We derive a nonlinear parabolic partial differential equation for the value of portfolios of options in the presence of proportional transaction costs. This assumes a Leland world of transacting after each time interval, which is of fixed length. The equation reduces to the modified variance...

Davis, Panas, and Zariphopoulou (1993) and Hodges and Neuberger (1989) have presented a very appealing model for pricing European options in the presence of rehedging transaction costs. In their papers the 'maximization of utility' leads to a hedging strategy and an option value. The latter is...

In this article, we present a flexible approach to the valuation of Parisian and similar exotic options. The approach is based on the numerical solution of a fundamental partial differential equation and can easily accommodate variations like American early exercise features, different payoff...

In this paper we model the value of a firm based on its current earnings and cash balances. The value is modelled on the assumption that earnings follow a mean-reverting process. The effect of advertising on earnings is modelled, and the condition for optimal advertising derived. The value of...

In this paper we consider the problem of hedging options in the presence of costs in trading the underlying asset. This work is an asymptotic analysis of a stochastic control problem, as in Hodges & Neuberger (1989) and Davis, Panas & Zariphopoulou (1993) . We derive a simple expression for the...

In this paper we model the value to a firm of undertaking market research into a particular product opportunity. The way in which information about the potential of the project arrives and knowledge evolves during the life of the project is modeled using the theory of optimal filtering. The...

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. We establish pricing equations for various passport options including the multi-asset passport and those with discrete trading...

Parisian options are barrier options for which the knock-in/knock-out feature is only activated after the price process has spent a certain prescribed, consecutive time beyond the barrier. This specification is motivated by the need to make the option more robust against short-term movements of...

There is no room in the classical Black-Scholes framework for the market view of an investor. The investor in derivatives needs to know the volatility of the underlying, that is the 'choppiness' of the market, but the direction is irrelevant. Suppose we have two stocks A and B having the same...