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D. Duffie (1992)
Dynamic Asset Pricing Theory
Therefore x u (k; h) must lie between the minimum and maximum possible values of A k+1 at node (k+1; h+1), namely e A(k+1; h+1; 0) and e A(k+1; h+1; (h+1)(k?h))
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A. Ruttiens. Classical replica. RISK
For part (3), observe that since the payoff function (x ? L) + is a convex function of x, so is the value function V (k; h; x). By definition
S. Turnbull, L. Wakeman (1991)
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The analogous claim for x d (k; h) is shown similarly. This claim combined with part (1) of the lemma implies part
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Flexible convolution
J. Hull, Alan White (1993)
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and w 1 ; w 2 ; defined as in that paragraph We know that x u (k; h) is a convex combination x 1 +(1?)x 2 where x 1 = e A(k+1; h+1; b), x 2 = e A(k+1; h+1; b+1) By induction assumption
Leonard Rogers, Z. Shi (1995)
The value of an Asian optionJournal of Applied Probability, 32
P. Ritchken, L. Sankarasubramanian, Anand Vijh (1993)
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P. Chalasani, S. Jha, A. Varikooty (1998)
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A. Kemna, A. Vorst (1990)
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Comparison with the Hull-White method In this section we compute roughly the number of grid points of the form e mh that the
Edmond Levy (1992)
Pricing European average rate currency optionsJournal of International Money and Finance, 11
Hull-White method needs to consider, in order to obtain an accuracy comparable to ours
P. Chalasani, S. Jha, A. Varikooty (1999)
Accurate Approximations for European Asian Options
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We present simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial model. We introduce a new refined version of the Cox-Ross-Rubinstein (1979) binomial lattice of stock prices. Each node in the lattice is partitioned into ‘nodelets’, each of which represents all paths arriving at the node with a specific geometric stock price average. The upper bound uses an interpolation idea similar to the Hull-White (1993) method. From the backward-recursive upper-bound computation, we estimate a good exercise rule that is consistent with the refined lattice. This exercise rule is used to obtain a lower bound on the option price using a modification of a conditional-expectation based idea from Rogers-Shi (1995) and Chalasani-Jha-Varikooty (1998). Our algorithms run in time proportional to the number of nodelets in the refined lattice, which is smaller than n4/20 for n > 14 periods.
Review of Derivatives Research – Springer Journals
Published: Oct 14, 2004
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