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Pricing variance swaps under stochastic volatility and stochastic interest rate

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

Abstract

In this paper, we investigate the effects of imposing stochastic interest rate driven by the Cox–Ingersoll–Ross process along with the Heston stochastic volatility model for pricing variance swaps with discrete sampling times. A dimension reduction mechanism based on the framework of Little and Pant (2001) is applied which later reduces to solving two three-dimensional partial differential equations. A semi-closed form solution to the fair delivery price of a variance swap is obtained via the derivation of characteristic functions. Practical implementation of this hybrid model is demonstrated through numerical simulations.

Suggested Citation

  • Cao, Jiling & Lian, Guanghua & Roslan, Teh Raihana Nazirah, 2016. "Pricing variance swaps under stochastic volatility and stochastic interest rate," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 72-81.
    • Handle: RePEc:eee:apmaco:v:277:y:2016:i:c:p:72-81
    DOI: 10.1016/j.amc.2015.12.027
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    2. Jiling Cao & Teh Raihana Nazirah Roslan & Wenjun Zhang, 2018. "Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1359-1379, December.
    3. Kim, See-Woo & Kim, Jeong-Hoon, 2020. "Pricing generalized variance swaps under the Heston model with stochastic interest rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 1-27.
    4. Xu, De-xuan & Yang, Ben-zhang & Kang, Jian-hao & Huang, Nan-jing, 2021. "Variance and volatility swaps valuations with the stochastic liquidity risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    5. Ben-zhang Yang & Jia Yue & Nan-jing Huang, 2017. "Variance swaps under L\'{e}vy process with stochastic volatility and stochastic interest rate in incomplete markets," Papers 1712.10105, arXiv.org, revised Mar 2018.
    6. Ben-Zhang Yang & Jia Yue & Nan-Jing Huang, 2019. "Equilibrium Price Of Variance Swaps Under Stochastic Volatility With Lévy Jumps And Stochastic Interest Rate," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-33, June.
    7. Yang, Ben-Zhang & Yue, Jia & Wang, Ming-Hui & Huang, Nan-Jing, 2019. "Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 73-84.
    8. Kim, See-Woo & Kim, Jeong-Hoon, 2018. "Analytic solutions for variance swaps with double-mean-reverting volatility," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 130-144.
    9. Kim, See-Woo & Kim, Jeong-Hoon, 2019. "Variance swaps with double exponential Ornstein-Uhlenbeck stochastic volatility," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 149-169.
    10. Tao Liu & Malik Zaka Ullah & Stanford Shateyi & Chao Liu & Yanxiong Yang, 2023. "An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    11. Ah-Reum Han & Jeong-Hoon Kim & See-Woo Kim, 2021. "Variance Swaps with Deterministic and Stochastic Correlations," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1059-1092, April.

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