American option pricing under the double Heston model based on asymptotic expansion

Zhang, S. M.; Feng, Yaqin

doi:10.1080/14697688.2018.1478119

Cited by 16 publications

(5 citation statements)

References 38 publications

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“…Zhang & Oosterlee (2013) showed how to use the COS method to pricing arithmetic and geometric Asian options under exponential Lévy processes. Zhang & Feng (2018) found the price of American put options under the double Heston (1993) model using the COS method. Zhang et al (2012) analyzed the efficiency properties of pricing commodity options with earlyexercise.…”

Section: Introductionmentioning

confidence: 99%

Recovering Probability Functions With Fourier Series

Silva

Baczynski²,

Vicente

2023

Pesqui. Oper.

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The COS method was introduced in Fang & Oosterlee (2008) and then was applied to pricing a variety of stock options for continuous random variables. This paper adapts the Fourier-cosine series (COS) method to recover discrete probability mass functions. We approximate mixture and compound probability distributions with cosine series. Enormous precision and computational speed are the qualities of the function estimates here obtained. We also develop the pricing framework to trade derivatives subject to discrete random variables. We apply the method to calculate, for the first time, the price of an interest rate derivative of recent vintage introduced in the Brazilian financial market. Parameter calibration confirms the quality of the model.

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Section: Introductionmentioning

confidence: 99%

Recovering Probability Functions With Fourier Series

Silva

Baczynski²,

Vicente

2023

Pesqui. Oper.

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“…Dufe et al [28] and Christofersen et al [29] proposed two-factor or multifactor Heston model to solve the problems exposed by the single-factor Heston model. Zhang and Feng [30] derived American option pricing formula under the two-factor Heston model by using the asymptotic expansion method, and the results show that two-factor Heston model is superior to the Heston model in pricing short-term American options. Zhong and Deng [31] explored geometric Asian option pricing under double Heston model and stochastic interest rate, the numerical results show that the long-term stochastic volatility and short-term stochastic volatility have signifcant efects on option pricing.…”

Section: Introductionmentioning

confidence: 99%

Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model

Deng

2023

Mathematical Problems in Engineering

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In this paper, we consider the pricing problem for the extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of the logarithm of two asset prices is derived by using the Feynman–Kac theorem and one-order Taylor approximation expansion. The semiclosed analytical pricing formulas of the European extremum options including option on maximum and option on minimum of two underlying assets are derived by using measure change technique and Fourier transform approach. Some numerical examples are provided to analyze the pricing results of extremum options under affine model, nonaffine model, Black–Scholes model, and the influences of some model parameters on the option. Numerical results show that the analytical pricing formulas have higher computational efficiency and accuracy than those of Monte Carlo simulation method. Also, results of sensitivity analysis report that the nonaffine models are more effective than other existing models in capturing the effect of volatility on option pricing.

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“…Christoffersen, Heston and Jacobs ( 2009 ) proposed a two-factor Heston model, named the double Heston model, with fast and slow factors which are all mean reverting and showed that the model can explain the dynamics of market more flexibly than the classical Heston model. Using this model, Gauthier and Possamai ( 2011 ) improved the European option pricing formula given by Christoffersen et al Moreover, Zhang and Feng ( 2019 ) and Fallah and Mehrdoust ( 2019 ) studied the pricing of American options under the double Heston model. However, it costs too much time for calibration under the double Heston model because the number of the model parameters is twice that of the Heston model.…”

Section: Introductionmentioning

confidence: 99%