Erik Lindström

Are Option Values Stochastic? On Effects of State and Parameter Uncertainty

	
Abstract

In the talk we analyze option values in the Black&Scholes framework, when
agents only have access to a finite sequence of observations. This is
the case for all real world applications. It will be shown that option
values predicted by the Black & Scholes formula will be stochastic and
hence have to be treated as such. The reason for this is that agents
cannot observe one of the parameters (the volatility) used in the
valuation formula. Furthermore, different agents use different
estimators and different sets of data to estimate the parameter. This
adds to making the de facto market volatility stochastic, even in the
Black & Scholes market. Additional theoretical support for stochastic
option values is obtained when stochastic volatility (latent factor)
models are introduced. The additional stochastic element is
essentially the non-linear filtering problem, as the volatility is
unobservable, while the standard option valuation framework explicitly
assumes the latent volatility to be known. However, assuming that the
agents are aware of this problem and that they are using the best
possible projection of the stochastic values to values measurable with
respect to the available information generates some interesting
stylized facts on the volatility structure which are consistent with
the observed option volatility structure.

Keywords: Option pricing; parameter estimation; optimal filtering;
          bias correction; Bayesian analysis.