For a Markov process $x_t$, the forward measure $P^T$ over the time interval $[0,T]$ is defined by the Radon-Nikodym derivative $dP^T/dP = M\exp(-\int_0^Tc(x_s)ds)$, where $c$ is a given non-negative function and $M$ is the normalizing constant. In this paper, the law of $x_t$ under the forward...

An investor faced with a contingent claim may eliminate risk by (super-) hedging in a financial market. As this is often quite expensive, we study partial hedges which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal...

In a complete financial market every contingent claim can be hedged perfectly. In an incomplete market it is possible to stay on the safe side by superhedging. But such strategies may require a large amount of initial capital. Here we study the question what an investor can do who is unwilling...

We consider the problem of pricing European forward starting options in the presence of stochastic volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution within Heston’s stochastic volatility...

We extend the short rate model of Vasicek (1977) to include jumps in the local mean. Conditions ensuring existence of a unique equivalent martingale measure are given, implying that the model is arbitrage-free and complete. We develop efficient numerical methods for computation of zero coupon...

Standard derivative pricing theory is based on the assumption of agents acting as price takers on the market for the underlying asset. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative security. Our analysis extends...

A passport option, as introduced and marketed by Bankers Trust, is a call option on the balance of a trading account. The strategy that this account follows is chosen by the option holder, subject to position limits. <p>We derive a simplified form for the price of the passport option using local...</p>

The paper shows that in the presence of transaction costs, there exists a viable price system in which prices of call options are arbitrarily close to the price of the stock. The construction of such an example is possible no matter how small the volatility of the stock or how small the...

This paper discusses a new approach to contingent claim valuation in general incomplete market models. We determine the neutral derivative price which occurs if investors maximize their local utility and if derivative demand and supply are balanced. We also introduce the sensitivity process of a...

We analyze the joint convergence of sequences of discounted stock prices and Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We illustrate the general...