We develop a new approach to valuing and hedging basket options. We consider baskets of assets with potentially negative portfolio weights (spread options are a subclass of such basket options). The basket distribution is approximated using a generalized family of log-normal distributions. This...

This paper considers the problem of pricing American options when the dynamics of the underlying are driven both by stochastic volatility following a square root process as used by Heston (1993) and by a Poisson jump process as introduced by Merton (1976). The two-factor homogeneous...

In this paper, we evaluate anytime Bermudan options, a class of path-dependent American options, by Monte Carlo simulation. Assuming that the state variable is Markovian, we show that the price of the path-dependent American option satisfies a dynamic programming equation. The continuation value...

This paper applies a dynamic programming methodology to the valuation problem for the flexibility to switch. In our model, flexibility provides an investor with the right, or option, to perform a switch between a less profitable and a more profitable project at no cost. In contrast to previous...

Many derivatives prices and their Greeks are closed-form expressions in the Black-Scholes model; when the terminal distribution is a mixed lognormal, prices and Greeks for these derivatives are then a weighted average of these closed-form) expressions. They can therefore be calculated easily and...

This paper presents an efficient methodology for the discrete Asian options consistent with different types of underlying densities, especially non-normal returns as suggested by the empirical literature (Mandelbrot (1963) and Fama (1964)). The interest of this method is its flexibility compared...

Applied cryptography and network security could bring a new commerce architecture for valuable but uncertain digital objects in an open network. This paper models the digital objects as security token, which is abbreviated into a word coinage setok. Each setok has its price, values, and...

We consider American versions of multiple asset options when the underlying assets follow jump-diffusion processes, for example exchange options and max-options. We consider various representations of the option value and in particular apply Fourier transform techniques to the integro-partial...