A Black-Scholes type model for American options will be considered where the underlying asset price experiences Brownian motion with random jumps. The mathematical problem is an obstacle problem forâ€¦ (More)

It is well known that early exercise of an American put may not be optimal for some time before the asset goes ex dividend. This in turn implies that the early exercise boundary is not as smooth asâ€¦ (More)

This paper considers the problem of numerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Hestonâ€¦ (More)

The influence of the analytical properties of the Black-Scholes PDE formulation for American and Asian options on the quality of the numerical solution is discussed. It appears that numerical methodsâ€¦ (More)

transforms review applies almost exclusively to sections on numerical transforms. Chapter 2 deals with polynomial approximation using Chebyshev, discrete Fourier, Lagrange, and Faber polynomials.â€¦ (More)

Extensive calculations are performed routinely by financial institutions to price options and to hedge portfolios. Invariably, these computations involve the solution of the Black Scholes partialâ€¦ (More)

The valuation of American Options can often be reduced to the study of a free boundary value problem for a partial differential equation. This paper will discuss how the Method of Lines (MOL) can beâ€¦ (More)

A Black-Scholes type model for American options will be considered where the underlying asset price experiences Brownian motion with random jumps. The mathematical problems is an obstacle problem forâ€¦ (More)