Options

• J. R. Birge, " Quasi-Monte Carlo Approaches to Option Pricing," Technical Report 94-19, Department of Industrial and Operations Engineering, University of Michigan, 1994 (Revised June 1995). (This ps file does not contain the figures. They separately given as the following gif giles: Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11, Fig. 12, Fig. 13.)

  Abstract

  Complications such as varying interest rates and complex contingencies can prohibit analytical computation of option prices. A typical approach is to rely on Monte Carlo simulation in these cases and to use statistical properties of assumed random sequences. This approach has two drawbacks. First, the validity of a pseudo-random sequence for statistical randomness is somewhat questionable. Second, even assuming randomness, the error from central limit arguments decreases slowly, inversely proportional to the square root of the number of observations. Quasi-Monte Carlo sequences, on the other hand, do not rely on a randomness assumption and have order of magnitude better asymptotic error rates. We show how quasi-Monte Carlo sequences can be used in option pricing, give some analytical justfication for their preference over crude or pseudo-Monte Carlo methods, and present some empirical evidence based on simple call option models.