Skip to main content
placeholder image

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

Journal Article


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.

Publication Date


  • 2017

Citation


  • Li, T. Ray. & Rodrigo, M. R. (2017). Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms. European Journal of Applied Mathematics, 28 (5), 789-826.

Scopus Eid


  • 2-s2.0-85001555222

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6363

Number Of Pages


  • 37

Start Page


  • 789

End Page


  • 826

Volume


  • 28

Issue


  • 5

Place Of Publication


  • United Kingdom

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.

Publication Date


  • 2017

Citation


  • Li, T. Ray. & Rodrigo, M. R. (2017). Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms. European Journal of Applied Mathematics, 28 (5), 789-826.

Scopus Eid


  • 2-s2.0-85001555222

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6363

Number Of Pages


  • 37

Start Page


  • 789

End Page


  • 826

Volume


  • 28

Issue


  • 5

Place Of Publication


  • United Kingdom