An entropy-driven cosmic expansion

We examine the evolution of the Friedmann Universe within our recent model of space-time identified with an elastic continuous medium whose deformations are described by a vector field constrained to obey a generalized four-dimensional version of the equilibrium equations of standard elasticity. It is found that the demand that the entropy associated with such elastic deformations be always extremal during the expansion of such a Universe turns these equilibrium equations into a single differential equation governing the evolution of the Hubble parameter H. The solution to the resulting dynamics admits both a power-law expansion, analogous to the one induced by an inflaton field, as well as a power-law expansion analogous to the one induced by a phantom field. Analyzing both types of expansions via the induced elastic energy and pressure permits to assign the former to the early Universe and the latter to its late-time expansion. We discuss the possible way for the dynamics to avoid the Big Rip singularity that would otherwise result. We succinctly discuss the possible way to avoid also the Big Bang singularity and how to obtain the large scale structure of the Universe from the present model.Comment: 15 pages. Matches the published versio

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

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

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