Sensitivity of option prices via fuzzy Malliavin calculus

In this paper, we define the Malliavin derivative and the Skorohod integral for fuzzy stochastic processes for the sensitivity analysis of the option prices. The price dynamics could be modelled by equations involving uncertainties that lead to modelling with fuzzy processes in equations. We introduce a fuzzy stochastic differential equation for financial pricing models under an asset price that follows a fuzzy stochastic process. If there is no explicit solution to the equations, the sensitivity analysis, and the estimates are computationally expensive, and the result will be inaccurate due to the estimates and the derivative of the payoff function. The Malliavin calculus and the integration by parts formula in fuzzy space can be exploited to bypass the derivative of the payoff function.(c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper defines the Malliavin derivative and Skorohod integral for fuzzy stochastic processes in order to analyze the sensitivity of option prices. It introduces a fuzzy stochastic differential equation for financial pricing models and shows how the Malliavin calculus and integration by parts formula in fuzzy space can be used to bypass the derivative of the payoff function, improving computational efficiency and accuracy.