Pricing Risky Options Simply

Abstract

This paper is a follow-up of (Aurell and Życzkowski, 1996) [2] and (Aurell et al. 1996) [1]. We show that the prescription of pricing option by minimizing risk can be solved in a way that is quite similar to the Black–Scholes' approach. For a given discrete-time price process we determine an auxillary process, generally a pseudo-probability taking both negative and positive values, such that the price of the option in our prescription is the expected value upon maturation with respect to the auxillary process. We present a conjecture due to G. Wolczyńska that this auxillary process is in fact a (pseudo)-Markov process which admits a very simple description. Numerical results are presented in favor of the conjecture.