Title

Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms

RIS ID

111404

Publication Details

Li, T. Ray. & Rodrigo, M. R. (2016). Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms. European Journal of Applied Mathematics, Online First 1-38.

Abstract

In this article, we use Mellin transforms to derive alternative results for option pricing and implied volatility estimation when the underlying asset price is governed by jump-diffusion dynamics. The current well known results are restrictive since the jump is assumed to follow a predetermined distribution (e.g., lognormal or double exponential). However, the results we present are general since we do not specify a particular jump-diffusion model within the derivations. In particular, we construct and derive an exact solution to the option pricing problem in a general jump-diffusion framework via Mellin transforms. This approach of Mellin transforms is further extended to derive a Dupire-like partial integro-differential equation, which ultimately yields an implied volatility estimator for assets subjected to instantaneous jumps in the price. Numerical simulations are provided to show the accuracy of the estimator.

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Link to publisher version (DOI)

http://dx.doi.org/10.1017/S0956792516000516