A closed form approach to valuing and hedging basket options

We develop a new approach to valuing and hedging basket 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 of the option price, and performs remarkably well in terms of the hedging error. We analyze the option price sensitivities with respect to the assets' volatilities and correlations; and explain the seemingly paradoxical phenomenon of negative volatility vegas