Evaluations of barrier-crossing probabilities of Wiener paths

Park, C.; Schuurmann, F. J.

doi:10.1017/s002190020009433x

Cited by 27 publications

(50 citation statements)

References 6 publications

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“…Equation (37) is consistent with Park and Schuurmann ((1976), thm. 1) and similar to the integral equation used by Longstaff and Schwartz ((1995), eq.…”

Section: The First Passage Time Densitysupporting

confidence: 65%

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Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

Nunes¹

2009

J. Financ. Quant. Anal.

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This paper proposes an alternative characterization of the early exercise premium that is valid for any Markovian and diffusion underlying price process as well as for any parameterization of the exercise boundary. This new representation is shown to provide the best pricing alternative available in the literature for medium-and long-term American option contracts, under the constant elasticity of variance model. Moreover, the proposed pricing methodology is also extended easily to the valuation of American options on defaultable equity and possesses appropriate asymptotic properties.

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“…Equation (37) is consistent with Park and Schuurmann ((1976), thm. 1) and similar to the integral equation used by Longstaff and Schwartz ((1995), eq.…”

Section: The First Passage Time Densitysupporting

confidence: 65%

“…Following Kuan and Webber (2003), the next proposition shows that such first passage time density can be efficiently computed, for any exercise boundary specification, through the standard partition method proposed by Park and Schuurmann (1976).…”

Section: The First Passage Time Densitymentioning

confidence: 99%

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

Nunes¹

2009

J. Financ. Quant. Anal.

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“…Following (Park and Schuurmann 1976, Theorem 2), next proposition recovers the two optimal hitting time densities involved in Eqs. 68 and 69 as the implicit solutions of two simultaneous integral equations.…”

Section: A More General Setupmentioning

confidence: 81%

“…49 through the standard partition method proposed by Park and Schuurmann (1976). Corollary 1, together with Proposition 3, constitutes the quasi-analytical pricing solution proposed for the American put under a general Gauss-Markov and multifactor HJM framework.…”

Section: Proposition 3 For the Pricing Model Described In Definition mentioning

confidence: 93%

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

Nunes

2010

Rev Deriv Res

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“…Durbin developed a technique in (Durbin, 1971) for computing boundarycrossing probabilities for the Brownian motion and Poisson processes. C. Park and F. J. Schuurmann have refined and augmented that technique (Park & Schuurmann, 1976). We will now demonstrate how their method can be applied to our problems.…”

Section: Ornstein-uhienbeck Distributionsmentioning

confidence: 99%

Refined distributions for a multi-risk stochastic process

Beekman

Fuelling

1977

Scandinavian Actuarial Journal

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This paper considers a collective risk model formed linearly from four stochastic processes. The first process involves random sums of random variables, and portrays the insurance claims. The other three processes are Ornstein-Uhlenbeck processes which serve as models for the random deviations in assumptions about investment performance, operating expenses, and lapse expenses. The model presented earlier (Beekman 1975b(Beekman , 1976 is improved by using both calendar and operational times. Ornstein-Uhlenbeck distributions for finite time periods are derived, and tables are furnished. Probabilities of extreme deviations for the multi-risk process are discussed. The examples in (Beekman 1975b(Beekman , 1976 are reconsidered, and made more realistic by an improved treatment of the time variables.

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Evaluations of barrier-crossing probabilities of Wiener paths

Abstract: Let {W(t), 0 ≦ t < ∞} be the standard Wiener process. The main purpose of this paper is to present ways of obtaining probabilities of Wiener paths crossing certain curves on various intervals. The results are extended to other kinds of Gaussian processes.

Cited by 27 publications

References 6 publications

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

Refined distributions for a multi-risk stochastic process

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Evaluations of barrier-crossing probabilities of Wiener paths

Abstract: Let {W(t), 0 ≦ t &lt; ∞} be the standard Wiener process. The main purpose of this paper is to present ways of obtaining probabilities of Wiener paths crossing certain curves on various intervals. The results are extended to other kinds of Gaussian processes.

Cited by 27 publications

References 6 publications

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

Refined distributions for a multi-risk stochastic process

Contact Info

Product

Resources

About

Abstract: Let {W(t), 0 ≦ t < ∞} be the standard Wiener process. The main purpose of this paper is to present ways of obtaining probabilities of Wiener paths crossing certain curves on various intervals. The results are extended to other kinds of Gaussian processes.