COS method for option pricing under a regime-switching model with time-changed Lévy processes

Tour, Geraldine; Thakoor, Nawdha; Tangman, Désiré Yannick

doi:10.1080/14697688.2017.1412494

Cited by 37 publications

(11 citation statements)

References 48 publications

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“…Tese models can be generally classifed as Lévy processes for the above stochastic processes. Lévy processes have gained increasing importance in the option pricing literature due to the well-known faws of the classical Black-Scholes geometric Brownian motion model [4]. Tey include the Brownian motion Poisson process and the compound Poisson process.…”

Section: Introductionmentioning

confidence: 99%

Application of Malliavin Calculus in Mean-Variance Hedging Strategy

Liu

Chen

Zhang

et al. 2022

Mathematical Problems in Engineering

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This paper considers an approach of Malliavin calculus to obtain the hedging ratio for mean-variance hedging (MVH) strategy under the stochastic volatility model with pure jump Lévy process (SVJ). Specifically speaking, there exists a correspondence between the martingale representation theorem and the Clark-Ocone formula for a square integrable contingent claim. Therefore, we can replace the diffusion term coefficients with the functions containing Malliavin derivatives to get a closed-form representation for the MVH strategy. By fast Fourier transform (FFT) algorithm, some numerical examples are performed to analyze the sensitivity of MVH strategy concerning strike price and current time.

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Section: Introductionmentioning

confidence: 99%

Application of Malliavin Calculus in Mean-Variance Hedging Strategy

Liu

Chen

Zhang

et al. 2022

Mathematical Problems in Engineering

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“…For example, Deng et al [31] used the 1D COS method for equity-indexed annuity products under general exponential Lévy models; Alonso-García et al [32] extended the 1D COS method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdraw benefit riders. The latest research on Fourier transform was given by Zhang et al [33], Chan [34], Zhang and Liu [35], Have and Oosterlee [36], Shimizu and Zhang [37], Tour [38], Zhang [39], and Wang et al [40].…”

Section: Introductionmentioning

confidence: 99%

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Yong

Guan

et al. 2019

Mathematics

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Recently, the valuation of variable annuity products has become a hot topic in actuarial science. In this paper, we use the Fourier cosine series expansion (COS) method to value the guaranteed minimum death benefit (GMDB) products. We first express the value of GMDB by the discounted density function approach, then we use the COS method to approximate the valuation Equations. When the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process, explicit equations for the cosine coefficients are given. Some numerical experiments are also made to illustrate the efficiency of our method.

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“…The prices of the risky assets involved are often modeled as the exponential of a Markov‐modulated Brownian motion without synchronous jumps; we refer to Elliott et al for a good overview of the literature and financial applications of regime‐switching models. There exists also a wide range of studies that consider MMLPs without synchronous jumps for the dynamics of the risky assets; see, eg, Konikov and Madan, Elliott and Osakwe, Ramponi and Tour et al…”

Section: Introductionmentioning

confidence: 99%

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Deelstra

Kozpınar

Simon

2018

Appl Stoch Models Bus & Ind

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This paper considers the evaluation of spread and basket options when the underlying asset prices are driven by Markov-modulated Lévy processes with synchronous jumps. In particular, the asset prices may jump whenever there is a change of phase of the underlying Markov process. We further allow for dependence between the different price dynamics. In this general regime-switching framework, we provide lower and upper bounds to the exact option prices based upon ideas from the literature without regime switching. These bounds are obtained via univariate Fourier inversion under the assumption that the joint characteristic functions of the Markov-modulated Lévy processes are known. We study these obtained spread and basket option price approximations in different regime-switching models. Several numerical experiments are included and these show that, especially, the lower bounds have a very high precision.

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COS method for option pricing under a regime-switching model with time-changed Lévy processes

Cited by 37 publications

References 48 publications

Application of Malliavin Calculus in Mean-Variance Hedging Strategy

Application of Malliavin Calculus in Mean-Variance Hedging Strategy

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

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