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Pricing American options: A comparison of Monte Carlo simulation approaches
 Journal of Computational Finance
, 1999
"... A number of Monte Carlo simulationbased approaches have been proposed within the past decade to address the problem of pricing Americanstyle derivatives. The purpose of this paper is to empirically test some of these algorithms on a common set of problems in order to be able to assess the strength ..."
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Cited by 38 (7 self)
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A number of Monte Carlo simulationbased approaches have been proposed within the past decade to address the problem of pricing Americanstyle derivatives. The purpose of this paper is to empirically test some of these algorithms on a common set of problems in order to be able to assess the strengths and weaknesses of each approach as a function of the problem characteristics. In addition, we introduce another simulationbased approach that parameterizes the early exercise curve and casts the valuation problem as an optimization problem of maximizing the expected payoff (under the martingale measure) with respect to the associated parameters, the optimization problem carried out using a simultaneous perturbation stochastic approximation (SPSA) algorithm.
Free boundary and optimal stopping problems for American Asian options
 Finance and Stochastics
"... Abstract We give a complete and selfcontained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American pathdependent options. The framework is sufficiently general to include geometric Asian options with nonconstant volatility and recent p ..."
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Cited by 19 (9 self)
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Abstract We give a complete and selfcontained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American pathdependent options. The framework is sufficiently general to include geometric Asian options with nonconstant volatility and recent pathdependent volatility models.
Characterization of optimal stopping regions of American Asian and lookback options
 Mathematical Finance
, 2006
"... A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and ..."
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Cited by 12 (3 self)
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A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and time. From the ordering properties of the values of American lookback options and American Asian options, we deduce the corresponding nesting relations between the exercise regions of these American options. We illustrate how some properties of the exercise regions of the American Asian options can be inferred from those of the American lookback options.
Pricing AmericanStyle Derivatives with European Call Options
 Management Science
, 2006
"... doi 10.1287/mnsc.1050.0447 ..."
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What you should know about simulation and derivatives
 Naval Res. Logist
, 2008
"... Abstract: Derivatives (or gradients) are important for both sensitivity analysis and optimization, and in simulation models, these can often be estimated efficiently using various methods other than bruteforce finite differences. This article briefly summarizes the main approaches and discusses are ..."
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Cited by 8 (4 self)
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Abstract: Derivatives (or gradients) are important for both sensitivity analysis and optimization, and in simulation models, these can often be estimated efficiently using various methods other than bruteforce finite differences. This article briefly summarizes the main approaches and discusses areas in which the approaches can most fruitfully be applied: queueing, inventory, and finance.
A Numerical Procedure for Pricing Americanstyle Asian Options
, 2000
"... . Pricing Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no analytical solution is available. Pricing their Americanstyle counterparts, which provide early exercise opportunities, poses the add ..."
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Cited by 3 (0 self)
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. Pricing Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no analytical solution is available. Pricing their Americanstyle counterparts, which provide early exercise opportunities, poses the additional di#culty of solving a dynamic optimization problem to determine the optimal exercise strategy. We develop a numerical method for pricing Americanstyle Asian options based on dynamic programming combined with finiteelement piecewisepolynomial approximation of the value function. Numerical experiments show convergence, consistency, and e#ciency. Some theoretical properties of the value function and of the optimal exercise strategy are also established. (Option pricing, Asian Options, Pathdependent options, American Options, Dynamic Programming, Piecewise Polynomials) 1 1 Introduction A financial derivative is a contract which provides its holder a future payment that depends on...
Optimal Stock Selling/Buying Strategy with reference to the Ultimate Average*
, 2010
"... We are concerned with the optimal decision to sell or buy a stock in a given period with reference to the ultimate average of the stock price. More precisely, we aim to determine an optimal selling (buying) time to maximize (minimize) the expectation of the ratio of the selling (buying) price to the ..."
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Cited by 3 (1 self)
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We are concerned with the optimal decision to sell or buy a stock in a given period with reference to the ultimate average of the stock price. More precisely, we aim to determine an optimal selling (buying) time to maximize (minimize) the expectation of the ratio of the selling (buying) price to the ultimate average price over the period. This is an optimal stopping time problem which can be formulated as a variational inequality problem. The problem gives rise to a free boundary that corresponds to the optimal selling (buying) strategy. We provide a partial di®erential equation approach to characterize the free boundary (or equivalently, the optimal selling (buying) region). It turns out that the optimal selling strategy is bangbang, which is the same as that obtained by Shiryaev, Xu and Zhou (2008b) taking the ultimate maximum of the stock price as benchmark, whereas the optimal buying strategy can be a feedback one subject to the type of averaging and parameter values. Moreover, by a thorough characterization of free boundary, we reveal that the bangbang optimal selling strategy heavily depends on the assumption that no timevesting restrictions are imposed. If a timevested stock is considered, then the optimal selling strategy can also be a feedback one. In terms of a similar analysis developed by the present paper, the same phenomenon can be proved when
Efficient Sensitivity Analysis of Mortgage Backed Securities
"... Because of the complicated behavior of their cash flows, mortgagebacked securities (MBS) are almost always priced using Monte Carlo simulation. Sensitivity analysis is a critical component of these simulations. Risk managers need these numbers to hedge their exposure to interest risk and prepayment ..."
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Cited by 1 (0 self)
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Because of the complicated behavior of their cash flows, mortgagebacked securities (MBS) are almost always priced using Monte Carlo simulation. Sensitivity analysis is a critical component of these simulations. Risk managers need these numbers to hedge their exposure to interest risk and prepayment risk. In order to carry this out in a computationally efficient manner, we derive perturbation analysis (PA) gradient estimators in a general setting, without restrictions to any specific interest rate model or prepayment model. Then we apply the estimators to the HullWhite interest rate model and a common prepayment model to derive the corresponding specific PA gradient estimators, assuming the shock of interest rate term structure takes the form of a Fourierlike harmonic series. Numerical experiments comparing finite difference (FD) gradient estimators with our PA estimators indicate that the PA estimators can provide better accuracy than FD estimators while using much lower computational cost. In the test case of 5 duration and 25 convexity estimators, the computational time is reduced by 97.2%. Using the estimators, we analyze the impact of term structure shifts on various mortgage products. Based on insights gained from the analysis, we propose a new product that could potentially benefit mortgage borrowers and investors.
REAL OPTIONS VALUATION
"... Managerial flexibility has value. The ability of their managers to make smart decisions in the face of volatile market and technological conditions is essential for firms in any competitive industry. This advanced tutorial describes the use of Monte Carlo simulation and stochastic optimization for t ..."
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Managerial flexibility has value. The ability of their managers to make smart decisions in the face of volatile market and technological conditions is essential for firms in any competitive industry. This advanced tutorial describes the use of Monte Carlo simulation and stochastic optimization for the valuation of real options that arise from the abilities of managers to influence the cash flows of the projects under their control. Option pricing theory supplements discounted cash flow methods of valuation by considering managerial flexibility. Managers ’ options to take actions that affect real investment projects are comparable to options on the sale or purchase of financial assets. Just as a financial option derives much of its value from the potential price movements of the underlying financial asset, a real option derives much of its value from the potential fluctuations of the cash flows generating the value of the investment project. 1
Pricing America Options: A Comparison of Monte Carlo Simulation Approaches
 Journal of Computational Finance
, 2000
"... A number ofM onte Carlo simulationbased approaches have been proposed within the past decade to address the problem of pricing Americanstyle derivatives. The purpose of this paper is to empirically test some of these algorithms on a common set of problems in order to be able to assess the strength ..."
Abstract
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A number ofM onte Carlo simulationbased approaches have been proposed within the past decade to address the problem of pricing Americanstyle derivatives. The purpose of this paper is to empirically test some of these algorithms on a common set of problems in order to be able to assess the strengths and weaknesses of each approach as a function of the problem characteristics. In addition, we introduce another simulationbased approach that parameterizes the early exercise curve and casts the valuation problem as an optimization problem of maximizing the expected payo# (under the martingale measure) with respect to the associated parameters, the optimization problem carried out using a simultaneous perturbation stochastic approximation (SPSA) algorithm. Keywords: American options, M nte Carlo simulation, options pricing, stochastic approximation, early exercise. # This work was su1 orted in part by the NSFu27 Grant DMI9713720,and by theSemicondu49 Research Corporationsutio Grant 97F...