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

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

Explosive Roots in Level Vector Autoregressive Models

Level vector autoregressive (VAR) models are used extensively in empirical macroeconomic research. However, estimated level VAR models may contain explosive roots, which is at odds with the widespread consensus among macroeconomists that roots are at most unity. This paper investigates the frequency of explosive roots in estimated level VAR models in the presence of stationary and nonstationary variables. Monte Carlo simulations based on datasets from the macroeconomic literature reveal that the frequency of explosive roots exceeds 40% in the presence of unit roots. Even when all the variables are stationary, the frequency of explosive roots is substantial. Furthermore, explosion increases significantly, to as much as 100% when the estimated level VAR coefficients are corrected for small-sample bias. These results suggest that researchers estimating level VAR models on macroeconomic datasets encounter explosive roots, a phenomenon that is contrary to common macroeconomic belief, with a very high frequency. Monte Carlo simulations in the paper reveal that imposing unit roots in the estimation can substantially reduce the frequency of explosion. Hence one way to mitigate explosive roots is to estimate vector error correction models.Level VAR Models, Explosive Roots, Bias Correction

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