Distribution of the Exchange Rate Implicit in Option Prices: Application to TASE

This study presents a method of estimating the implied distribution of the future NIS/$ exchange rate implicit in the NIS/$ options traded on the TASE (Tel Aviv Stock Exchange), using options with the same maturity but different strike prices. The distribution of the exchange rate as perceived by the markets is reflected by the option prices with different strike prices, because of the high sensitivity of the prices to expected developments in the financial markets. The distribution estimated here is a double-log-normal distribution of the exchange rate that combines two separate log-normal distributions of the exchange rate. The estimation used here has an advantage over the usual log-normal distribution in that it identifies market expectations regarding the future course of the exchange rate that incorporate the possibility that this will not be continuous, thus enabling more extensive information to be derived from the markets. In addition to expected changes in the exchange rate and the risk level, the model also enables us calculate the possibility of a jump in the exchange rate, and of leptokurtosis and skewness in the distribution. A non-technical summary of the study is given in Appendix A.