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American Options (american + option)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	87%

Selected Abstracts

CRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODEL

MATHEMATICAL FINANCE, Issue 3 2005
Etienne ChevalierArticle first published online: 10 JUN 200
We consider an American put option on a dividend-paying stock whose volatility is a function of the stock value. Near the maturity of this option, an expansion of the critical stock price is given. If the stock dividend rate is greater than the market interest rate, the payoff function is smooth near the limit of the critical price. We deduce an expansion of the critical price near maturity from an expansion of the value function of an optimal stopping problem. It turns out that the behavior of the critical price is parabolic. In the other case, we are in a less regular situation and an extra logarithmic factor appears. To prove this result, we show that the American and European critical prices have the same first-order behavior near maturity. Finally, in order to get an expansion of the European critical price, we use a parity formula for exchanging the strike price and the spot price in the value functions of European puts. [source]

PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHOD

MATHEMATICAL FINANCE, Issue 1 2010
Jin E. Zhang
This paper studies the critical stock price of American options with continuous dividend yield. We solve the integral equation and derive a new analytical formula in a series form for the critical stock price. American options can be priced and hedged analytically with the help of our critical-stock-price formula. Numerical tests show that our formula gives very accurate prices. With the error well controlled, our formula is now ready for traders to use in pricing and hedging the S&P 100 index options and for the Chicago Board Options Exchange to use in computing the VXO volatility index. [source]

Analytical Valuation of American Options on Jump-Diffusion Processes

MATHEMATICAL FINANCE, Issue 1 2001
Chandrasekhar Reddy Gukhal
We derive analytic formulas for the value of American options when the underlying asset follows a jump-diffusion process and pays continuous dividends. They early exercise premium has a form very different form from that for diffusion processes, and this can be attributed to the discontinuous nature of the price paths. Analytical formulas are derived for several distributions of the jump amplitude. [source]

Randomized Stopping Times and American Option Pricing with Transaction Costs

MATHEMATICAL FINANCE, Issue 1 2001
Prasad Chalasani
In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surprising feature of our upper hedging price representation is that it requires the use of randomized stopping times (Baxter and Chacon 1977), just as ordinary stopping times are needed in the absence of transaction costs. We also represent the upper hedging price as the optimum value of a variety of optimization problems. Additionally, we show a two-player game where at Nash equilibrium the value to both players is the upper hedging price, and one of the players must in general choose a mixture of stopping times. We derive similar representations for the lower hedging price as well. Our results make use of strong duality in linear programming. [source]

Richardson extrapolation techniques for the pricing of American-style options

THE JOURNAL OF FUTURES MARKETS, Issue 8 2007
Chuang-Chang Chang
In this article, the authors reexamine the American-style option pricing formula of R. Geske and H.E. Johnson (1984), and extend the analysis by deriving a modified formula that can overcome the possibility of nonuniform convergence (which is likely to occur for nonstandard American options whose exercise boundary is discontinuous) encountered in the original Geske,Johnson methodology. Furthermore, they propose a numerical method, the Repeated-Richardson extrapolation, which allows the estimation of the interval of true option values and the determination of the number of options needed for an approximation to achieve a given desired accuracy. Using simulation results, our modified Geske,Johnson formula is shown to be more accurate than the original Geske,Johnson formula for pricing American options, especially for nonstandard American options. This study also illustrates that the Repeated-Richardson extrapolation approach can estimate the interval of true American option values extremely well. Finally, the authors investigate the possibility of combining the binomial Black,Scholes method proposed by M. Broadie and J.B. Detemple (1996) with the Repeated-Richardson extrapolation technique. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:791,817, 2007 [source]

Knock-in American options

THE JOURNAL OF FUTURES MARKETS, Issue 2 2004
Min Dai
A knock-in American option under a trigger clause is an option contract in which the option holder receives an American option conditional on the underlying stock price breaching a certain trigger level (also called barrier level). We present analytic valuation formulas for knock-in American options under the Black-Scholes pricing framework. The price formulas possess different analytic representations, depending on the relation between the trigger stock price level and the critical stock price of the underlying American option. We also performed numerical valuation of several knock-in American options to illustrate the efficacy of the price formulas. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:179,192, 2004 [source]

Regularity of the free boundary of an American option on several assets,

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2009
Peter Laurence
We establish the C, regularity of the free boundary for an American option on several assets in the case where the payoff is convex and the assets follow correlated geometric Brownian motions. Our work builds on results concerning the qualitative properties and initial regularity of the free boundary by Broadie and Detemple; Jaillet, Lamberton, and Lapeyre; and Villeneuve. © 2008 Wiley Periodicals, Inc. [source]

The effects of taxation on put-call parity

ACCOUNTING & FINANCE, Issue 3 2009
Karen Alpert
G13 Abstract Share and option transactions are taxed differently, which means that the after-tax cash flows used to establish put-call parity will differ depending on which option is exercised. This paper derives the after-tax put-call parity relationship for European and American options with or without dividends. Using Australian data for the period July 1999 to June 2002, the after-tax put-call parity relationship explains 88.3 per cent of no-tax lower boundary violations and 78.8 per cent of no-tax upper boundary violations. The violation are larger for more thinly traded securities, providing some evidence that traders are able to profit from the tax discontinuities that affect investors in options. [source]

PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHOD

CALLABLE PUTS AS COMPOSITE EXOTIC OPTIONS

MATHEMATICAL FINANCE, Issue 4 2007
Christoph Kühn
Introduced by Kifer (2000), game options function in the same way as American options with the added feature that the writer may also choose to exercise, at which time they must pay out the intrinsic option value of that moment plus a penalty. In Kyprianou (2004) an explicit formula was obtained for the value function of the perpetual put option of this type. Crucial to the calculations which lead to the aforementioned formula was the perpetual nature of the option. In this paper we address how to characterize the value function of the finite expiry version of this option via mixtures of other exotic options by using mainly martingale arguments. [source]

A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS

MATHEMATICAL FINANCE, Issue 4 2006
Ross A. Maller
This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity. [source]

First-Order Schemes in the Numerical Quantization Method

MATHEMATICAL FINANCE, Issue 1 2003
V. Bally
The numerical quantization method is a grid method that relies on the approximation of the solution to a nonlinear problem by piecewise constant functions. Its purpose is to compute a large number of conditional expectations along the path of the associated diffusion process. We give here an improvement of this method by describing a first-order scheme based on piecewise linear approximations. Main ingredients are correction terms in the transition probability weights. We emphasize the fact that in the case of optimal quantization, many of these correcting terms vanish. We think that this is a strong argument to use it. The problem of pricing and hedging American options is investigated and a priori estimates of the errors are proposed. [source]

American options on assets with dividends near expiry

MATHEMATICAL FINANCE, Issue 3 2002
J. D. Evans
Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate D to the interest rate r. For D>r the put boundary near expiry tends parabolically to the value rK/D where K is the strike price, while for D,r the boundary tends to K in the parabolic-logarithmic form found for the case D=0 by Barles et al. (1995) and by Kuske and Keller (1998). For the call, these two behaviors are interchanged: parabolic and tending to rK/D for D[source]

Analytical Valuation of American Options on Jump-Diffusion Processes

Numerical valuation of options under Kou's model

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Jari ToivanenArticle first published online: 6 AUG 200
Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a linear complementarity problem (LCP) with the same operator. Spatial differential operators are discretized using finite differences on nonuniform grids and time stepping is performed using the implicit Rannacher scheme. For the evaluation of the integral term easy to implement recursion formulas are derived which have optimal computational cost. When pricing European options the resulting dense linear systems are solved using a stationary iteration. Also for pricing American options similar iterations can be employed. A numerical experiment demonstrates that the described method is very efficient as accurate option prices can be computed in a few milliseconds on a PC. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Pricing American options by canonical least-squares Monte Carlo

THE JOURNAL OF FUTURES MARKETS, Issue 2 2010
Qiang Liu
Options pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. This study proposes an approach called canonical least-squares Monte Carlo (CLM) to price American options. CLM proceeds in three stages. First, given a set of historical gross returns (or price ratios) of the underlying asset for a chosen time interval, a discrete risk-neutral distribution is obtained via the canonical approach. Second, from this canonical distribution independent random samples of gross returns are taken to simulate future price paths for the underlying. Third, to those paths the least-squares Monte Carlo algorithm is then applied to obtain early exercise strategies for American options. Numerical results from simulation-generated gross returns under geometric Brownian motions show that the proposed method yields reasonably accurate prices for American puts. The CLM method turns out to be quite similar to the nonparametric approach of Alcock and Carmichael and simulations done with CLM provide additional support for their recent findings. CLM can therefore be viewed as an alternative for pricing American options, and perhaps could even be utilized in cases when the nature of the underlying process is not known. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:175,187, 2010 [source]

Pricing American options on foreign currency with stochastic volatility, jumps, and stochastic interest rates

THE JOURNAL OF FUTURES MARKETS, Issue 9 2007
Jia-Hau Guo
By applying the Heath,Jarrow,Morton (HJM) framework, an analytical approximation for pricing American options on foreign currency under stochastic volatility and double jump is derived. This approximation is also applied to other existing models for the purpose of comparison. There is evidence that such types of jumps can have a critical impact on earlyexercise premiums that will be significant for deep out-of-the-money options with short maturities. Moreover, the importance of the term structure of interest rates to early-exercise premiums is demonstrated as is the sensitivity of these premiums to correlation-related parameters. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:867,891, 2007 [source]