Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate

Yanhong Zhong,Guohe Deng

doi:10.1155/2019/4316272

Abstract

This paper presents an extension of double Heston stochastic volatility model by incorporating stochastic interest rates and derives explicit solutions for the prices of the continuously monitored fixed and floating strike geometric Asian options. The discounted joint characteristic function of the log-asset price and its log-geometric mean value is computed by using the change of numeraire and the Fourier inversion transform technique. We also provide efficient approximated approach and analyze several effects on option prices under the proposed model. Numerical examples show that both stochastic volatility and stochastic interest rate have a significant impact on option values, particularly on the values of longer term options. The proposed model is suitable for modeling the longer time real-market changes and managing the credit risks.

Highlights

Asian option is a special type of option contract in which the payoff depends on the average of the underlying asset price over some predetermined time interval
This paper presents an extension of double Heston stochastic volatility model by incorporating stochastic interest rates and derives explicit solutions for the prices of the continuously monitored fixed and floating strike geometric Asian options
The average considered can be a arithmetic or geometric one and it can be calculated either discretely, for which the average is taken over the underlying asset prices at discrete monitoring time points, or continuously, for which the average is calculated via the integration of the underlying asset price over the monitoring time period

Summary

Introduction

Asian option is a special type of option contract in which the payoff depends on the average of the underlying asset price over some predetermined time interval. See Alizadeh et al [20], Fiorentini et al [21], Chernov et al [22], Gourieroux [23], Christoffersen et al [24], Romo [25], and Nagashima et al [26] for the empirical results To address this issue, multifactor SV models have recently generated attention in the option pricing literature. We study the pricing of the continuously monitored geometric Asian options under dbH stochastic volatility model with stochastic interest rate framework (hereafter, dbH-SI model). This paper provides a semiexplicit valuation formula for the geometric Asian options with fixed or floating strike price, which is extremely useful for the arithmetic average option valuation via Monte Carlo methods with control variables.

Model Formulation

The Joint Characteristic Function

Pricing Geometric Asian Option

Numerical Examples

Findings

Conclusions