Nov 28, 2005
This is a very popular and interesting product. The underlying is actually a forward contract and the pricing should be done using the forward. A popular Accumulator product that we have come across in the Asian market is of this particular form:
In a 252 business day period if on any day the stock price of a particular listed stock, say, HSBC, as quoted on a stock exchange (say, the Hong Kong Stock Exchange) is equal to or greater than the KO (knock out) rate then the contract gets knocked off otherwise the buyer is obliged to buy the stock at the strike price. (All prices are in HKD)
Current Spot of HSBC = $126
Strike Price (K) = 97% of the current spot
Knock-out Level (KO) = 104% of the current spot
This is a very simple product to price and the price of the Accumulator is simply the P & L of the product. In other words, the Price of the product is:
We ran a simple Monte Carlo pricing engine with HSBC spot at 126.00 strike at 122.22 (see the term sheet above) and the knock-out level at 131.04 (see the term sheet above). We used 11% for the stock volatility and 4% as the risk free rate and did a simulation over 252 business days. The only assumption we made was that any amount of the stock can be bought continuously every day, without any additional transaction costs or liquidity concerns. For 2000 simulation runs we got a price of 0.496%.
Accumulators can also be constructed using two or more stocks. We would invited comments from readers on this product and if they can share some of the structures with us.
Any comments and queries can
be sent through our
More on Quantitative Finance >>
back to top