Partial Derivative Approach for Option Pricing in a Simple Stochastic Volatility Model

TL;DR

This paper introduces a novel partial derivative approach to option pricing in a stochastic volatility model with jump discontinuities, offering new insights and solutions for market risk assessment.

Contribution

It presents a new method based on partial derivatives for pricing options in a model with stochastic volatility jumps, allowing flexible risk premium considerations.

Findings

Recovered existing solutions in the literature

Derived new solutions using the partial derivative framework

Provided a flexible approach to market price of volatility risk

Abstract

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial derivative equations, which gives a different perspective to the problem. Within our framework we can easily consider several prescriptions for the market price of volatility risk, and interpret their financial meaning. Thus, we recover solutions previously cited in the literature as well as obtain new ones.