to one, then the market precludes arbitrage opportunities. This is the case covered by the first statement of the FTAP. In the more realistic situation that there are more possible future states than assets, the market can still be arbitrage free but the pricing vector, the martingale measure, might not be unique. The agent can still be consistent in selecting which particular martingale measure they choose to use, but another agent might choose a different measure, such that the two do not agree on a price. In the context of the Law of One Price, this means that we cannot hedge, replicate or cover, a position in the market, such that the portfolio is riskless. The significance of the second statement of the FTAP is that it tells us that in the sensible world of imperfect knowledge and transaction costs, a model within the framework of the FTAP cannot give a precise price. When faced with incompleteness in markets, agents need alternative ways to price assets and behavioural techniques have come to dominate financial theory. This feature was realised in The Port Royal Logic when it recognised the role of transaction costs in lotteries.

Financial Forward Rate “Strings” (Didactic 1)

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Imagine that Julie wants to invest $1 for two years. She can devise two possible strategies. The first one is to put the money in a one-year bond at an interest rate r1. At the end of the year, she must take her money and find another one-year bond, with interest rate r1/2 which is the interest rate in one year on a loan maturing in two years. The final payoff of this strategy is simply (1 + r1)(1 + r1/2). The problem is that Julie cannot know for sure what will be the one-period interest rate r1/2 of next year. Thus, she can only estimate a return by guessing the expectation of r1/2.

Instead of making two separate investments of one year each, Julie could invest her money today in a bond that pays off in two years with interest rate r2. The final payoff is then (1 + r2)2. This second strategy is riskless as she knows for sure her return. Now, this strategy can be reinterpreted along the line of the first strategy as follows. It consists in investing for one year at the rate r1 and for the second year at a forward rate f2. The forward rate is like the r1/2 rate, with the essential difference that it is guaranteed : by buying the two-year bond, Julie can “lock in” an interest rate f2 for the second year.

This simple example illustrates that the set of all possible bonds traded on the market is equivalent to the so-called forward rate curve. The forward rate f(t,x) is thus the interest rate that can be contracted at time t for instantaneously riskless borrowing 1 or lending at time t + x. It is thus a function or curve of the time-to-maturity x2, where x plays the role of a “length” variable, that deforms with time t. Its knowledge is completely equivalent to the set of bond prices P(t,x) at time t that expire at time t + x. The shape of the forward rate curve f(t,x) incessantly fluctuates as a function of time t. These fluctuations are due to a combination of factors, including future expectation of the short-term interest rates, liquidity preferences, market segmentation and trading. It is obvious that the forward rate f (t, x+δx) for δx small can not be very different from f (t,x). It is thus tempting to see f(t,x) as a “string” characterized by a kind of tension which prevents too large local deformations that would not be financially acceptable. This superficial analogy is in the follow up of the repetitious intersections between finance and physics, starting with Bachelier who solved the diffusion equation of Brownian motion as a model of stock market price fluctuations five years before Einstein, continuing with the discovery of the relevance of Lévy laws for cotton price fluctuations by Mandelbrot that can be compared with the present interest of such power laws for the description of physical and natural phenomena. The present investigation delves into how to formalize mathematically this analogy between the forward rate curve and a string. We formulate the term structure of interest rates as the solution of a stochastic partial differential equation (SPDE), following the physical analogy of a continuous curve (string) whose shape moves stochastically through time.

The equation of motion of macroscopic physical strings is derived from conservation laws. The fundamental equations of motion of microscopic strings formulated to describe the fundamental particles derive from global symmetry principles and dualities between long-range and short-range descriptions. Are there similar principles that can guide the determination of the equations of motion of the more down-to-earth financial forward rate “strings”?

Suppose that in the middle ages, before Copernicus and Galileo, the Earth really was stationary at the centre of the universe, and only began moving later on. Imagine that during the nineteenth century, when everyone believed classical physics to be true, that it really was true, and quantum phenomena were non-existent. These are not philosophical musings, but an attempt to portray how physics might look if it actually behaved like the financial markets. Indeed, the financial world is such that any insight is almost immediately used to trade for a profit. As the insight spreads among traders, the “universe” changes accordingly. As G. Soros has pointed out, market players are “actors observing their own deeds”. As E. Derman, head of quantitative strategies at Goldman Sachs, puts it, in physics you are playing against God, who does not change his mind very often. In finance, you are playing against Gods creatures, whose feelings are ephemeral, at best unstable, and the news on which they are based keep streaming in. Value clearly derives from human beings, while mass, charge and electromagnetism apparently do not. This has led to suggestions that a fruitful framework to study finance and economy is to use evolutionary models inspired from biology and genetics.

This does not however guide us much for the determination of “fundamental” equa- tions, if any. Here, we propose to use the condition of absence of arbitrage opportunity and show that this leads to strong constraints on the structure of the governing equations. The basic idea is that, if there are arbitrage opportunities (free lunches), they cannot live long or must be quite subtle, otherwise traders would act on them and arbitrage them away. The no-arbitrage condition is an idealization of a self-consistent dynamical state of the market resulting from the incessant actions of the traders (ar- bitragers). It is not the out-of-fashion equilibrium approximation sometimes described but rather embodies a very subtle cooperative organization of the market.

We consider this condition as the fundamental backbone for the theory. The idea to impose this requirement is not new and is in fact the prerequisite of most models developed in the academic finance community. Modigliani and Miller [here and here] have indeed emphasized the critical role played by arbitrage in determining the value of securities. It is sometimes suggested that transaction costs and other market imperfections make irrelevant the no-arbitrage condition. Let us address briefly this question.

Transaction costs in option replication and other hedging activities have been extensively investigated since they (or other market “imperfections”) clearly disturb the risk-neutral argument and set option theory back a few decades. Transaction costs induce, for obvious reasons, dynamic incompleteness, thus preventing valuation as we know it since Black and Scholes. However, the most efficient dynamic hedgers (market makers) incur essentially no transaction costs when owning options. These specialized market makers compete with each other to provide liquidity in option instruments, and maintain inventories in them. They rationally limit their dynamic replication to their residual exposure, not their global exposure. In addition, the fact that they do not hold options until maturity greatly reduces their costs of dynamic hedging. They have an incentive in the acceleration of financial intermediation. Furthermore, as options are rarely replicated until maturity, the expected transaction costs of the short options depend mostly on the dynamics of the order flow in the option markets – not on the direct costs of transacting. For the efficient operators (and those operators only), markets are more dynamically complete than anticipated. This is not true for a second category of traders, those who merely purchase or sell financial instruments that are subjected to dynamic hedging. They, accordingly, neither are equipped for dynamic hedging, nor have the need for it, thanks to the existence of specialized and more efficient market makers. The examination of their transaction costs in the event of their decision to dynamically replicate their options is of no true theoretical contribution. A second important point is that the existence of transaction costs should not be invoked as an excuse for disregarding the no-arbitrage condition, but, rather should be constructively invoked to study its impacts on the models…..

Nobel Prize in Economics and Crimino(logy)/(genic). How Contracts Work? Note Quote.

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How has the Swedish Central Bank’s committee that awards prizes in Economics in honor of Nobel responded to the field’s abject failures regarding the recent financial crisis and the Great Recession?  A lesser group would display humility, acknowledge its failures, and promise a fundamental rethink of the field.  Neoclassical economists, however, are made of sterner stuff.  The committee’s response is to praise the discipline for its theoretical advances and proposed policies related to finance, regulation, and corporate governance. Oliver Hart, and Bengt Holmström exemplify this pattern.

The economics prize is a bit different. It was created by Sweden’s Central Bank in 1969, nearly 75 years later. The award’s real name is the “Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.” It was not established by Nobel, but supposedly in memory of Nobel. It’s a ruse and a PR trick, and I mean that literally. And it was done completely against the wishes of the Nobel family.

Sweden’s Central Bank quietly snuck it in with all the other Nobel Prizes to give free-market economics for the 1% credibility. One of the Federal Reserve banks explained it succinctly, “Few realize, especially outside of economists, that the prize in economics is not an “official” Nobel. . . . The award for economics came almost 70 years later—bootstrapped to the Nobel in 1968 as a bit of a marketing ploy to celebrate the Bank of Sweden’s 300th anniversary.” Yes, you read that right: “a marketing ploy.”

The Economics Prize has nestled itself in and is awarded as if it were a Nobel Prize. But it’s a PR coup by economists to improve their reputation,” Nobel’s great great nephew Peter Nobel told AFP in 2005, adding that “It’s most often awarded to stock market speculators …. There is nothing to indicate that [Alfred Nobel] would have wanted such a prize.

Members of the Nobel family are among the harshest, most persistent critics of the economics prize, and members of the family have repeatedly called for the prize to be abolished or renamed. In 2001, on the 100th anniversery of the Nobel Prizes, four family members published a letter in the Swedish paper Svenska Dagbladet, arguing that the economics prize degrades and cheapens the real Nobel Prizes. They aren’t the only ones.

Scientists never had much respect for the new economic Nobel prize. In fact, a scientist who headed Nixon’s Science Advisory Committee in 1969, was shocked to learn that economists were even allowed on stage to accept their award with the real Nobel laureates. He was incredulous: “You mean they sat on the platform with you?”

Why economics? To answer that question we have to go back to Sweden in the 1960s.

Around the time the prize was created, Sweden’s banking and business interests were busy trying to ram through various so-called “free-market” economic reforms. Their big objective at the time was to loosen political oversight and control over the country’s central bank. According to Philip Mirowski, a professor at the University of Notre Dame who specializes in the history of economics, the

Bank of Sweden was trying to become more independent of democratic accountability in the late 60s, and there was a big political dispute in Sweden as to whether the bank could have effective political independence. In order to support that position, the bank needed to claim that it had a kind of scientific credibility that was not grounded in political support.

Promoters of central bank independence couched their arguments in the obscure language of neoclassical economic theory of market efficiency. The problem was that few people in Sweden took their neoclassical babble very seriously, and saw their plan for central bank independence for what it was: an attempt to transfer control over economic matters from democratically elected government and place into the hands of big business interests, giving them a free hand in running Sweden’s economy without pesky interference from labor unions, voters and elected officials.

For the first few years, the Swedish Central Bank Prize in Economics went to fairly mainstream and maybe even semi-respectable economists. But after establishing the award as credible and serious, the prizes took a hard turn to the right. Over the next decade, the prize was awarded to the most fanatical supporters of theories that concentrated wealth among the top 1% of industrialized society of our time. At the time of the prizes, neoclassical economics were not fully accepted by the media and political establishment. But the Nobel Prize changed all that. What started as a project to help the Bank of Sweden achieve political independence, ended up boosting the credibility of the most regressive strains of free-market economics, and paving the way for widespread acceptance of libertarian ideology.

The Swedish Riksbank awarded this year’s Nobel prize for economic sciences to Oliver Hart, a British economist at Harvard University, and Bengt Holmstrom, a Finnish economist at MIT, for their work improving our understanding of how and why contracts work, and when they can be made to work better.

Their work focuses attention on the necessity of trade-offs in setting contract terms; it is yet another in a series of recent prizes which explores the unavoidable imperfections in many critical markets. Mr Holmstrom’s analyses of insurance contracts describe the inevitable trade-off between the completeness of an insurance contract and the extent to which that contract encourages moral hazard. From an insurance perspective, the co-payments that patients must sometimes make when receiving treatment are a waste; it would be better for people to be able to insure fully. Yet because insurers cannot know that all patients are receiving only the treatment they need and no more, they employ co-payments as a way to lean against the problem of moral hazard: that some people will choose to use much more health care than they need when the pool of all those being insured picks up the bill. A common and important thread in work by Messrs Hart and Holmstrom is the role of power in planning co-operative ventures. Individuals or firms with the ability to hold up arrangements – by withholding their service or the use of a resource they own – wield economic power. That power allows them to capture more of the value generated by a co-operative effort, and potentially to sink it entirely, even if the venture would yield big gains for all participants and society as a whole. Contracts exist to shape power relationships. In some cases, they are there to limit the exercise of hold-up power so that a venture can go forward. In others, they are intended to create or protect certain power relationships in order to encourage good behaviour: workers or firms with the right to exit a relationship, for instance, force other parties to that relationship to take their interests into account. The broader lesson – that power matters – is one economics too often neglects.

The theory holds that the contracting costs between economic units are shaped by the nature of the interaction between them. These costs are not operational costs, such as commission fees or transportation costs. Instead, they stem from the lack of clarity and enforceability of the terms of the interaction and each unit’s dependence on the interaction. And, in the words of today’s prize winners, they cause contracts to be incomplete. 

Difficulties in Negotiating a Transaction

Difficulties in Monitoring an Ongoing Transaction

Difficulties in Enforcing an Agreement

When managers spot these sorts of problems on the horizon, a deal that potentially will create value may not get done because the contract is bound to be incomplete. The danger is that the contract will not specify how to resolve conflicts in the future. This is because the agreement between the parties does not cover all contingencies, all issues, or all possible states of the world. To govern a partnership successfully, then, you need to manage the gaps in the contract. Traditional management techniques call for command and control in these situations, to respond quickly and decisively to new conditions. But this solution is missing from typical partnerships, most of which are characterized by a sharing of control. It may be a formal joint venture with shared ownership or a looser arrangement whereby one party controls certain parts of the joint project and the other party controls others. So, each partner’s control in these combinations is also incomplete.

Neoclassical economic dogma is that money is the “high power” incentive.  Normal humans know that this is preposterous.  The highest power incentives are rarely monetary.  People give up their lives for others.  Some of them do so nominally for “duty, honor, country,” but actually because of the effects of “small unit cohesion.” A second neoclassical dogma is ignoring fraud and predation.  The 2016 prizes show how, despite their knowledge of the falsity of the implicit assumption, neoclassical economists repeatedly ignore the manners in which CEOs shape perverse incentives and render the Laureates’ compensation and governance policies criminogenic.  A third neoclassical dogma is, implicitly, to assume that perverse incentives do not influence CEOs and those they suborn.  Holmström and Steven N. Kaplan’s article about corporate governance in light of the Enron-era frauds unintentionally displayed this third neoclassical dogma about incentives. The fourth dogma is that regulation cannot succeed because it lacks “high power” incentives. Criminologists’ understanding of incentives and how CEOs set and pervert incentives is far more sophisticated than neoclassical economists’ myths about incentives.  Criminologists provide the content to how CEOs that predate “rig the system.”  Criminologists agree that perverse financial incentives are important contributors to white-collar crime.