Pricing of FX options in the MPT/CIR jump-diffusion model with approximative fractional stochastic volatility

Kang, Jian-hao; Yang, Bohan; Huang, Nan-jing

doi:10.1016/j.physa.2019.121871

Cited by 6 publications

(4 citation statements)

References 30 publications

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“…We developed a double Heston model with approximative fractional stochastic volatility in this article. It is an extensive study based on the study of Ahlip et al [26] and Kang et al [22]. Since approximative fractional Brownian motion can replace fractional Brownian motion, we introduced it to double Heston model by modeling the dynamics of the stock price and one factor of the variance with approximative fractional process and it is our contribution to this article.…”

Section: Resultsmentioning

confidence: 99%

“…Several authors also developed an option pricing model with approximative fractional Brownian motion from a different point of view. Kang et al [22] developed an approximative fractional stochastic volatility model to study foreign exchange (FX) options. ey derived the pricing formula and used some numerical approach to examine the impact of the long-memory parameter and the positive approximation factor on the option prices.…”

Section: Introductionmentioning

confidence: 99%

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Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

Chang

Wang

2021

Mathematical Problems in Engineering

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We establish double Heston model with approximative fractional stochastic volatility in this article. Since approximative fractional Brownian motion is a better choice compared with Brownian motion in financial studies, we introduce it to double Heston model by modeling the dynamics of the stock price and one factor of the variance with approximative fractional process and it is our contribution to the article. We use the technique of Radon–Nikodym derivative to obtain the semianalytical pricing formula for the call options and derive the characteristic functions. We do the calibration to estimate the parameters. The calibration demonstrates that the model provides the best performance among the three models. The numerical result demonstrates that the model has better performance than the double Heston model in fitting with the market implied volatilities for different maturities. The model has a better fit to the market implied volatilities for long-term options than for short-term options. We also examine the impact of the positive approximation factor and the long-memory parameter on the call option prices.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

Chang

Wang

2021

Mathematical Problems in Engineering

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“…Therefore, it would be crucial and interesting to extend the results of this paper to JSDEs driven by general Lévy processes. We also note that various theoretical results with applications for SDEs driven by fractional Brownian motions (fBms) have been studied extensively in literature; for instance, we refer the reader to [2,4,6,16,34] and the references therein. Thus, it would be important to extend our results to JSDEs driven by fBms.…”

Section: Discussionmentioning

confidence: 99%

Strong solutions for jump-type stochastic differential equations with non-Lipschitz coefficients

2019

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“…Some authors also developed option pricing model with approximative fractional Brownian motion under a creative framework. Kang et al [32] presented a FX option pricing model, and the dynamics of FX and the variance are specified with an approximative fractional process.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility

Chang

Wang

2021

Mathematics

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Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since approximative fractional Brownian motion is more proper for application than Brownian motion in building option pricing models based on financial market data. We are the first to adopt the creative model. We derive the pricing formula for the options and the formula for the characteristic function. We also estimate the parameters with the loss function for the model and two nested models and compare the performance among those models based on the market data. The outcome illustrates that the model offers the best performance among the three models. It demonstrates that approximative fractional Brownian motion is more proper for application than Brownian motion.

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Pricing of FX options in the MPT/CIR jump-diffusion model with approximative fractional stochastic volatility

Cited by 6 publications

References 30 publications

Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

Strong solutions for jump-type stochastic differential equations with non-Lipschitz coefficients

Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility

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