Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity

Huang, Jiexiang; Zhu, Wei; Ruan, Xinfeng

doi:10.1155/2013/875606

“…ey derived the characteristic function and did some numerical study based on it by applying FFT. Several authors presented models combing stochastic volatility, stochastic interest rates, and jumps with stochastic intensity [32,33].…”

Section: Introductionmentioning

confidence: 99%

Option Pricing under Double Stochastic Volatility Model with Stochastic Interest Rates and Double Exponential Jumps with Stochastic Intensity

Chang

¹

,

Wang

²

2020

Mathematical Problems in Engineering

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We present option pricing under the double stochastic volatility model with stochastic interest rates and double exponential jumps with stochastic intensity in this article. We make two contributions based on the existing literature. First, we add double stochastic volatility to the option pricing model combining stochastic interest rates and jumps with stochastic intensity, and we are the first to fill this gap. Second, the stochastic interest rate process is presented in the Hull–White model. Some authors have concentrated on hybrid models based on various asset classes in recent years. Therefore, we build a multifactor model with the term structure of stochastic interest rates. We also approximated the pricing formula for European call options by applying the COS method and fast Fourier transform (FFT). Numerical results display that FFT and the COS method are much faster than the numerical integration approach used for obtaining the semi-closed form prices. The COS method shows higher accuracy, efficiency, and stability than FFT. Therefore, we use the COS method to investigate the impact of the parameters in the stochastic jump intensity process and the existence of the process on the call option prices. We also use it to examine the impact of the parameters in the interest rate process on the call option prices.

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“…Numerical techniques may include Monte Carlo simulation and finite difference methods [7,10]. The FFT technique in option pricing was introduced by Carr and Madan [5], and has since gained popularity in option pricing because its algorithm offers computational efficiency by employing the characteristic function of the log price which is known in closed-form for many models discussed in the literature [17,27,32,33,34]. In Ibrahim et al [19], the FFT technique has been applied to price the holder-extendable call options in the Black-Scholes environment, while in this study, we aim to apply the FFT technique to price the holder-extendable call options under the Heston model [14].…”

Section: Introductionmentioning

confidence: 99%

Pricing holder-extendable call options with mean-reverting stochastic volatility

Ibrahim

¹

,

Hernández

²

,

O’Hara

³

et al. 2020

ANZIAMJ

2

0

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Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls. doi:10.1017/S1446181119000142

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“…Numerical techniques may include MCS and finite difference methods (FDMs) [7,10]. The fast Fourier transform (FFT) technique in option pricing was introduced by Carr and Madan [5] and has since gained popularity in option pricing because its algorithm offers computational efficiency by employing the characteristic function of the log price, which is known in closed-form for many models discussed in the literature [17,28,[33][34][35]. Ibrahim et al [20] applied the FFT technique to price the holder-extendable call options in the Black-Scholes environment [2], while, in this study, we aim to apply the FFT technique to price the holder-extendable call options under the Heston model [14].…”

Section: Introductionmentioning

confidence: 99%

Pricing Holder-Extendable Call Options With Mean-Reverting Stochastic Volatility

Ibrahim¹,

Hernández²,

O’Hara³

et al. 2019

ANZIAM J.

2

0

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Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls.

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Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity

Cited by 6 publications

References 16 publications

Option Pricing under Double Stochastic Volatility Model with Stochastic Interest Rates and Double Exponential Jumps with Stochastic Intensity

Option Pricing under Double Stochastic Volatility Model with Stochastic Interest Rates and Double Exponential Jumps with Stochastic Intensity

Pricing holder-extendable call options with mean-reverting stochastic volatility

Pricing Holder-Extendable Call Options With Mean-Reverting Stochastic Volatility

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