Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

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

doi:10.2139/ssrn.2485692

Cited by 6 publications

(19 citation statements)

References 64 publications

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“…In order to explore the economic consequences of incorporating regime switching into the Heston-CIR model, we present Figure 5.2 which shows the difference between our pricing formula in (5.51) versus the Heston-CIR model without regime switching in [19].…”

Section: Effect Of Regime Switchingmentioning

confidence: 99%

Pricing variance swaps under stochastic volatility and stochastic interest rate

Cao

Lian

Roslan

2016

Applied Mathematics and Computation

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Section: Effect Of Regime Switchingmentioning

confidence: 99%

Pricing variance swaps under stochastic volatility and stochastic interest rate

Cao

Lian

Roslan

2016

Applied Mathematics and Computation

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“…Kim [23] proves that the introduction of stochastic interest rate can indeed get better results. Cao et al [24] combined the Heston [16] stochastic volatility model with Cox-Ingersoll-Ross (CIR) [25] stochastic interest rate model, using the dimension reduction technology in Little and Pant [15] and characteristic function, they obtained a semi-closed solution of variance swaps under the CIR-Heston hybrid model. Cao et al [26] further extended the partial coefficient correlation model to the full correlation structure model, and presented a semi-closed solution through the derivation of characteristic function.…”

Section: Introductionmentioning

confidence: 99%

“…Cao et al [26] further extended the partial coefficient correlation model to the full correlation structure model, and presented a semi-closed solution through the derivation of characteristic function. Based on the work of [20,24], Zhao [27] introduced the Vasicek interest rate process to the MRG(mean-reverting Gaussian) model to obtain a closed-form solution. Recently, Xu et al [28] obtained the pricing formula of variance swaps with the liquidity risk of the underlying assets.…”

Section: Introductionmentioning

confidence: 99%

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A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

2021

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At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results ; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and Ito^’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable.

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“…Results showed that their model is excellent in terms of producing small errors compared with the original model. Recently, Cao et al (2016) and Roslan (2016) investigated the effects of imposing stochastic interest rate driven by the CIR process along with the Heston stochastic volatility model for pricing discretely sampled variance swaps with the actual-return realized variance, and a semi-closed-form solution to the fair delivery price of a variance swap is obtained.…”

Section: Introductionmentioning

confidence: 99%

A closed-form pricing formula for variance swaps under MRG–Vasicek model

Han

Zhao

2019

Comp. Appl. Math.

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In this paper, the pricing problems of variance swaps with discrete sampling times are studied, where the volatility of underlying assets follows a mean-reverting Gaussian (MRG in short) process, and the instantaneous interest rate is described by classical Vasicek model. By using measure transformation, Feynman-Kac formula and Fourier transform algorithm, a closedform analytic pricing formula for variance swaps with the actual-return realized variance is presented.

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Pricing Variance Swaps Under Stochastic Volatility and Stochastic Interest Rate

Cited by 6 publications

References 64 publications

Pricing variance swaps under stochastic volatility and stochastic interest rate

Pricing variance swaps under stochastic volatility and stochastic interest rate

A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

A closed-form pricing formula for variance swaps under MRG–Vasicek model

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