Analysis of Power exchange option value of dollar base on gold by using of time series

In this paper, we first present the pricing equation for American and European type of standard and power exchange options. Then we tested 501 price of gold and dollar from first day of Persian month Farvardin of year 1391 to the first day of Persian month Tir of year 1394, by using time series and ARCH, GARCH, MAR-ARCH, ARMA-GARCH, GJR-GARCH models in order to determines power of assets exchange to calculate value of power exchange option dollar on base of gold in near future.
Finally, by comparing the mean square error of observation and conditional variance by considering AIC and BIC measures, we choose an appropriate model of above models. Also Christoffersen and Kupiec, as an appropriate model tests are used for forecasting and analysis the behavior of gold and dollar power option pricing.