We discuss here an alternative interpretation of the familiar binomial lattice approach to option pricing, illustrating it with reference to pricing of barrier options, one- and two-sided, with fixed, moving or partial barriers, and also the pricing of American put options. It has often been...

We firstly consider an investor faced with the classical Merton problem of optimal investment in a log-Brownian asset and a fixed-interest bond, but constrained only to change portfolio (and, if relevant, consumption) choices at times which are a multiple of h. We show that the cost of this...

In a sequence of fascinating papers, Leland and Leland and Toft have investigated various properties of the debt and credit of a firm which keeps a constant profile of debt and chooses its bankruptcy level endogenously, to maximise the value of the equity. One feature of these papers is that the...

A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths, it is well known that the variance swap...

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>

In this article we are interested in option pricing in markets with bubbles. A bubble is defined to be a price process which, when discounted, is a local martingale under the risk-neutral measure but not a martingale. We give examples of bubbles both where volatility increases with the price...

<Para ID="Par1">We consider the problem of giving a robust, model-independent, lower bound on the price of a forward starting straddle with payoff <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$|F_{T_{1}} - F_{T_{0}}|$</EquationSource> </InlineEquation>, where 0T <Subscript>0</Subscript>T <Subscript>1</Subscript>. Rather than assuming a model for the underlying forward price (F <Subscript> t </Subscript>)<Subscript> t≥0</Subscript>, we assume that call prices for maturities T...</subscript></subscript></subscript></subscript></subscript></equationsource></inlineequation></para>