Derivatives Models on Models

8

Asian Pyramid Power

with Jørgen Haug and William Margrabe

Asian options are among the more popular forms of exotic options. Even though they can be priced by Monte Carlo simulation it is not a popular approach among practitioners. A swarm of researchers from academia and the industry have therefore churned out a number of closed form approximations for arithmetic average options,¹ and there seems to be no end to the interest in improving the approximations in search of the last penny. We choose to focus not on the last penny but rather at the intuition behind the choice of volatility in Asian option pricing. We also demonstrate that it is important to take the term structure of plain vanilla option volatility into consideration. The implications of a term structure of volatility for Asian option valuation have received scant attention in the literature, and most off-the-shelf systems available to Wall Street delivers only Asian option models that ignore the term structure. Could it be that the hunt for the last penny has made academics and practitioners blind to the big bucks? Before we discuss the effect of calibrating Asian options to the term structure of volatility, let us kick off with the intuition behind the relationship between Asian option volatility and the well known rule of thumb that Asian option volatility equals the spot volatility divided by the square root of three.

In 1997 Bill Margrabe (a.k.a. Dr Risk) asked a question on his web page www.margrabe.com regarding ...