Hedging The Risk In The Continuous Time Option Pricing Model With Stochastic Stock Volatility

TL;DR

This paper addresses the challenge of constructing a self-financing hedge in continuous-time option pricing models with stochastic volatility, highlighting the importance of verifying the self-financing condition for theoretical consistency.

Contribution

It demonstrates that existing replicating methods violate the self-financing constraint and proposes a correct method for forming a self-financing hedge under stochastic volatility.

Findings

Existing methods violate the self-financing condition

A correct self-financing hedge is derived for stochastic volatility models

Ensures theoretical consistency in option pricing with stochastic volatility

Abstract

In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order for the theory to be self-consistent. The replicating methods in existing finance literature are shown to violate the self-financing constraint when the underlying asset has stochastic volatility. Correct self-financing hedge is formed in this article.