Option pricing, Bayes risks and Applications

TL;DR

This paper links option pricing to Bayesian risk minimization, providing new formulas and interpretations for European and American call options using statistical decision theory.

Contribution

It introduces a Bayesian risk-based approach to option pricing, offering new formulas and economic insights, and extends to American options.

Findings

Bayes risk provides a new interpretation of option prices.

Derived formulas for European call options under various models.

New expression for American call option pricing.

Abstract

A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obtaining C for some stock-price models using the underlying probability instead of the risk neutral probability and giving R_B an economic interpretation. When logarithmic stock prices follow Brownian motion, discrete normal mixture and hyperbolic Levy motion the obtained B-prices are "fair" prices. A new expression for the price of American call option is also obtained and statistical modeling of R_B can be used when pricing European and American call options.