Basket option pricing with the algorithms of piecewise lognormal interpolation

A basket option is an option on a portfolio of multiple risky assets. There is no analytical solution for basket option pricing, because the payoff of a basket option is determined by the weighted average of the prices of the multiple underlying assets. This study presents an approximation approach for valuing basket options by the algorithms of piecewise lognormal interpolation. The idea is to partition the time axis into collection of small intervals, in which the multiple lognormal average price process is approximated by a simple lognormal with the same first and second moments at the endpoints of the time intervals. Numerical examples of basket option with two stocks illustrate the accuracy of the approach when compared with results from Monte Carlo (MC) simulations. This method can be extrapolated to other complex option pricing, such as combination of options.