ABSTRACT
This chapter reviews the traditional risk measures based on the Fisher Black and M. Scholes continuous model and finds the limitations of these measures. It explains the corresponding risk measures in Mark Rubinstein’s discrete model. The chapter compares the traditional risk measures in the continuous and the discrete models. It also compares skewness and kurtosis of the returns of options. In the literature of economic and financial studies, risk is most often defined as the standard deviation of random variables. The standard deviation is a good and effective measure of risk only for stochastic variables with symmetric distributions. The chapter analyzes the skewness and kurtosis measures in the Black and Scholes model, and describes formulas of skewness and kurtosis for both call and put options in the discrete model. It also analyzes the three means of measuring risks, the standard deviation, the systematic risk beta, and skewness and kurtosis, in the Black and Scholes continuous model and Rubinstein’s discrete model.
