Asian option pricing under sub-fractional vasicek model

Lichao Tao; Yuefu Lai; Yanting Ji; Xiangxing Tao; Lichao Tao; Yuefu Lai; Yanting Ji; Xiangxing Tao

doi:10.3934/QFE.2023020

Quantitative Finance and Economics

2023, Volume 7, Issue 3: 403-419. doi: 10.3934/QFE.2023020

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Research article

Asian option pricing under sub-fractional vasicek model

1.
School of Engineering Cost, Zhejiang College of Construction, Hangzhou 311231, P. R. China
2.
School of Information and Electronic Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China
3.
Department of Mathematics and Statistics, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China

Received: 07 June 2023 Revised: 08 August 2023 Accepted: 21 August 2023 Published: 31 August 2023
JEL Codes: C15, C32, C63

This paper investigates the pricing formula for geometric Asian options where the underlying asset is driven by the sub-fractional Brownian motion with interest rate satisfying the sub-fractional Vasicek model. By applying the sub-fractional $ {\rm{It\hat o}} $ formula, the Black-Scholes (B-S) type Partial Differential Equations (PDE) to Asian geometric average option is derived by Delta hedging principle. Moreover, the explicit pricing formula for Asian options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the stock price, the Hurst index, the speed of interest rate adjustment, and the volatilities and their correlation for the Asian option and the interest rate model, respectively. The results show that the main parameters such as Hurst index have a significant influence on the price of Asian options.
- sub-fractional Brownian motion,
- vasicek model,
- zero-coupon bond,
- Asian option pricing
Citation: Lichao Tao, Yuefu Lai, Yanting Ji, Xiangxing Tao. Asian option pricing under sub-fractional vasicek model[J]. Quantitative Finance and Economics, 2023, 7(3): 403-419. doi: 10.3934/QFE.2023020

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Abstract

This paper investigates the pricing formula for geometric Asian options where the underlying asset is driven by the sub-fractional Brownian motion with interest rate satisfying the sub-fractional Vasicek model. By applying the sub-fractional $ {\rm{It\hat o}} $ formula, the Black-Scholes (B-S) type Partial Differential Equations (PDE) to Asian geometric average option is derived by Delta hedging principle. Moreover, the explicit pricing formula for Asian options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the stock price, the Hurst index, the speed of interest rate adjustment, and the volatilities and their correlation for the Asian option and the interest rate model, respectively. The results show that the main parameters such as Hurst index have a significant influence on the price of Asian options.

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