Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets
Author
Pınar, M. Ç.
Date
2013Source Title
Optimization Letters
Print ISSN
1862-4472
Electronic ISSN
1862-4480
Volume
7
Issue
1
Pages
63 - 78
Language
English
Type
ArticleItem Usage Stats
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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.
Keywords
American optionsMixed-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