In this paper we present a new model for pricing and hedging a portfolio of derivatives that takes into account the effect of an extreme movement in the underlying. We make no assumptions about the timing of this 'crash' or the probability distribution of its size, except that we put an upper...

Jump diffusion models have two weaknesses: they don't allow you to hedge and the parameters are very hard to measure. Nobody likes a model that tells you that hedging is impossible (even though that may correspond to common sense) and in the classical jump-diffusion model of Merton the best that...

This paper proves that the optimal exercise time for the holder of an American option depends upon the physical drift of the underlying asset and the utility of the option holder. We illustrate our results by applying them to several families of utility functions, namely the CARA, the HARA, and...

We explain the ideas behind the valuation of options with early exercise features, so called American options. We also aim to clarify some popular misconceptions about when an American option should be exercised. These misconceptions seem to be prevalent among both academics and practitioners.

We show how to use 'uncertainty' in place of the more traditional Brownian 'randomness' to model a short-term interest rate. The advantage of this model is principally that it is difficult to show statistically that it is wrong. Whether the model is useful for pricing fixed-income products is...

Two of the authors (DE and PW) recently introduced a non-probabilistic spot interest rate model. The key concepts in this model are the non-diffusive nature of the spot rate process and the uncertainty in the parameters. The model assumes the worst possible outcome for the spot rate path when...

The modelling of credit risk, credit derivatives and non-hedgeable securities in general is currently in a poor state. Ideas from equity options theory have been adopted for credit risk, but have not been adapted for the peculiarities of this more complex world. This brief paper is a review and...

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the writer is liable for the loss. Multi-asset passport options and passport options with discrete constraints are studied. For the first ones the pricing equations...