Accurate approximations for Asian options. (English) Zbl 0952.91029

Aingworth, Donald; Motwani, Rajeev; Oldham, Jeffrey D.

Proceedings of the 11th annual ACM-SIAM symposium on Discrete algorithms. San Francisco, CA, USA, January 9-11, 2000. Philadelphia, PA: SIAM. 891-900 (2000).

Summary: The authors present an asymptotic fully-polynomial approximation scheme for pricing Asian options on the lattice. For an option with strike price \(X\) on an \(n\)-step binomial tree, we give an \(O(kn^2)\) time algorithm with one-sided error of \(nX/k\), for any positive \(k\). our technique works for both European Asian and American Asian options and is powerful enough to extend to other path-dependent options with similar properties. They also show several heuristic optimizations to this algorithm which maintain similar guarantees and present some experimental results. This is the first algorithm for Asian options to give guaranteed error bounds in polynomial time.
For the entire collection see [Zbl 0933.00039].

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
90C59	Approximation methods and heuristics in mathematical programming
90C60	Abstract computational complexity for mathematical programming problems
91B74	Economic models of real-world systems (e.g., electricity markets, etc.)

Keywords:

pricing Asian options; heuristic optimizations; polynomial time