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Bounds for path-dependent options

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Title: Bounds for path-dependent options
Authors: Brown, DJ
Ibragimov, R
Walden, J
Item Type: Journal Article
Abstract: We develop new semiparametric bounds on the expected payoffs and prices of European call options and a wide range of path-dependent contingent claims. We first focus on the trinomial financial market model in which, as is well-known, an exact calculation of derivative prices based on no-arbitrage arguments is impossible. We show that the expected payoff of a European call option in the trinomial model with martingale-difference log-returns is bounded from above by the expected payoff of a call option written on an asset with i.i.d. symmetric two-valued log-returns. We further show that the expected payoff of a European call option in the multiperiod trinomial option pricing model is bounded by the expected payoff of a call option in the two-period model with a log-normal asset price. We also obtain bounds on the possible prices of call options in the (incomplete) trinomial model in terms of the parameters of the asset’s distribution. Similar bounds also hold for many other contingent claims in the trinomial option pricing model, including those with an arbitrary convex increasing payoff function as well as for path-dependent ones such as Asian options. We further obtain a wide range of new semiparametric moment bounds on the expected payoffs and prices of path-dependent Asian options with an arbitrary distribution of the underlying asset’s price. These results are based on recently obtained sharp moment inequalities for sums of multilinear forms and U-statistics and provide their first financial and economic applications in the literature. Similar bounds also hold for many other path-dependent contingent claims.
Issue Date: 1-Nov-2015
Date of Acceptance: 23-Jul-2015
URI: http://hdl.handle.net/10044/1/67732
DOI: https://dx.doi.org/10.1007/s10436-015-0265-1
ISSN: 1614-2446
Publisher: Springer (part of Springer Nature)
Start Page: 433
End Page: 451
Journal / Book Title: Annals of Finance
Volume: 11
Issue: 3-4
Copyright Statement: © 2015 Springer-Verlag Berlin Heidelberg. The final publication is available at Springer via https://dx.doi.org/10.1007/s10436-015-0265-1
Keywords: Social Sciences
Business, Finance
Business & Economics
Option bounds
Trinomial model
Binomial model
Semiparametric bounds
Option prices
Expected payoffs
Path-dependent contingent claims
Asian options Moment inequalities
1502 Banking, Finance And Investment
Publication Status: Published
Online Publication Date: 2015-09-19
Appears in Collections:Imperial College Business School