Implied betas for the Frankel–Wei regression framework
利用期权隐含波动率估计Frankel-Wei回归框架中的隐含贝塔，发现每种货币的平均贝塔和平均隐含贝塔恰好为0.5。
The Frankel–Wei regression framework measures the relationship between one currency and another currency solely by using foreign exchange rates as regression variables, where investors choose a common numéraire for the foreign exchange rates. When the common numéraire is a single currency, the foreign exchange rates are bilateral exchange rates. Option implied volatilities are easily estimated from listed option prices for bilateral exchange rates. In this paper, we use the implied volatilities to estimate implied betas for the Frankel–Wei regression framework. We show that the average beta and the average implied beta are both exactly 0.5, for each currency in a system of currencies.