Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets

Date
2013
Authors
Pınar, M. Ç.
Advisor
Instructor
Source Title
Optimization Letters
Print ISSN
1862-4472
Electronic ISSN
1862-4480
Publisher
Volume
7
Issue
1
Pages
63 - 78
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arbitrage assumption with a "no good-deal assumption" defined using an arbitrage-adjusted Sharpe ratio criterion we formulate the problem of computing the pricing and hedging of an American option in a financial market described by a multi-period, discrete-time, finite-state scenario tree as a large-scale mixed-integer conic optimization problem. We report computational results with off-the-shelf mixed-integer conic optimization software.

Course
Other identifiers
Book Title
Keywords
American options, Mixed-integer second-order cone optimization, American options, Computational results, Conic optimization, Contingent claims, Financial market, Finite-state, Incomplete financial markets, Incomplete markets, Mixed-integer, Multi-period, No arbitrage, Scenario tree, Second order cone, Second-order cone programming, Sharpe ratios, Commerce, Decision trees, Finance, Optimization, Risk perception, Integer programming
Citation
Published Version (Please cite this version)