Option Pricing Under a Double Exponential Jump Diffusion Model

Kou, Steven; Wang, Hui

doi:10.1287/mnsc.1030.0163

Cited by 516 publications

(237 citation statements)

References 49 publications

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“…In Section 3, we introduce a numerical algorithm and analyze its convergence properties. In the last section we give numerical examples to illustrate the competitiveness of our algorithm and price American, Barrier and European options for the models of [17] and [18].…”

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confidence: 99%

Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions

Bayraktar

Xing

2009

Math Meth Oper Res

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Abstract. We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically computed using the classical finite difference methods. We prove the convergence of this numerical scheme and present examples to illustrate its performance.

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confidence: 99%

Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions

Bayraktar

Xing

2009

Math Meth Oper Res

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“…Among them are the log-normal jump-amplitude distribution used by Merton [47] in his pioneering jump-diffusion finance paper (see also Hanson and Westman [25]), the log-double-exponential distribution used by Kou and coauthor [39,40], and the log-uniform and log-double-uniform distributions used by Hanson and coauthors [26,27,58,59,56]. Since it is difficult to determine what the market jump-amplitude distribution is, the double-uniform distribution is the simplest distribution that clearly satisfies the critical fat-tail property and allows separation of crash and rally behaviors by the double composite property.…”

Section: Optimal Portfolio Problem and Underlying Svjd Modelmentioning

confidence: 99%

“…The appeal of the log-uniform jump model is that it is consistent with the stock exchange introduction of circuit breakers [3] in 1988 to limit extreme changes, such as occurred in the crash of 1987, in stages. On the contrary, the normal [47,2,24] and double-exponential jump [39,40] models have an infinite domain, which is not a problem for the diffusion part of the jump-diffusion distribution since the contribution in the dynamic programming formulation is local appearing only in partial derivatives. However, the influence of the jump part in dynamic programming is global through integrals with integrands that have shifted arguments.…”

Section: Introductionmentioning

confidence: 99%

Optimal Portfolio Problem for Stochastic-Volatility, Jump-Diffusion Models with Jump-Bankruptcy Condition: Practical Theory

Hanson

2008

SSRN Journal

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This paper treats the risk-averse optimal portfolio problem with consumption in continuous time with a stochastic-volatility, jump-diffusion (SVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SVJD model with double-uniform jumpamplitude distributions and time-varying market parameters for the optimal portfolio problem. Although unlimited borrowing and short-selling play an important role in pure diffusion models, it is shown that borrowing and short selling are constrained for jump-diffusions. Finite range jump-amplitude models can allow constraints to be very large in contrast to infinite range models which severely restrict the optimal instantaneous stock-fraction to [0,1]. The reasonable constraints in the optimal stock-fraction due to jumps in the wealth argument for stochastic dynamic programming jump integrals remove a singularity in the stock-fraction due to vanishing volatility. Main modifications for the usual constant relative risk aversion (CRRA) power utility model are for handling the partial integro-differential equation (PIDE) resulting from the additional variance independent variable, instead of the ordinary integro-differential equation (OIDE) found for the pure jump-diffusion model of the wealth process. In addition to natural constraints due to jumps when enforcing the positivity of wealth condition, other constraints are considered for all practical purposes under finite market conditions. Also, a computationally practical solution of Heston's (1993) square-root-diffusion model for the underlying asset variance is derived. This shows that the nonnegativity of the variance is preserved through the proper singular limit of a simple perfect-square form. An exact, nonsingular solution is found for a special combination of the Heston stochastic volatility parameters.

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“…Some other optimal stopping problems in such a model were solved, for example, in [9], [16]- [17], [13]- [14], [3]- [4] and [7]. The key point in solving optimal stopping problems for jump processes established in [18]- [19] is that the smooth fit at the optimal boundary may break down and then be replaced by the continuous fit (see also [2] for necessary and sufficient conditions for the occurrence of smooth-fit condition and references to the related literature, and [20] for an extensive overview).…”

Section: Introductionmentioning

confidence: 99%

The integral option in a model with jumps

Gapeev

2008

Statistics & Probability Letters

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To cite this version:Pavel V. Gapeev. The integral option in a model with jumps. Statistics and Probability Letters, Elsevier, 2009, 78 (16) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTThe integral option in a model with jumps Pavel V. Gapeev * Dedicated to the memory of Heiner ZieschangWe present a closed form solution to the considered in [15] optimal stopping problem for the case of geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The result can be interpreted as pricing perpetual integral options in a model with jumps.

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Option Pricing Under a Double Exponential Jump Diffusion Model

Cited by 516 publications

References 49 publications

Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions

Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions

Optimal Portfolio Problem for Stochastic-Volatility, Jump-Diffusion Models with Jump-Bankruptcy Condition: Practical Theory

The integral option in a model with jumps

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