Calibration of time-dependent volatility for European options under the fractional Vasicek model

Jiajia Zhao; Zuoliang Xu; Jiajia Zhao; Zuoliang Xu

doi:10.3934/math.2022617

AIMS Mathematics

2022, Volume 7, Issue 6: 11053-11069. doi: 10.3934/math.2022617

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Calibration of time-dependent volatility for European options under the fractional Vasicek model

Jiajia Zhao ,
Zuoliang Xu ^,

School of Mathematics, Renmin University of China, Beijing 100872, China

Received: 11 February 2022 Revised: 22 March 2022 Accepted: 23 March 2022 Published: 06 April 2022
MSC : 65M32, 91G20, 90C32

In this paper, we calibrate the time-dependent volatility function for European options under the fractional Vasicek interest rate model. A fully implicit finite difference method is applied to solve the partial differential equation of option pricing numerically. To find the volatility function, we minimize a cost function that is the sum of the squared errors between the theoretical prices and market prices with Tikhonov $ L_2 $ regularization and $ L_{1/2} $ regularization respectively. Finally numerical experiments with simulated and real market data verify the efficiency of the proposed methods.
- calibration,
- fractional Vasicek model,
- European option,
- regularization,
- numerical methods
Citation: Jiajia Zhao, Zuoliang Xu. Calibration of time-dependent volatility for European options under the fractional Vasicek model[J]. AIMS Mathematics, 2022, 7(6): 11053-11069. doi: 10.3934/math.2022617

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Abstract

In this paper, we calibrate the time-dependent volatility function for European options under the fractional Vasicek interest rate model. A fully implicit finite difference method is applied to solve the partial differential equation of option pricing numerically. To find the volatility function, we minimize a cost function that is the sum of the squared errors between the theoretical prices and market prices with Tikhonov $ L_2 $ regularization and $ L_{1/2} $ regularization respectively. Finally numerical experiments with simulated and real market data verify the efficiency of the proposed methods.

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