Pricing generalized variance swaps under the Heston model with stochastic interest rates

See Woo Kim, Jeong Hoon Kim

Research output: Contribution to journalArticle

Abstract

Unlike vanilla variance swaps, generalized variance swaps such as gamma, corridor variance and conditional variance swaps are expected to be not free from interest rates because of their weight processes. To examine the impact of stochastic interest rates on the generalized variance swaps, this paper considers discrete sampling times and the Heston stochastic volatility model incorporated by stochastic interest rates driven by the Cox–Ingersoll–Ross process. Based on the explicit calculation of the discounted characteristic function of Duffie et al. (2000), we obtain exact solutions for the fair strike prices of the generalized variance swaps for an affine version of the hybrid model. The solutions are given in closed form expression for the vanilla variance and gamma swaps and in Fourier integral expression for the corridor and conditional variance swaps. We apply the projection techniques of Grzelak and Oosterlee (2011) to the original non-affine model with a generalized correlation structure and obtain affine approximate solutions. We show the effects of stochastic interest rates on the strike prices of the generalized variance swaps.

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalMathematics and Computers in Simulation
Volume168
DOIs
Publication statusPublished - 2020 Feb

Fingerprint

Heston Model
Stochastic Interest Rates
Generalized Variance
Swap
Pricing
Stochastic models
Costs
Sampling
Conditional Variance
Discrete Sampling
Fourier Integral
Stochastic Volatility Model
Correlation Structure
Hybrid Model
Interest Rates
Characteristic Function
Closed-form
Approximate Solution
Exact Solution
Projection

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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abstract = "Unlike vanilla variance swaps, generalized variance swaps such as gamma, corridor variance and conditional variance swaps are expected to be not free from interest rates because of their weight processes. To examine the impact of stochastic interest rates on the generalized variance swaps, this paper considers discrete sampling times and the Heston stochastic volatility model incorporated by stochastic interest rates driven by the Cox–Ingersoll–Ross process. Based on the explicit calculation of the discounted characteristic function of Duffie et al. (2000), we obtain exact solutions for the fair strike prices of the generalized variance swaps for an affine version of the hybrid model. The solutions are given in closed form expression for the vanilla variance and gamma swaps and in Fourier integral expression for the corridor and conditional variance swaps. We apply the projection techniques of Grzelak and Oosterlee (2011) to the original non-affine model with a generalized correlation structure and obtain affine approximate solutions. We show the effects of stochastic interest rates on the strike prices of the generalized variance swaps.",
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Pricing generalized variance swaps under the Heston model with stochastic interest rates. / Kim, See Woo; Kim, Jeong Hoon.

In: Mathematics and Computers in Simulation, Vol. 168, 02.2020, p. 1-27.

Research output: Contribution to journalArticle

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