Pricing Options Under a Generalized Markov-Modulated Jump-Diffusion Model

Elliott, Robert J.; Siu, Tak Kuen; Chan, Laval; Lau, John W.

doi:10.1080/07362990701420118

Cited by 103 publications

(56 citation statements)

References 23 publications

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“…However, using our general framework, it is trivial to extend these results to other control problems and stochastic processes. For example, all the analysis presented here can be applied to Markov modulated jump diffusions [18], provided that the integral terms are discretized in the usual fashion [17]. In addition, these techniques can also be applied to switching problems [34].…”

Section: Discussionmentioning

confidence: 99%

“…One significant advantage of our general approach is that our convergence results can be immediately applied to any type of optimal control problem (not just an American constraint) based on regime switching or Markov modulated jump diffusions [18]. We should also mention that these methods can also be applied to switching problems [34], which arise, for example, in optimal operation of power plants.…”

Section: Introductionmentioning

confidence: 99%

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Methods for Pricing American Options under Regime Switching

Huang¹,

Forsyth²,

Labahn³

2011

SIAM J. Sci. Comput.

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Abstract. We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations. Numerical tests indicate that a fixed point policy iteration, coupled with a direct control formulation, is a reliable general purpose method. Finally, we remark that we formulate the American problem as an abstract optimal control problem; hence our results are applicable to more general problems as well. Key words. regime switching, American options, iterative methods AMS subject classifications. 65N06, 93C20DOI. 10.1137/1108209201. Introduction. The standard approach to valuation of contingent claims (also known as derivatives) is to specify a stochastic process for the underlying asset and then construct a dynamic, self-financing hedging portfolio to minimize risk. The initial cost of constructing the portfolio is then considered to be the fair value of the contingent claim. This has been used with great success in the case of stochastic processes having constant volatility in the case of both European and (the more difficult) American options.However, it is well known that a financial model which follows a stochastic process having constant volatility is not consistent with market prices. Recent research has shown that models based on stochastic volatility, jump diffusion, and regime switching processes produce better fits to market data. A nonexhaustive list of regime switching applications includes insurance [22] [3], and interest rate dynamics [27]. Regime switching models are intuitively appealing, and computationally inexpensive compared to a stochastic volatility jump diffusion model.In this paper we study numerical techniques for the solution of American option contracts under regime switching. While our examples focus on problems with constant properties in each regime, the numerical methods developed can easily be applied to cases where the properties in each regime are more complex. An example would be the use of price-dependent regime switching (i.e., default hazard rates) in convertible bond pricing [4]. A number of different methods has been proposed for handling American options under regime switching models. Semianalytic approaches have been

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Methods for Pricing American Options under Regime Switching

Huang¹,

Forsyth²,

Labahn³

2011

SIAM J. Sci. Comput.

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“…Option pricing using regime switching has been the subject of considerable study in the mathematical finance literature because of the rich dynamics permitted by this class of models (e.g., , Elliott, Siu, Chan and Lau (2007)). 6 However, the pricing of general regime-switching models requires the computationally expensive solution of a system of partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

What is beneath the surface? Option pricing with multifrequency latent states

Calvet

Fearnley

Fisher

et al. 2015

Journal of Econometrics

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We introduce a tractable class of non-ane price processes with multifrequency stochastic volatility and jumps. The specications require few xed parameters and deliver fast option pricing. One key ingredient is a tight link between jumps and volatility regimes, as asset pricing theory suggests. Empirically, the model matches implied volatility surfaces and their dynamics with-out requiring parameter recalibration. A variety of metrics show improvements over traditional benchmarks in-and out-of-sample. AbstractWe introduce a tractable class of non-affine price processes with multifrequency stochastic volatility and jumps. The specifications require few fixed parameters and deliver fast option pricing. One key ingredient is a tight link between jumps and volatility regimes, as asset pricing theory suggests. Empirically, the model matches implied volatility surfaces and their dynamics without requiring parameter recalibration. A variety of metrics show improvements over traditional benchmarks in-and out-of-sample.

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“…Under the risk-neutral measure, see Elliot et al [15] for details, the stochastic process for the underlying asset S t is 25 dS t S t = r αt dt + σ αt dB t , t ≤ 0,…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, regime switching models are computationally inexpensive com- 15 pared to stochastic volatility jump diffusion models and have versatile applications in other fields, like electric markets [3], valuation of stock loans [35], forestry valuation [7], natural gas [8] and insurance [17].…”

Section: Introductionmentioning

confidence: 99%

A new efficient numerical method for solving American option under regime switching model

Egorova

Jódar

2016

Computers & Mathematics with Applications

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A system of coupled free boundary problems describing American put option pricing under regime switching is considered. In order to build numerical solution firstly a front-fixing transformation is applied. Transformed problem is posed on multidimensional fixed domain and is solved by explicit finite difference method. The numerical scheme is conditionally stable and is consistent with the first order in time and second order in space. The proposed approach allows the computation not only of the option price but also of the optimal stopping boundary. Numerical examples demonstrate efficiency and accuracy of the proposed method. The results are compared with other known approaches to show its competitiveness.

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Pricing Options Under a Generalized Markov-Modulated Jump-Diffusion Model

Cited by 103 publications

References 23 publications

Methods for Pricing American Options under Regime Switching

Methods for Pricing American Options under Regime Switching

What is beneath the surface? Option pricing with multifrequency latent states

A new efficient numerical method for solving American option under regime switching model

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