We study the short time behavior of the early exercise boundary for American style put options in the Black–Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integ...

Recently a reparametrized version of HJM model has been proposed which leads naturally to the innnite dimensional Markov process of forward curves. In this paper we discuss some consequences of the Markovian structure of forward rate dynamics. In particular, we obtain price of the swaption as a solution to the innnite dimensional "Black-Scholes" partial diierential equation.

We introduce a new class of strategies for hedging derivative securities in the presence of transaction costs assuming lognormal continuous time prices for the underlying asset We do not assume necessarily that the payo is convex as in Leland or that transaction costs are small compared to the price changes between portfolio adjustments as in Hoggard Whalley and Wilmott The type of hedging stra...

In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying the one-dimensional solvable processes with the class of integrable superpotentials introduced recently in supersymmetric quantum mechanics, we obtain new anal...

Abstract Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work appropriate for capturing market fluctuations which random white noise has the potential to accurately estimate put option premiums while providing good numerical convergence. aim of pape...

A technique is proposed for the construction of Green’s functions for terminal-boundary value problems of the Black-Scholes equation. The technique permits an application to a variety of problems that vary by boundary conditions imposed. This is possible by extension of an approach that was earlier developed for partial differential equations in applied mechanics. The technique is based on the ...