Pricing European Call Options Using a Pseudospectral Method

G. Linde, M. Åberg. 2004: Pricing European Call Options Using a Pseudospectral Method. Written in English. Uppsala, Sweden. The aim of the project is to price European call options with a pseudospectral method (PS). An option is a financial asset that can be resembled to a lottery coupon. In a predefined time in the future the option is either worthless or worth more than it was bought for. Black–Scholes partial differential equation presented in 1973 was the main cause to the prestigious award Scholes was awarded in 1997, namely the Bank of Sweden Prize in Economic Science in Memory of Alfred Nobel. Since options diligently has been priced with the use of finite differences it works as a comparison to the results of PS. The set of points used when discretizing Black–Scholes equation is the Chebyshev points. The spatial convergence rate for PS is the same as for FD. When the initial condition is approximated with orthogonal Chebyshev polynomials and the domain is truncated the convergence rate increases significantly. The success is due to the transport of the maximum error to the region close to the left boundary and hence away from the exercise price, which is the region of most interest. Under these circumstances the maximum spatial error when using 100 grid points is of order 10−5 with PS compared to 10−2 with FD. The successful result in this work is achieved for the case when the option depends on one underlying asset. It would be of interest to try a more comprehensive approach than done in this work to expand it to more than one dimension.