The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore...

This paper introduces a "dual" way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound...

It is possible to specify a model for interest rates in various ways, by giving the dynamics of the spot rate or of the forward rates, for example. A less well-developed approach is to specify the law of the state-price density process directly. In abstract, the state-price density process is a...

Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an...

Volatility estimators based on high, low, opening and closing prices have been developed, and perform well on simulated data, but on real data they frequently give lower values for volatility than the simple open-close estimator. This may be due to the fact that for real data, the maximum (or...