Hedging of Options in the Presence of Jump Clustering
36 Pages Posted: 3 Dec 2018
Date Written: November 26, 2018
Abstract
This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.
Keywords: self-excitation, Hawkes process, minimum variance hedging, options pricing, shot noise process
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Hedging of Options in the Presence of Jump Clustering
This is a Risk Journals paper. Risk Journals charges $73.00 .
File name: SSRN-id3290709.pdf
Size: 739K
If you wish to purchase the right to make copies of this paper for distribution to others, please select the quantity.
