Pricing Vulnerable Options with Jump Clustering

Abstract

This paper presents a valuation of vulnerable European options using a model with self‐exciting Hawkes processes that allow for clustered jumps rather than independent jumps. Many existing valuation models can be regarded as special cases of the model proposed here. Using numerical analyses, this study also performs sensitivity analyses and compares the results to those of existing models for European call options. The results show that jump clustering has a significant impact on the option value. © 2017 Wiley Periodicals, Inc. Jrl Fut Mark

Pricing variance swaps under the Hawkes jump‐diffusion process

“…Therefore, the Hawkes jump‐diffusion model allows for both volatility and jump clustering. As a typical example of its application in derivatives pricing, Ma and Xu () and Ma and Xu () adopted Hawkes jump‐diffusion processes in modeling the structure credit risk as well as pricing vulnerable options, respectively, demonstrating that jump clustering will significantly affect the final results.…”

VIX term structure: The role of jump propagation risks

“…Motivated by the clustering of jumps in the market, we study the impact of jump propagation risks on the variance term structure. Our study is also related to the stream of literature applying the Hawkes jump model in finance (e.g., Aït‐Sahalia et al, 2015; Aït‐Sahalia & Hurd, 2015; Du & Luo, 2019; Hainaut, 2016; Ma et al, 2017; Maneesoonthorn et al, 2017). Specifically, our study extends other studies that use the Hawkes process to examine a variety of financial assets.…”

Pricing VIX options with volatility clustering

“…For example, Grothe, Korniichuk, and Manner () used self‐exciting Hawkes processes to study the extreme negative returns in the European and U.S. financial markets. Ma, Shrestha, and Xu () adopted Hawkes jump‐diffusion processes to value vulnerable options and emphasized the role of self‐exciting jumps in option prices. The applications of Hawkes processes are especially successful in the context of high‐frequency finance.…”