2019
DOI: 10.1002/fut.21997
|View full text |Cite
|
Sign up to set email alerts
|

Abstract: 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 … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

1
15
0

Year Published

2021
2021
2022
2022

Publication Types

Select...
7

Relationship

0
7

Authors

Journals

citations
Cited by 22 publications
(16 citation statements)
references
References 51 publications
1
15
0
Order By: Relevance
“…As a typical example of its application in derivatives pricing, Ma et al (2017) [20] presented a model for obtaining price valuation of vulnerable European options using a model with self-exciting Hawkes processes that allow for clustered jumps. Recently, Liu and Zhu (2019) [18] presented 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. These articles brought new insights into modeling the asset price dynamics by considering jump clustering.…”
mentioning
confidence: 99%
“…As a typical example of its application in derivatives pricing, Ma et al (2017) [20] presented a model for obtaining price valuation of vulnerable European options using a model with self-exciting Hawkes processes that allow for clustered jumps. Recently, Liu and Zhu (2019) [18] presented 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. These articles brought new insights into modeling the asset price dynamics by considering jump clustering.…”
mentioning
confidence: 99%
“…There are numerous methods in the literature of pricing variance swaps, both analytically and numerically (see [13] for an extensive review). Nevertheless, a pricing formula or procedure that relies on a certain stochastic process, for instance, Lévy process [14], MRG-Vasicek model [17], or Hawkes jump-diffusion model [18], may suffer from a lack of parsimony or might not fit the real data well due to the inappropriateness of model assumptions (see, for instance, [14]).…”
Section: Pricing Variance Swapmentioning
confidence: 99%
“…In Equation (2), we describe the DGP of short‐term vt with a variance jump component JtvdNt, shown to be important for pricing variance assets in previous studies (e.g., Aït‐Sahalia et al, 2020; Bardgett et al, 2019; Gehricke & Zhang, 2020). Unlike Liu and Zhu (2019) and Cao et al (2020), we allow for a stochastic central tendency of the instantaneous variance in Equation (3). Egloff et al (2010), Luo and Zhang (2012), Elkamhi et al (2016), Gehricke and Zhang (2020), and many others show that the use of stochastic mt is useful for capturing the term structure of financial derivatives.…”
Section: Modelmentioning
confidence: 99%
“…Many studies provide empirical evidence that the VIX and its derivatives are sensitive to jump risk (e.g., Dew‐Becker et al, 2017; Duan & Yeh, 2010; Eraker & Wu, 2017; Lin, 2007; Mencía & Sentana, 2013; Park, 2016). Recent empirical evidence indicates that the Hawkes jump model (Hawkes, 1971) can capture jump propagation risks in the market and is essential for asset pricing (e.g., Aït‐Sahalia et al, 2015; Boswijk et al, 2015; Du & Luo, 2019; Liu & Zhu, 2019). We depart from these studies and seek to answer whether embedding jump propagation risks in the return dynamics can improve the fit performance of a model and what role the Hawkes jump model plays in the representation of the VIX term structure under different circumstances.…”
Section: Introductionmentioning
confidence: 99%