Pricing and Hedging American Options: A Recursive Integration Method

Huang, Jing-Zhi; Subrahmanyam, Marti G.; Yu, G. George

doi:10.1093/rfs/9.1.277

Cited by 244 publications

(114 citation statements)

References 27 publications

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“…Broadie and Detemple (1996) derive lower bounds for the critical stock price and use them to obtain bounds for the American call option price. Huang, Subrahmanyam and Yu (1996), Little, Pant and Hou (2000) and Sullivan (2000) study numerical schemes which solve the integral equation which implicitly defines the early exercise boundary.…”

Section: Numerical Approximations Of the Optimal Exercise Boundarymentioning

confidence: 99%

A two-step simulation procedure to analyze the exercise features of American options

Basso

Nardon

Pianca

2004

Decisions Econ Finan

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In this contribution we propose a two-step simulation procedure that enables to compute the exercise features of American options and analyze the properties of the optimal exercise times and exercise probabilities. The first step of the procedure is based on the calculation of an accurate approximation of the optimal exercise boundary. In particular, we use a smoothed binomial method which effectively reduces the fluctuating behavior of a discrete boundary. In the second step the boundary is used to define a stopping rule which is embodied in a Monte Carlo simulation method. A broad experimental analysis is carried out in order to test the procedure and study the behavior of the exercise features.

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Section: Numerical Approximations Of the Optimal Exercise Boundarymentioning

confidence: 99%

A two-step simulation procedure to analyze the exercise features of American options

Basso

Nardon

Pianca

2004

Decisions Econ Finan

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“…Huang et al (1996), Ju (1998), Detemple and Tian (2002) have studied the implementations of the EEP methods for pricing the American put options. However their approaches are based on low-order approximations.…”

Section: Introductionmentioning

confidence: 99%

High-Accuracy Integral Equation Approach for Pricing American Options with Stochastic Volatility

Ma¹,

Zhou²

2011

IJEF

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The paper concerns high-order collocation implementation of the integral equation approach for pricing American options with stochastic volatility. As shown in Detemple and Tian (2002) , the value of American options can be written as the sum of the corresponding European option price and the early exercise premium (EEP). This EEP representation results in a nonlinear Volterra integral equation for the optimal exercise boundary. There are no efficient and reliable numerical methods for solving the integral equations in the literature. The aim of this paper is to develop a high-order collocation method for solving the nonlinear integral equations. Collocation methods are widely studied in the area of numerical integral equations. After the exercise boundary is resolved, the value of the American options is obtained by evaluating the EEP representation.

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“…However, quite often a challenge for adopting a numerical approach is to prove the convergency of the scheme for the nonlinearity involved in pricing American options and many of the hitherto proposed methods still require intensive computation before a solution of reasonable accuracy can be obtained. In some cases, such as the explicit finite-difference scheme, the method may not even converge, as pointed out by Huang et al [13].…”

Section: Introductionmentioning

confidence: 99%

“…It is envisaged that this type of approaches will become more and more attractive for a recent trend of algorithmic trading, the core of which is high-speed computation for the value of a portfolio, which may consists of stocks and their options. Typical methods in this category include the compound-option approximation method [11], the quadratic approximation method [2,17], the interpolation method [14], the capped option approximation [6] and the integral-equation method [8,13,16].…”

Section: Introductionmentioning

confidence: 99%

A simple approximation formula for calculating the optimal exercise boundary of American puts

Zhu

2010

J. Appl. Math. Comput.

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In this paper, a simple algorithm to improve the computational accuracy of the analytical approximation for the value of American put options and their optimal exercise boundary proposed by Zhu (Int. J. Theor. Appl. Finance 9 (7): 2006) is presented. In the current approach, Zhu's simple approximation formula is used as an initial guess for the optimal exercise boundary of American put options. The determination of an improved optimal exercise boundary is then achieved by setting a null value of the Theta of option on the optimal exercise boundary. Numerical test results show that the improvement in accuracy is indeed significant in determining the optimal exercise boundary.

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Pricing and Hedging American Options: A Recursive Integration Method

Cited by 244 publications

References 27 publications

A two-step simulation procedure to analyze the exercise features of American options

A two-step simulation procedure to analyze the exercise features of American options

High-Accuracy Integral Equation Approach for Pricing American Options with Stochastic Volatility

A simple approximation formula for calculating the optimal exercise boundary of American puts

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