Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus

TL;DR

This paper develops a Malliavin calculus-based method for computing option Greeks in models with stochastic volatility and interest rates, enabling efficient Monte Carlo simulations for various option types.

Contribution

It extends Malliavin calculus techniques to hybrid stochastic models, allowing accurate Greek computation even with non-differentiable payoffs.

Findings

Effective Monte Carlo algorithms demonstrated

Applicable to various option payoffs

Handles non-differentiable payoffs efficiently

Abstract

This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Malliavin calculus for the computation of Greeks: Delta, Vega, and Rho and it extends the method slightly. The main results show that Malliavin calculus allows a running Monte Carlo (MC) algorithm to present numerical implementations and to illustrate its effectiveness. The main advantage of this method is that once the algorithms are constructed, they can be used for numerous types of option, even if their payoff functions are not differentiable.