We explicitly solve the pricing problem for perpetual American puts and calls, and provide an efficient semi-explicit pricing procedure for options with finite time horizon. Contrary to the standard approach, which uses the price process as a primitive, we model the price process as the expected...

As is well known, the classic Black­Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non­normal return innovations. Second,...

We analyze the specifications of option pricing models based on time- changed Levy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process...

Montecarlo methods can be used to price derivatives for which closed evaluation formulas are not available or difficult to derive. A drawback of the method can be its high computational cost, especially if applied to basket options, whose payoffs depend on more than one asset. This article...

We propose an approximate static hedging procedure for multivariate derivatives. The hedging portfolio is composed of statically held simple univariate options, optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio. The...

This paper extends a recent martingale representation result of [N-S] for a Levy process to filtrations generated by a rather large class of semimartingales. As in [N-S], we assume the underlying processes have moments of all orders, but here we allow angle brackets to be stochastic. Following...

A simple transform of a standard uniform variate is given for simulation of the maximum attained by a Wiener process with drift, conditioned upon the level attained by the process over an arbitrary time interval. The transform arises directly from inversion of the joint distribution function of...

By analyzing fictitious options - a unique approach - significant mispricing due to the formula of Black and Scholes can be shown systematically and independent from market distortion. Even options based on fictitious, lognormally distributed courses are not valued properly. According to the Law...

In this paper, a class of regular quadratic Gaussian processes is defined to characterize quadratic term structure models (QTSMs) in a general Markovian setting. The primary motivation for this definition is to provide a more general model for the quadratic term structure of the forward curve,...

This note proposes a method for pricing high-dimensional American options based on modern methods of multidimensional interpolation. The method allows using sparse grids and thus mitigates the curse of dimensionality. A framework of the pricing algorithm and the corresponding interpolation...