What’s a basket worth?

Peter Laurence and Tai-Ho Wang take a significant step in the valuation of basket options with positive and fixed weights. These model all index options, price, cap or equal weighted. Departing from the usual Black-Scholes framework, the authors provide no-arbitrage, model-independent upper and lower bounds and hedging strategies for such basket options, using options on the component stocks, the stocks themselves and cash as hedging instruments. The bounds and hedging ratios are given in closed form, providing a far-reaching generalisation of the early work of Merton, who had considered the question of the upper bound in a special case

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