Option pricing in a regime‐switching model using the fast Fourier transform

Liu, R. H.; Zhang, Q.; Yin, Gang

doi:10.1155/jamsa/2006/18109

Cited by 55 publications

(32 citation statements)

References 27 publications

(31 reference statements)

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“…As in Carr and Madan () and Liu et al (), we define the dampened call option price by

c (0, T, k) ≔ {normale}^{α k} \frac{C (0, T, k)}{S_{0}},

where α is called the dampening coefficient and is assumed to be positive such that

c (0, T, k)

is square integrable with respect to k over the entire real line. We consider the Fourier transform of the dampened call price

c (0, T, k)

ψ (0, T, u) = \int_{double-struckR} e^{i u k} c false(0, T, k false) normald k, i = \sqrt{- 1} .

For each

t \in T

and

u \in R

, let

ϕ_{Y (t) | {scriptF}^{boldX} (t)} (0, t, u) ≔ {normalE}^{θ} [{normale}^{i u Y (t)} | {scriptF}^{boldX} (t)],

and

{\overset{true˜}{ϕ}}_{Y (t) | {scriptF}^{boldX} (t)} (0, t, u) ≔ exp (- \int_{0}^{t} r false(s false) normald s) ϕ_{Y (}

…”

Section: Option Valuation Using the Fast Fourier Transformmentioning

confidence: 99%

Option Valuation Under a Double Regime‐Switching Model

Shen

Fan

Siu

2013

Journal of Futures Markets

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This paper is concerned with option valuation under a double regime‐switching model, where both the model parameters and the price level of the risky share depend on a continuous‐time, finite‐state, observable Markov chain. In this incomplete market set up, we first employ a generalized version of the regime‐switching Esscher transform to select an equivalent martingale measure which can incorporate both the diffusion and regime‐switching risks. Using an inverse Fourier transform, an analytical option pricing formula is obtained. Finally, we apply the fast Fourier transform method to compute option prices. Numerical examples and empirical studies are used to illustrate the practical implementation of our method. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:451–478, 2014

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“…As in Carr and Madan () and Liu et al (), we define the dampened call option price by

c (0, T, k) ≔ {normale}^{α k} \frac{C (0, T, k)}{S_{0}},

where α is called the dampening coefficient and is assumed to be positive such that

c (0, T, k)

is square integrable with respect to k over the entire real line. We consider the Fourier transform of the dampened call price

c (0, T, k)

ψ (0, T, u) = \int_{double-struckR} e^{i u k} c false(0, T, k false) normald k, i = \sqrt{- 1} .

For each

t \in T

and

u \in R

, let

ϕ_{Y (t) | {scriptF}^{boldX} (t)} (0, t, u) ≔ {normalE}^{θ} [{normale}^{i u Y (t)} | {scriptF}^{boldX} (t)],

and

{\overset{true˜}{ϕ}}_{Y (t) | {scriptF}^{boldX} (t)} (0, t, u) ≔ exp (- \int_{0}^{t} r false(s false) normald s) ϕ_{Y (}

…”

Section: Option Valuation Using the Fast Fourier Transformmentioning

confidence: 99%

Option Valuation Under a Double Regime‐Switching Model

Shen

Fan

Siu

2013

Journal of Futures Markets

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“…European style options with regime-switching are treated in a number of articles (see Guo [11], Yao et al [19], Buffington and Elliott [5], Bollen [4], Liu et al [17], among others). In contrast, American options are far less studied and only a few special cases are considered.…”

Section: Introductionmentioning

confidence: 99%

New Numerical Scheme for Pricing American Option With Regime-Switching

Khaliq

Liu

2009

Int. J. Theor. Appl. Finan.

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This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we implement an implicit approach by explicitly treating the nonlinear terms and/or the linear terms from other regimes, resulting in computationally efficient algorithms. We establish an upper bound condition for the time step size and prove that under the condition the implicit schemes satisfy a discrete version of the positivity constraint for American option values. We compare the implicit schemes with a tree model that generalizes the Cox-Ross-Rubinstein (CRR) binomial tree model, and with an analytical approximation solution for two-regime case due to Buffington and Elliott. Numerical examples demonstrate the accuracy and stability of the new implicit schemes.

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“…Following Carr and Madan (1999) and Liu et al (2006), let α be the dampening coefficient, we can calculate the Fourier transform of the dampened call option price as follows:…”

Section: Valuation Of Point-to-point Eiasmentioning

confidence: 99%