Abstract

Estimating the representative agent's or the market's degree of risk aversion from securities prices has a long history. However, it is only since this century that scholars have begun using options data to do so. Options provide a particularly promising context for studying risk preferences. Embedded in the prices of traded options is rich information set relating to various aspects of the underlying asset. One piece of embedded information is the state price density. To the best of my knowledge, the implied risk aversion deriving from state price density or the "risk neutral" distribution has not been well studied in Canadian context. In this paper, the author investigates the volatility smile derived from call options on the Canadian S&P/TSX 60 Index, which is one of the most heavily traded index options in the Canadian market. Then from the option pricing function, the author recovers the risk neutral distribution by using the nonparametric approach--the regularization method proposed by Jackwerth and Rubinstein (1996). The final step is to compare the option inferred risk neutral distribution with the estimated actual distribution of index prices based on, for example, the historical price path over the same time interval. The relationship between these two distributions depends on the preference (utility) of investors about money, as they grow richer or poorer. Knowing both distributions allows us to infer what the preferences must be within an economy to be consistent with the option price and the historical returns.