European Option Pricing with Stochastic Volatility models under Parameter Uncertainty

TL;DR

This paper explores how parameter uncertainty in stochastic volatility models impacts European option pricing, proposing a control framework and demonstrating empirical effectiveness with S&P 500 data.

Contribution

It introduces a control-based approach to incorporate parameter uncertainty into stochastic volatility models and derives explicit equations for Heston's model.

Findings

Conservative model-prices cover 98% of market prices for European calls.

Explicit equations for Heston's model under parameter uncertainty.

Numerical solutions demonstrate practical applicability.

Abstract

We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and formalise the problem as a control problem where the control acts on the parameters to maximise/minimise the option value. Through a dual representation with backward stochastic differential equations, we obtain explicit equations for Heston's model and investigate several numerical solutions thereof. In an empirical study, we apply our results to market data from the S&P 500 index where the model is estimated to historical asset prices. We find that the conservative model-prices cover 98% of the considered market-prices for a set of European call options.