Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits

A. Oztukel, P. Wilmott

Abstract

In this paper we build upon the recently developed uncertain parameter framework for valuing derivatives in a worst-case scenario. We start by deriving a stochastic volatility model based on a simple analysis of time-series data. We use this stochastic model to examine the time evolution of volatility from an initial known value to a steady-state distribution in the long run. This empirical model is then incorporated into the uncertain parameter option valuation framework to provide 'confidence limits' for the option value.

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