The proposal of a calculation method for stable numeraire price using the exchange values of financial assets

Abstract

In this study, we propose the use of exchange value as the stable numeraire for pricing financial assets. The price of currency is used to illustrate our method. In the currency market, the price of a currency is usually measured by using its exchange rate to another currency, for example, the dollar-yen rate. We point out that the price of currency can also be measured by using the proposed numeraire, namely the exchange value. In particular, we calculated the exchange values of different currencies from their exchange rates under a statistical approximation. Finally, probability distributions of differently measured price returns are compared with each other to evaluate the stability with the use of the proposed numeaire.