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

Han, Yuecai; Zhao, Longxiao

doi:10.1007/s40314-019-0905-6

Cited by 8 publications

(7 citation statements)

References 31 publications

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“…There are numerous methods in the literature of pricing variance swaps, both analytically and numerically (see [13] for an extensive review). Nevertheless, a pricing formula or procedure that relies on a certain stochastic process, for instance, Lévy process [14], MRG-Vasicek model [17], or Hawkes jump-diffusion model [18], may suffer from a lack of parsimony or might not fit the real data well due to the inappropriateness of model assumptions (see, for instance, [14]).…”

Section: Pricing Variance Swapmentioning

confidence: 99%

A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

Jiang

Zhou

et al. 2021

Front. Appl. Math. Stat.

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Estimates of risk-neutral densities of future asset returns have been commonly used for pricing new financial derivatives, detecting profitable opportunities, and measuring central bank policy impacts. We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the normal inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the Chicago Board Options Exchange website.

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Section: Pricing Variance Swapmentioning

confidence: 99%

A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

Jiang

Zhou

et al. 2021

Front. Appl. Math. Stat.

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“…In order to verify this point, we need to compare the results of stochastic interest rates under different parameters. According to Cao [24] and Zhao [27], the long-term mean of stochastic interest rate η has a great influence on the formula, but the mean-reverting speed h and volatility ξ have little impact. Hence, to improve efficiency, we only select different long-term mean values, then take h = 1.2 and ξ = 0.01.…”

Section: Monte Carlo Simulationsmentioning

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%

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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“…What's more, compared with Kim et al [33,34], we apply a stochastic analysis approach that there is no need to solve PDEs and make the solution quite simplified. By the mean time, the parameters of the DMR (Heston-CIR) model play an important role in the approximate solution that is different from the effect of the stochastic rate on the result decreases [4].…”

Section: Introductionmentioning

confidence: 99%

An analytic solution and an approximate solution for log‐return variance swaps under double‐mean‐reverting volatility

Mao,

Liu

2023

Math Methods in App Sciences

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Variance swaps is a kind of financial instrument that plays an important role in volatility risk management. In this paper, we study the pricing problem of log‐return variance swaps under the double mean reversion DMR (Heston‐CIR) model. Compared with Kim's work, we introduce the square‐root process into the diffusion term of the long‐term mean and present a stochastic approach that greatly simplify the solution of the problem without solving PDEs. An analytical solution and approximate solution are obtained. Some numerical examples show that the exact solution and MC simulation fit well. It is worth mentioning that the difference between the approximate solution and the exact solution is small when the parameters are selected appropriately. By the mean time, the parameter of the long‐term mean has an important impact on the solution, which implies that the introduction of a multi‐factor model is necessary.

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

Cited by 8 publications

References 31 publications

A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps

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

An analytic solution and an approximate solution for log‐return variance swaps under double‐mean‐reverting volatility

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