Very Fast Algorithms for Barrier Option Pricing and the Ballot Problem
Resource
The Journal of Derivatives 5 (3): 68-79
Journal
The Journal of Derivatives
Journal Volume
5
Journal Issue
3
Pages
68-79
Date Issued
1998
Date
1998
Author(s)
Abstract
Combinatorial methods are extremely useful for designing fast yet simple algorithms for pricing European-style barrier options. Closed-form formulas for standard European-style barrier options can then be easily derived. Combinatorial formulas under the trinomial modelare also presented- The common practice in the literature compares algorithms in terms of the number of time steps required to reach convergence. We illustrate the pitfalls of this custom by evaluating the performance of our binomial model-based algorithm and the trinomial tree algorithm, whose superiority over the binomial model is widely accepted. Contrary to common belief our algorithm emerges the dear winner, In fact, the performance gap is two orders of magnitude. Also shattered is the myth that the binomial model must converge extremely slowly when the current stock price is very close to the barrier.
Type
journal article
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