Journal ArticleDOI
Laplace transforms and installment options
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In this article, an integral equation is derived for the position of the free boundary by applying a partial Laplace transform to the underlying partial differential equation for the value of the security.Abstract:
An installment option is a derivative financial security where the price is paid in installments instead of as a lump sum at the time of purchase. The valuation of these options involves a free boundary problem in that at each installment date, the holder of the derivative has the option of continuing to pay the premiums or allowing the contract to lapse, and the decision will depend upon whether the present value of the expected pay-off is greater or less than the present value of the remaining premiums. Using a model installment option where the premiums are paid continuously rather than on discrete dates, an integral equation is derived for the position of this free boundary by applying a partial Laplace transform to the underlying partial differential equation for the value of the security. Asymptotic analysis of this integral equation allows us to deduce the behavior of the free boundary close to expiry.read more
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Analytical and Numerical Methods for Pricing Financial Derivatives
TL;DR: In this paper, the role of protecting financial portfolios and protecting financial portfolio is discussed in the context of option pricing under transaction costs, as well as the dependence of option prices on model parameters.
Journal ArticleDOI
Valuation of American Continuous-Installment Options
Pierangelo Ciurlia,Ilir Roko +1 more
TL;DR: In this paper, the authors presented three approaches to value American continuous-installment options written on assets without dividends or with continuous dividend yield, and derived closed-form formulas by approximating the optimal stopping and exercise boundaries as multipiece exponential functions, which is compared to the finite difference method to solve the inhomogeneous Black-Scholes PDE and a Monte Carlo approach.
Journal ArticleDOI
Comparison of Numerical and Analytical Approximations of the Early Exercise Boundary of the American Put Option
Martin Lauko,Daniel Sevcovic +1 more
TL;DR: In this paper, the authors present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends.
Journal ArticleDOI
Valuing continuous-installment options
TL;DR: Valuing European continuous-installment options written on dividend-paying assets in the standard Black-Scholes-Merton framework using the Laplace transform approach, which results in explicit Laplace transforms of the initial premium as well as its Greeks, which include the transformed stopping boundary in a closed form.
Journal ArticleDOI
Transformation Methods for Evaluating Approximations to the Optimal Exercise Boundary for Linear and Nonlinear Black-Scholes Equations
TL;DR: In this paper, the authors present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options, which can be modelled by class of generalized Black-Scholes equations.
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.
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The valuation of compound options
TL;DR: In this article, the authors present a theory for pricing options on options, or compound options, which can be generalized to value many corporate liabilities, and derive a new model for puts and calls corrects some important biases of the Black-Scholes model.
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Time to build, option value, and investment decisions
Saman Majd,Robert S. Pindyck +1 more
TL;DR: In this article, the authors use contingent claims analysis to derive optimal decision rules and to value such investments, and determine the effects of time to build, opportunity cost and uncertainty on the investment decision.
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On optimal stopping and free boundary problems
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Critical stock price near expiration
TL;DR: In this paper, the critical price of an American put option near expiration in the Black-Scholes model was studied and the main result was an estimate for the difference P (t)-K between the critical prices at time t and the exercise price as t approaches the maturity of the option.