The most basic and important object for any company trading energy commodities is a so-called Price Forward Curve, or PFC, providing prices in a fine granularity for a future period of time. Clearly, the PFC must be free of arbitrage with respect to the relevant set of forward prices at all...

In an arbitrage-free economy with non-zero bid-ask spreads the existence of payoffs whose price is lower than the price of a dominated payoff cannot be discarded in general. However, when the former price corresponds to trivial portfolios which involve buying or selling one unit of the basis...

We explain the valuation and correlation hedging of Foreign Exchange Basket Options in a multi-dimensional Black-Scholes model that allows including the smile. The technique presented is a fast analytic approximation to an accurate solution of the valuation problem.

In Monte Carlo simulation, Latin hypercube sampling (LHS) [McKay et al. (1979)] is a well-known variance reduction technique for vectors of independent random variables. The method presented here, Latin hypercube sampling with dependence (LHSD), extends LHS to vectors of dependent random...

This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining...

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation...

We model the dynamics of asset prices and associated derivatives by considerationof the dynamics of the conditional probability density process for the value of an assetat some specied time in the future. In the case where the asset is driven by Brownianmotion, an associated \master equation"...

In the existing literature on barrier options, much effort has been exerted to ensureconvergence through placing the barrier in close proximity to, or directly onto, thenodes of the tree lattice. In this paper we show that this may not be necessary toachieve accurate option price...

In this paper we consider the optimal stopping problem for general dynamic monetary utility functionals. Sufficient conditions for the Bellman principle and the existence of optimal stopping times are provided. Particular attention is payed to representations which allow for a numerical...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...