ROBUST BOUNDS FOR FORWARD START OPTIONS

We consider the problem of finding a model‐free upper bound on the price of a forward start straddle with payoff . The bound depends on the prices of vanilla call and put options with maturities T₁ and T₂ , but does not rely on any modeling assumptions concerning the dynamics of the underlying. The bound can be enforced by a super‐replicating strategy involving puts, calls, and a forward transaction. We find an upper bound, and a model which is consistent with T₁ and T₂ vanilla option prices for which the model‐based price of the straddle is equal to the upper bound. This proves that the bound is best possible. For lognormal marginals we show that the upper bound is at most 30% higher than the Black–Scholes price. The problem can be recast as finding the solution to a Skorokhod embedding problem with nontrivial initial law so as to maximize .     

Analysis of the US cruise line industry

The cruise line industry has been through a metamorphosis. From being a declining mode of travel in the 1960s, the cruise line industry turned the corner in the 1970s and became one of the fastest growing segments of the wider tourism industry during the 1980s. This paper examines the reasons behind this growth, the current structure of the US cruise industry and the issues facing the industry in the 1990s as it heads towards the next century.     

Model-independent hedging strategies for variance swaps

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 payoff can be replicated exactly using a portfolio of puts and calls and a dynamic position in the asset. This fact forms the basis of the VIX contract. But what if we are in the more realistic setting where the contract is based on discrete monitoring, and the underlying asset may have jumps? We show that it is possible to derive model-independent, no-arbitrage bounds on the price of the variance swap, and corresponding sub- and super-replicating strategies. Further, we characterise the optimal bounds. The form of the hedges depends crucially on the kernel used to define the variance swap.     

A multi-asset investment and consumption problem with transaction costs

Finance and Stochastics - In this article, we study a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We specialise to a...     

Static-arbitrage upper bounds for the prices of basket options

In this paper we investigate the possible values of basket options. Instead of postulating a model and pricing the basket option using that model, we consider the set of all models which are consistent with the observed prices of vanilla options, and, within this class, find the model for which the price of the basket option is largest. This price is an upper bound on the prices of the basket option which are consistent with no-arbitrage. In the absence of additional assumptions it is the lowest upper bound on the price of the basket option. Associated with the bound is a simple super-replicating strategy involving trading in the individual calls.