An alternative approach to the valuation of American options and applications

Kim, In Joon; Yu, G. George

doi:10.1007/bf01536395

Cited by 30 publications

(34 citation statements)

References 16 publications

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“…See [51] and [53] for numerical methods which try to solve the functional equation (8) iteratively. The representation in the equation (7) and the functional equation (8) are applied in a number of ways in the literature: Huang, Subrahmanyam, and Yu [38] have employed step functions, and Ju [48] a piecewise exponential function to approximate the early exercise boundary and used the equations to study pricing and hedging of American options.…”

Section: R(t −T) (Rk −δS(t −T))χ {S(t −T)mentioning

confidence: 99%

“…In our opinion the following have been prominent ideas: early attempts to obtain approximate prices [58,9], the integral representation of the early exercise premium [51,53,19], the analytic method of lines and its associated randomization method [17], and a homotopy method [80], analytic approximations of the early exercise boundary [20], and Monte Calro methods for American options. We discuss these key ideas and identify problems that need to be answered for further development of their methods.…”

Section: Introductionmentioning

confidence: 99%

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A Survey on American Options: Old Approaches and New Trends

Ahn¹,

Bae²,

Koo³

et al. 2011

Bulletin of the Korean Mathematical Society

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Abstract. This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

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Section: R(t −T) (Rk −δS(t −T))χ {S(t −T)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Survey on American Options: Old Approaches and New Trends

Ahn¹,

Bae²,

Koo³

et al. 2011

Bulletin of the Korean Mathematical Society

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“…As noted by Nelson and Ramaswamy ((1990), p. 418), the simple binomial processes approximation proposed by these authors becomes inaccurate as option maturity is increased. Alternatively, and as shown in Section VI, the integral approach suggested by Kim and Yu ((1996), sect. 3.4) and Detemple and Tian ((2002), prop. 3) is less efficient than the proposed pricing methodology, unless the recursive scheme is accelerated through Richardson extrapolation, in which case its accuracy may deteriorate for medium-and long-term options.…”

Section: Introductionmentioning

confidence: 97%

“…The proposed characterization possesses at least three advantages over the extended integral representation of Kim and Yu ((1996), eqs. 10 or 13): i) it converges to the perpetual American option price as the option maturity tends to infinity; ii) its accuracy does not deteriorate as the option maturity is lengthened; and iii) it can be adapted easily to the context of defaultable stock option pricing models.…”

Section: Introductionmentioning

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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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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“…As argued in Nunes (2009Nunes ( , page 1250, the optimal stopping approach offers a better speedaccuracy trade-off than the pricing methodology of Detemple and Tian (2002)-which is based on the (very time consuming) full recursive method of Huang et al (1996)-and the accelerated recursive scheme of Kim and Yu (1996), for valuing option contracts under the CEV assumption. Therefore, the accuracy and efficiency of the SHP approach for valuing American-style options under the CEV model will be compared against the option pricing framework proposed by Nunes (2009).…”

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confidence: 99%