An Empirical Model for Volatility of Returns and Option Pricing

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset prices after a finite time. We point out two problems with their formulation. First, we show that the option valuation is not uniquely determined; in particular , strategies based on the delta-hedge and CAPM (the Capital Asset Pricing Model) are shown to provide different valuations of an option although both hedges are instantaneoulsy riskfree. Second, asset returns are known not to be Gaussian distributed. Empirically, distributions of returns are seen to be much better approximated by an exponential distribution. This exponential distribution of asset prices can be used to develop a new pricing model for options that is shown to provide valuations that agree very well with those used by traders. We show how the Fokker-Planck formulation of fluctuat...

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Joseph L. McCauley, Gemunu H. Gunaratne
• Keywords: Asset Prices, Capital Asset Pricing Model, CORR 2002, Education, Exponential Distribution