A Closed Form Approach to the Valuation and Hedging of Basket and Spread Options

We develop a new approach to valuing and hedging basket and spread options. We consider baskets of assets with potentially negative portfolio weights (spread options are a subclass of such basket options). The basket distribution is approximated using a generalized family of log-normal distributions. This approximation copes with negative basket values as well as negative skewness of the basket distribution, and it provides closed formulae for the option price and greeks. Numerical simulations show our approach provides a very close approximation to the option price, and performs remarkably well in terms of the hedging error. We analyze option price sensitivities with respect to the assets’ volatilities and correlations; and explain the seemingly paradoxical phenomenon of negative volatility vegas.