Dynamic Programming Algorithms for the Ask and Bid Prices of American Options Under Small Proportional Transaction Costs

Dynamic Programming Algorithms for the Ask and Bid Prices of American Options Under Small Proportional Transaction Costs PDF Author: Tomasz Zastawniak
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Languages : en
Pages : 33

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Book Description
Dynamic programming algorithms are developed for computing the ask and bid prices of American contingent claims in a binary tree setting in the presence of small proportional transaction costs, extending the recursive construction of the Snell envelope. Associated with the pricing algorithms are iterative procedures for computing optimal hedging strategies for the writer as well as for the buyer of an American option. The bid and ask prices of an American option are represented in terms of the expectation of the option payoff evaluated at an optimal stopping time with respect to an optimal martingale probability measure. As a by-product a similar dynamic programming algorithm is obtained for pricing and hedging European contingent claims in the same setting.