Accumulator pricing

Accumulator is a highly path dependant derivative structure that has been introduced as a retail financial product in recent years and becomes very popular in some Asian cities with its speculative nature. Despite its popularity, its pricing formula is not well known especially when there is a barrier structure. When the barrier in an accumulator contract is applied continuously, this paper obtains exact analytic pricing formulae for immediate settlement and for delay settlement. For discrete barrier, we also obtain analytic formulae which can approximate the fair price of an accumulator under both settlement methods. Through Monte Carlo simulation, we show that the approximation is highly satisfactory. With price formulae in close forms, this paper further explains how to price the product fairly to fit into its zero-cost structure. The analytic formulae also help in computing the Greeks of an accumulator which are documented in this paper. An asymmetry can be observed here that when the buyer is suffering a loss, risk characteristics like delta and vega are substantially larger than when the buyer is enjoying a profit. This means that losing buyers will be more vulnerable to price changes and volatility changes than winning buyers. This is consistent with another observation in the paper that the value at risk for the buyer can be several times larger than that of the seller.