Sensitivity of option prices via fuzzy Malliavin calculus

Abstract

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.