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Pricing variance swaps under the Hawkes jump‐diffusion process
Author(s) -
Liu Weiyi,
Zhu SongPing
Publication year - 2019
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.21997
Subject(s) - jump diffusion , jump , variance (accounting) , stochastic volatility , econometrics , variance swap , volatility (finance) , diffusion process , mathematics , economics , jump process , diffusion , physics , forward volatility , service (business) , economy , accounting , quantum mechanics , thermodynamics
This paper presents an analytical approach for pricing variance swaps with discrete sampling times when the underlying asset follows a Hawkes jump‐diffusion process characterized with both stochastic volatility and clustered jumps. A significantly simplified method, with which there is no need to solve partial differential equations, is used to derive a closed‐form pricing formula. A distinguished feature is that many recently published formulas can be shown to be special cases of the one presented here. Some numerical examples are provided with results demonstrating that jump clustering indeed has a significant impact on the price of variance swaps.