On the sensitivity analysis of spread options using Malliavin calculus

TL;DR

This paper develops a Malliavin calculus-based method to compute price sensitivities of spread options, applicable to models with stochastic volatility and discontinuous payoffs, offering a flexible alternative to Fourier methods.

Contribution

It introduces a novel Malliavin calculus framework for spread option sensitivities that does not require characteristic functions and handles discontinuous payoffs.

Findings

Malliavin weights are independent of the payoff functional.

The approach is applicable to stochastic volatility models.

It provides tractable formulas for sensitivities without characteristic functions.

Abstract

In this paper we derive tractable formulae for price sensitivities of two-dimensional spread options using Malliavin calculus. In particular, we consider spread options with asset dynamics driven by geometric Brownian motion and stochastic volatility models. Unlike the fast Fourier transform approach, the Malliavin calculus approach does not require the joint characteristic function of underlying assets to be known and is applicable to spread options with discontinuous payoff functions. The results obtained reveal that the Malliavin calculus approach gives the price sensitivities in terms of the expectation of spread option payoff functional multiplied with some random variables (Malliavin weights) which are independent of the payoff functional. This is consistent with results in Fournie et al. [1]. The results also show the flexibility of Mallavin calculus approach when applied to spread options.