Double Asian-Barrier Straddle Baskets
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Abstract
The objective of this paper is to determine the price of a Double Asian-Barrier Straddle Basket and, to discuss the appropriate valuation techniques for such a complex derivative. The Straddle Basket discussed in this text is a basket of combined long positions in at-the-money call and put options on multiple underlying indices. Lower and upper knock-out barriers are imposed on the basket which relate to a moving average (Asian) of the basket value and will pay out nothing if triggered. Monte Carlo simulation is used to price the basket option and several methods are employed to improve the efficiency of the valuation process and attempt to benchmark and hedge the security. The results of this paper suggest that control variates are a simple and effective acceleration technique in providing an efficient pricing solution for the given derivative. Applying this method, a maximum acceleration factor of 6.65 is achieved while the obtained price of the certificate remains within the bounds of benchmark option prices.
. Conclusion
This project illustrates how variance reduction techniques can lead to substantial acceleration in numerical pricing of our derivative. This allows for efficient pricing which lends itself to pragmatic applications of this contract. We understand that the performance of the best performing control variate can be attributed to its high correlation with our product. This is fundamental for a financial engineer to understand when using Monte Carlo to price derivatives they manufacture. If they are able to create contracts which are closely related to other contracts, they will be easier to price efficiently. Constructing contracts of this fashion has the added benefit of an immediate candidate contract for which to hedge the new contract. This is a double edged sword, however, since creating products similar to other pre-existing products may be redundant if one is not careful in its construction. The feature which separates our contract from the correlated contract is the look-back feature in the barrier. This offers a different risk profile than the standard, instantaneous barrier since the purchaser of our contract is protected from rises in the mean of the underlyings in an ephemeral way; the will only be penalized for newly established, longer term trends of the average which persist for 30 days. Therefore, there is the potential for this type of product to have a different clientele than the instantaneous barrier counterpart, differentiating it and making its innovations useful.
With respect to the exercise of efficiently pricing this contract, the price we obtained for our instrument was within the benchmark range which we expected it to be. This is encouraging of the fact that our code was implemented correctly and gives us confidence that our price is correct. We faced many challenges when dealing with