Risk Analysis and Hedging of Parisian Options Under a Jump-Diffusion Model

Kim, Kyoung-Kuk; Lim, Dong-Young

doi:10.2139/ssrn.2657392

Cited by 2 publications

(2 citation statements)

References 25 publications

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“…In addition, Chesney and Gauthier (2006), Le et al (2016) and Lu et al (2018) studied American-style Parisian option pricing under the Black-Scholes model while Chesney and Vasiljević (2018) dealt with the hyper-exponential jump-diffusion model. As for the hedging of Parisian options, Kim and Lim (2016) developed a quasi-static strategy and tested it under the double-exponential jump-diffusion model.…”

Section: Introductionmentioning

confidence: 99%

A General Approach for Parisian Stopping Times under Markov Processes

Zhang,

2021

Preprint

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We propose a method based on continuous time Markov chain approximation to compute the distribution of Parisian stopping times and price Parisian options under general one-dimensional Markov processes. We prove the convergence of the method under a general setting and obtain sharp estimate of the convergence rate for diffusion models. Our theoretical analysis reveals how to design the grid of the CTMC to achieve faster convergence. Numerical experiments are conducted to demonstrate the accuracy and efficiency of our method for both diffusion and jump models. To show the versality of our approach, we develop extensions for multi-sided Parisian stopping times, the joint distribution of Parisian stopping times and first passage times, Parisian bonds and for more sophisticated models like regime-switching and stochastic volatility models.

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Section: Introductionmentioning

confidence: 99%

A General Approach for Parisian Stopping Times under Markov Processes

Zhang,

2021

Preprint

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“…Chung and Shih (2009); Ruas et al (2013) used calendar-spread approaches for American options whereas Chung et al (2013a,b); did for American barriers and for double barriers. Parisian options, which are classified as occupation time derivatives in Broadie and Detemple (2004), are added to the list (Kim and Lim, 2016). More recently, Kim and Lim (2019) proposed a recursive method for autocallable structured products based on the results developed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Static replication of barrier-type options via integral equations

Kim

Lim

2020

Quantitative Finance

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This study provides a systematic and unified approach for constructing exact and static replications for exotic options, using the theory of integral equations. In particular, we focus on barrier-type options including standard, double and sequential barriers. Our primary approach to static options replication is the DEK method proposed by Derman et al. (1995). However, our solution approach is novel in the sense that we study its continuous-time version using integral equations. We prove the existence and uniqueness of hedge weights under certain conditions. Further, if the underlying dynamics is time-homogeneous, then hedge weights can be explicitly found via Laplace transforms. Based on our framework, we propose an improved version of the DEK method. This method is applicable under general Markovian diffusion with killing.

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Risk Analysis and Hedging of Parisian Options Under a Jump-Diffusion Model

Cited by 2 publications

References 25 publications

A General Approach for Parisian Stopping Times under Markov Processes

A General Approach for Parisian Stopping Times under Markov Processes

Static replication of barrier-type options via integral equations

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