Journal ArticleDOI
Approximations for the values of american options
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In this paper, the free boundary is determined by an algebraic relation and an approximate solution derived, and a suitable modification of the approximate solution gives the exact solution, which implies the expression determined by the algebraic relations is the true critical price, at which the option should be exercised.Abstract:
The solution of the American option valuation problem is the solution of a parabolic partial differential equation satisfying free boundary conditions. The free boundary represents the critical price, at which the option should be exercised. In this paper the free boundary is determined by an algebraic relation and an approximate solution derived. A suitable modification of the approximate solution gives the exact solution. The uniqueness of the free boundary implies the expression determined by the algebraic relation is the true critical priceread more
Citations
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Journal ArticleDOI
Numerical Valuation of High Dimensional Multivariate American Securities
TL;DR: This work presents an efficient numerical technique that combines Monte Carlo simulation with a particular partitioning method of the underlying assets space, which is called Stratified State Aggregation (SSA), which can compute accurate approximations of prices of American securities with an arbitrary number of underlying assets.
Book ChapterDOI
Mathematics of Financial Markets
TL;DR: In this paper, the authors describe how the confluence of mathematical ideas, economic theory and computer technology proved so effective, and indicate how the theory relates to the practice of financial engineering.
Journal ArticleDOI
Optimal exercise boundary for an American put option
Rachel Kuske,Joseph B. Keller +1 more
TL;DR: In this article, the optimal exercise boundary near the expiration time for an American put option is determined by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation.
Journal ArticleDOI
A mathematical analysis of the optimal exercise boundary for american put options
Xinfu Chen,John Chadam +1 more
TL;DR: This work derive and rigorously prove high order asymptotic expansions for the early exercise boundary near expiry, and provides an ode iterative scheme which can reach its numerical fixed point in five iterations for all time to expiry.
Journal ArticleDOI
Compact finite difference method for American option pricing
TL;DR: In this article, the authors developed three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary, which can be cast as a partial differential equation.
References
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Journal ArticleDOI
The Pricing of Options and Corporate Liabilities
Fischer Black,Myron S. Scholes +1 more
TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Journal ArticleDOI
Martingales and stochastic integrals in the theory of continuous trading
TL;DR: In this paper, a general stochastic model of a frictionless security market with continuous trading is developed, where the vector price process is given by a semimartingale of a certain class, and the general Stochastic integral is used to represent capital gains.
Journal ArticleDOI
Efficient Analytic Approximation of American Option Values
TL;DR: In this article, the authors provide simple, analytic approximations for pricing exchange-traded American call and put options written on commodities and commodity futures contracts, which are accurate and considerably more computationally efficient than finite-difference, binomial, or compound-option pricing methods.