An Adaptive Method for Valuing an Option on Assets with Uncertainty in Volatility

TL;DR

This paper introduces an adaptive Bayesian method for valuing European call options on assets with stochastic volatility, reducing uncertainty in volatility estimates to improve pricing accuracy.

Contribution

It develops a novel adaptive approach combining Bayesian learning and stochastic dynamic programming to incorporate volatility uncertainty into option valuation.

Findings

Adaptive method reduces volatility uncertainty in option pricing.

Numerical results show a decrease in the estimated option price.

The approach improves the accuracy of valuation under stochastic volatility.

Abstract

We present an adaptive approach for valuing the European call option on assets with stochastic volatility. The essential feature of the method is a reduction of uncertainty in latent volatility due to a Bayesian learning procedure. Starting from a discrete-time stochastic volatility model, we derive a recurrence equation for the variance of the innovation term in latent volatility equation. This equation describes a reduction of uncertainty in volatility which is crucial for option pricing. To implement the idea of adaptive control, we use the risk-minimization procedure involving random volatility with uncertainty. By using stochastic dynamic programming and a Bayesian approach, we derive a recurrence equation for the risk inherent in writing the option. This equation allows us to find the fair price of the European call option. We illustrate numerically that the adaptive procedure leads to a decrease in option price.