### 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 language | English |
---|---|

Pages (from-to) | 1-27 |

Number of pages | 27 |

Journal | Mathematics and Computers in Simulation |

Volume | 168 |

DOIs | |

Publication status | Published - 2020 Feb |

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### 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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**Pricing generalized variance swaps under the Heston model with stochastic interest rates.** / Kim, See Woo; Kim, Jeong Hoon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Pricing generalized variance swaps under the Heston model with stochastic interest rates

AU - Kim, See Woo

AU - Kim, Jeong Hoon

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85073580620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073580620&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2019.07.013

DO - 10.1016/j.matcom.2019.07.013

M3 - Article

AN - SCOPUS:85073580620

VL - 168

SP - 1

EP - 27

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

ER -