Factor Models for Option Pricing

Options on stocks are priced using information on index options and viewing stocks in a factor model as indirectly holding index risk. The method is particularly suited to developing quotations on stock options when these markets are relatively illiquid and one has a liquid index options market to judge the index risk. The pricing strategy is illustrated on IBM and Sony options viewed as holding SPX and Nikkei risk respectively. Current Version: May 21, 2001 File Reference: vgsiapfm1pres.tex Tuesday, May 22, 2001 Risk Course on Correlation New York, NY Introduction and Overview • Consider the problem of pricing a stock option when there are very few (possibly none) liquid options written on the same underlying. • Suppose also that we have a liquid market for options on a major financial index which may or may not include the stock in question. • We show how one can price options on the individual stocks by viewing the risk of the stock as the sum of the index risk and an idiosyncratic firm-specific component. • The index risk is priced consistent with the index options market, while the idiosyncratic component is priced consistent with the true statistical probability, with no change of probability on this component.