Pricing path-dependent options under the Hawkes jump diffusion process | Zendy

Xingchun Wang | Zendy

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Pricing path-dependent options under the Hawkes jump diffusion process

Author(s) -

Xingchun Wang

Publication year - 2022

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2022024

Subject(s) - jump diffusion , jump , diffusion , path (computing) , jump process , path dependent , computer science , diffusion process , asset (computer security) , process (computing) , valuation of options , econometrics , economics , mathematics , physics , innovation diffusion , knowledge management , computer security , quantum mechanics , thermodynamics , programming language , operating system

In this paper, we investigate the pricing of a path-dependent option with default risk under the Hawkes jump diffusion process. For each asset, its dynamics are driven by a Hawkes jump diffusion process, and their diffusive components, Hawkes jumps as well as jump amplitudes are all correlated. In the proposed pricing framework, we obtain the prices of fader options with/without default risk in closed form. Finally, we present numerical examples to illustrate the prices of fader options with default risk.

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