AN ACCURATE ANALYTICAL APPROXIMA nON FOR THE PRICE OF A EUROPEAN-STYLE ARITHMETIC ASIAN OPTION

An accurate analytical approximation for the price of a European-style arithmetic Asian option David Vynckel, Marc Goovaerts2, Jan Dhaene2 For discrete arithmetic Asian options the payoff depends on the price average of the underlying asset. Due to the dependence struc-ture between the prices of the underlying asset, no simple exact pricing formula exists, not even in a Black-Scholes setting. In the recent lit-erature, several approximations and bounds for the price of this type of option are proposed. One of these approximations consists of re-placing the distribution of the stochastic price average by an ad hoc distribution (e.g. Lognormal or Inverse Gaussian) with the same first and second moment. In this paper we use a different approach and combine a lower and upper bound into a new analytical approxima-tion. This approximation can be calculated efficiently, turns out to be very accurate and moreover, it has the correct first and second mo-ment. Since the approximation is analytical, we can also calculate the corresponding hedging Greeks and construct a replicating strategy.