Asset Pricing with Random Volatility

TL;DR

This paper introduces a novel asset pricing model incorporating random volatility, enabling exact matching of market-implied distributions and providing explicit formulas for derivative pricing under a generalized framework.

Contribution

It develops a mixture diffusion process with random volatility that precisely matches risk-neutral distributions and derives closed-form pricing formulas for derivatives.

Findings

Exact matching of risk-neutral distributions for vanilla and forward start options

Explicit pricing formulas under Generalized Geometric Brownian Motion

Flexible modeling of asset price dynamics with random volatility

Abstract

This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed process can match exactly the risk-neutral distributions implied by both spot vanilla options and forward start options. We can also derive the explicit pricing formula for derivatives that have a closed-form solution under Generalized Geometric Brownian Motion.