On the valuation of variance swaps with stochastic volatility

Zhu, Song-Ping; Lian, Guanghua

doi:10.1016/j.amc.2012.08.006

Cited by 20 publications

(34 citation statements)

References 33 publications

(34 reference statements)

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“…Remark It should be mentioned that the method we present in Appendix has significantly simplified the solution procedure compared with the other two approaches (under stochastic volatility models) in the literature. The first approach is based on Little and Pant's finite‐difference method via solving a system of coupled partial differential equations (see Cao & Fang, ; Zhu & Lian, , ). The second approach simplified the first one via iterated expectations through applying the method of undetermined coefficients in partial differential equations (see Rujivan & Zhu, , ; Zhang, ).…”

Section: The Modelmentioning

confidence: 99%

“…Under the Heston's stochastic volatility model (Heston, ), there are quite a few approaches to obtain closed‐form formulas for variance swaps based on discretely sampled realized variance: Broadie and Jain () presented the first‐order approximation based on integrating the underlying stochastic process directly. Zhu and Lian (, ) managed to derive closed‐form formulas by solving a system of coupled partial differential equations, and Rujivan and Zhu (, ) simplified the partial differential equations by iterated expectations. Motivated by these methods, different types of local or stochastic volatility models are adopted to derive the corresponding formulas for pricing discretely sampled variance swaps.…”

Section: Introductionmentioning

confidence: 99%

“…This study contributes to the existing literature in several ways: First, the nature of jump clustering is included in the model and a closed‐form exact formula is presented. The proposed model is very general, of which the results obtained from the Black–Scholes model, Merton jump‐diffusion model, Heston stochastic volatility model, and their combinations can all be considered as special cases, which include Broadie and Jain (), Zhu and Lian (, ), Rujivan and Zhu (, ), and Zheng and Kowk (), etc. Second, we provide a significantly simplified method different from those reported in the literature to obtain the analytical formula without resorting to partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pricing variance swaps under the Hawkes jump‐diffusion process

Liu

Zhu

2019

J Futures Markets

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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 numerical examples are provided with results demonstrating that jump clustering indeed has a significant impact on the price of variance swaps.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pricing variance swaps under the Hawkes jump‐diffusion process

Liu

Zhu

2019

J Futures Markets

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“…Zhu and Lian [12,13] also presented an approach to obtain closed-form formula for variance swaps, under the Heston's two-factor stochastic volatility model embedded in the framework proposed by Little and Pant [1] , based on the discretely-sampled realized variance with the realized variance being defined as the average of the squared relative percentage increment of the underlying price. Unlike Broadie and Jain's [4] approach, Zhu and Lian [12] found a much simpler formula by solving the governing PDE system directly, by using Fourier transform method.…”

Section: Introductionmentioning

confidence: 99%

Pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck process

Jia

Zhang

2015

J Syst Sci Complex

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Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-related derivatives in the past few years. In this note, the authors develop analytical method for pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck (OU) process. By using Fourier transform algorithm, a closed-form solution for pricing variance swaps with stochastic volatility is obtained, and to give a comparison of fair strike value based on the discrete model, continuous model, and the Monte Carlo simulations.

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“…Among stochastic volatility models, the one proposed by [66] has received a lot of attentions, since it gives a satisfactory description of the underlying asset dynamics [34,37]. Recently, Zhu and Lian [119,120] used Heston model to derive a closed form exact solution to the price of variance swaps.…”

Section: The Heston-cir Modelmentioning

confidence: 99%