Pricing variance swaps under stochastic volatility and stochastic interest rate

Cao, Jiling; Lian, Guanghua; Roslan, Teh Raihana Nazirah

doi:10.1016/j.amc.2015.12.027

Cited by 20 publications

(24 citation statements)

References 55 publications

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“…To improve the pricing accuracy of these contracts, Zhu and Lian [18,19] developed closed-form pricing formulas of discretely sampled variance swaps based on the framework of Heston's stochastic volatility model where the interest rate followed a deterministic process. In [4], a hybridization of the Heston stochastic volatility model and the CIR stochastic interest rate model was considered. The hybrid model extended the Heston stochastic volatility model in [18] by modelling the interest rate as the CIR process.…”

Section: Resultsmentioning

confidence: 99%

“…Effect of regime-switching. In order to explore the effect of regime-switching, in Figure 2, we present results produced by formula (44) and by the Heston-CIR model without regime-switching in [4]. For the Heston-CIR model without regime-switching, we fix the parameter values to be θ * 1 = 0.05 and β * 1 = 0.05.…”

Section: 2mentioning

confidence: 99%

“…However, a simpler approach was explored in [15], where the Schwarts solution procedure was applied to derive an affine solution of PDEs. Recently, to extend the work in [18] where stochastic interest rates were ignored, Cao et al [4] employed a hybridization of the stochastic volatility model and the CIR interest rate model to investigate the pricing rates of variance swaps with discrete sampling. In [9], Elliott et al proposed a continuous-time Markovian-regulated version of the Heston stochastic volatility model to distinguish different states of a business cycle.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we address the issue of pricing discretely-sampled variance swaps under stochastic volatility and stochastic interest rate with regime-switching. We extend the framework of both [4] and [8] by incorporating the CIR stochastic interest rate into the Markov-modulated version of the Heston stochastic volatility model. This hybrid model possesses parameters that switch according to a continuous-time observable Markov chain process which can be interpreted as the states of an observable macroeconomic factor.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching

Cao

Roslan

Zhang

2018

Methodol Comput Appl Probab

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In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modeling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model parameters that switch according to a continuous-time observable Markov chain process. A semi-closed form pricing formula for variance swaps is derived. The pricing formula is assessed through numerical implementations, and the impact of including regimeswitching on pricing variance swaps is also discussed.2000 Mathematics Subject Classification. Primary 91G30; Secondary 91G20, 91B70.

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Section: Resultsmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching

Cao

Roslan

Zhang

2018

Methodol Comput Appl Probab

Self Cite

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“…Smith (2015) fi nds the leverage effects in the U.S. stock markets. The leverage effect suggests volatility shocks are negatively correlated with underlying asset price shock, it also accounts for a skewed distribution for the asset price observed by Carmichael and Coen (2013).…”

Section: Introductionmentioning

confidence: 99%

Pricing exotic option under stochastic volatility model

Li¹

2019

E+M

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This paper studies supershare and chooser options in a stochastic volatility economy. These two options are typical exotic options which suggest a broad range of usage and application in different fi nancial market conditions. Despite the popularity and longevity of the Black-Scholes model, the assumption of constant volatility in the Black-Scholes model contradicts to the existence of the non-fl at implied volatility surface observed in empirical studies. Although many studies are devoted to option pricing under stochastic volatility model in recent years, to the best of our knowledge, research on exotic option such as supershare and chooser option pricing have not been carried out in the stochastic volatility case. Supershare and chooser options are both important fi nancial instruments, research on these two exotic options in stochastic volatility model may give more insights on the pricing of supershare and chooser options. By extending the constant volatility in the Black-Scholes model, this paper studies the pricing problem of the supershare option and chooser options in a fast mean-reverting stochastic volatility scenario. Analytic approximation formulae for these two exotic options in fast mean-reverting stochastic volatility model are derived according to the method of asymptotic expansion which shows the approximation option price can be expressed as the combination of the zero-order and fi rst-order approximations. By incorporating the stochastic volatility effect, the numerical analysis in our model shows that stochastic volatility of underlying asset underprices the supershare options, while in the case of the chooser options its price in stochastic volatility model is higher than the price in the constant volatility model.

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Analytically pricing European options under a hybrid stochastic volatility and interest rate model with a general correlation structure

Lin

2023

Journal of Futures Markets

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In this paper, an additional factor is introduced into the Heston–Hull–White (HHW) hybrid model, which originally combines the Heston stochastic volatility model and the Hull–White stochastic interest rate model, to capture the correlation between the underlying price and the interest rate, while at the same time preserve the analytical tractability. With the analytical solution to the characteristic function of the underlying price being successfully derived, a closed‐form pricing formula for European options under the two‐factor HHW hybrid model is presented. Numerical experiments are also carried out to show the effect of the newly introduced factor. To further demonstrate the importance of introducing the correlation, we have also conducted an empirical study, comparing the performance of our model and that of the HHW model, based on European options written on S&P 500 index.

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Pricing variance swaps under stochastic volatility and stochastic interest rate

Cited by 20 publications

References 55 publications

Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching

Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching

Pricing exotic option under stochastic volatility model

Analytically pricing European options under a hybrid stochastic volatility and interest rate model with a general correlation structure

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