Does Coarse Thinking Matter for Option Pricing? Evidence from an Experiment

Mullainathan et al [Quarterly Journal of Economics, May 2008] present a model of coarse thinking or analogy based thinking. The essential idea behind coarse thinking is that people put situations into categories and the values assigned to attributes in a given situation are affected by the values of corresponding attributes in other co-categorized situations. We test this hypothesis in an experiment on financial options against the benchmark of arbitrage-free pricing. Firstly, we test whether a financial option is priced in analogy with its underlying stock (transference). Secondly, we test for whether variations in the analogy between a financial option and its underlying stock matter (framing). We find evidence in support of both transference and framing.Coarse Thinking, Financial Options, Arbitrage-Free Pricing

Stock Price Manipulation : The Role of Intermediaries

We set out to study stock price manipulation when the manipulator is in the role of an intermediary (broker). We find that in the absence of superior information, the broker can manipulate equilibrium outcomes without losing its credibility with respect to accurate forecasting. The result extends to the case when the broker prefers more investment to come into the market. However, when moderate competition among brokers is introduced, then the investors get a favored outcome. When competition exceeds a certain threshold, neither the brokers nor the investors get their respective favored outcomes. In any case, if the broker bias for more investment dominates competition, the brokers get their favorite outcome at the expense of investors.Stock Price Manipulation, Broker Manipulation, Broker Competition, Broker Bias, Emerging Markets

Thinking by analogy, systematic risk, and option prices

People tend to think by analogies and comparisons. Such way of thinking, termed coarse thinking by Mullainathan et al [Quarterly Journal of Economics, May 2008] is intuitively very appealing. We develop a new option pricing model based on the idea that the market consists of coarse thinkers as well as rational investors when limits to arbitrage (transaction costs) prevent rational investors from profiting at the expense of coarse thinkers. The new formula, which is a closed form solution to the model, is a generalization of the Black-Scholes formula. The new formula potentially provides a unified explanation for various implied volatility puzzles.Coarse Thinking, Option Pricing, Implied Volatility, Implied Volatility Skew, Systematic Risk, Investor Sentiment, Implied Volatility Term Structure

The Puzzle of a Unique Instrument in Emerging Markets of South Asia

A unique instrument has been associated with emerging markets of India and Pakistan. We show that the instrument can be considered a market response to the information gaps in these markets. The instrument may credibly transmit information and may eliminate information gaps. Hence, the birth of the instrument is, perhaps, an example of a creative market response to information problems.Information Asymmetry; Information Transmission; Emerging Markets; Perfect Bayesian Equilibria; Badla Finance

Information transmission and the emergence of a peculiar trading facility in certain emerging markets

A peculiar carry over transaction facility has been associated with emerging markets of India and Pakistan. We show that the trading facility can be considered a market response to the information gaps in these markets. Information can be credibly transmitted through this trading facility. Hence, the emergence of such a trading facility is, perhaps, an example of a creative market response to information problems.Information Asymmetry; Information Transmission; Emerging Markets; Perfect Bayesian Equilibria; Badla Finance

Coarse Thinking and Pricing a Financial Option

Mullainathan et al [Quarterly Journal of Economics, May 2008] present a formalization of the concept of coarse thinking in the context of a model of persuasion. The essential idea behind coarse thinking is that people put situations into categories and the values assigned to attributes in a given situation are affected by the values of corresponding attributes in other co-categorized situations. We derive a new option pricing formula based on the assumption that the market consists of coarse thinkers as well as rational investors. The new formula, called the behavioral Black-Scholes formula is a generalization of the Black-Scholes formula. The new formula provides an explanation for the implied volatility skew puzzle in index options. In contrast with the Black-Scholes model, the implied volatility backed-out from the behavioral Black-Scholes formula is a constant. This finding suggests that the volatility skew (smile) may be a reflection of coarse thinking. That is, the skew is seen if rational investors are assumed to exist when actual investors are heterogeneous; coarse thinkers and rational investors.Coarse Thinking, Financial Options, Rational Pricing. Implied Volatility, Implied Volatility Skew, Implied Volatility Smile, Black-Scholes Model

Information Transmission in Emerging Markets: The Case of a Unique Financing Instrument

Information flows are necessary for well-functioning financial markets. However, in many emerging markets, the legal and institutional preconditions for proper information flow are not met. How do such markets respond? We argue that they respond by developing innovative information transmission mechanisms. We identify one such mechanism associated with the evolution of equity markets in South Asia. The mechanism operates through a financing instrument unique to India and Pakistan, called badla in local parlance. We develop a signaling model in which a broker-financier signals his private information to investors by choosing various levels of financing to provide in the badla market for stocks. A fully separating equilibrium exists allowing full discrimination of various types of stocks. Hence, information transmission takes place through this channel.Signaling, Information Transmission, Separating Equilibrium, Badla-Financing, Emerging Markets

Coarse Thinking and Collusion in Bertrand Duopoly with Increasing Marginal Costs

Mullainathan, Schwartzstein, & Shleifer [Quarterly Journal of Economics, May 2008] put forward a model of coarse thinking. The essential idea behind coarse thinking is that agents put situations into categories and then apply the same model of inference to all situations in a given category. We extend the argument to strategies in a game-theoretic setting and propose the following: Agents split the choice-space into categories in comparison with salient choices and then choose each option in a given category with equal probability. We provide an alternative explanation for the puzzling results obtained in a Bertrand competition experiment as reported in Abbink & Brandts [Games and Economic Behavior, 63, 2008]Laboratory experiments, Oligopoly, Price competition, Co-ordination games, Coarse Thinking

The social norm of leaving the toilet seat down: A game theoretic analysis

We model the toilet seat problem as a 2 player non-cooperative game. We find that the social norm of leaving the toilet seat down is inefficient. However, to the dismay of “mankind”, we also find that the social norm of leaving the seat down after use is a trembling-hand perfect equilibrium. Hence, sadly, this norm is not likely to go away.Trembling-hand perfection; social norm

Ambiguity, Infra-Marginal Investors, and Market Prices

It is difficult to explain the price insensitive or infra-marginal behavior, an example of which is the behavior of credit markets during the recent financial crisis, by risk aversion alone. It is known that infra-marginal behavior may arise with ambiguity aversion. Furthermore, there appears to be fairly strong evidence of a close connection between ambiguity and conformity. Here we propose an extension of the standard ambiguity framework to incorporate conformity. We find that there are open sets of state-price ratios over which the entire market is price insensitive or infra-marginal. This result has important implications for market equilibrium and volatilityAmbiguity, Infra-Marginal Behavior, Arrow Securities