Valuation of Spread and Basket Options

This study adopts the unbounded-system distribution of the Johnson (1949) distribution family to approximate the basket/spread distribution and derive a versatile pricing model. This pricing model can price both basket and spread options, and thus, the risks of issuing both options can be consistently and efficiently integrated and managed. Furthermore, the pricing model can instantly price basket/spread options (almost as short in time as the Black-Scholes model (Black and Scholes, 1973)), and the results are quite accurate compared with the Monte Carlo simulation results. The method for computing Greeks is also presented. Finally, numerical examples are provided to demonstrate the implementation of the pricing model, and show the economic intuitions of Greeks for basket and spread options, and for an option portfolio consisting of both options.