Sharpe-ratio pricing and hedging of contingent claims in incomplete markets by convex programming
Author(s)
Date
2008-08Source Title
Automatica
Print ISSN
0005-1098
Electronic ISSN
1873-2836
Publisher
Elsevier
Volume
44
Issue
8
Pages
2063 - 2073
Language
English
Type
ArticleItem Usage Stats
167
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Abstract
We analyze the problem of pricing and hedging contingent claims in a financial market described by a multi-period, discrete-time, finite-state
scenario tree using an arbitrage-adjusted Sharpe-ratio criterion. We show that the writer’s and buyer’s pricing problems are formulated as conic
convex optimization problems which allow to pass to dual problems over martingale measures and yield tighter pricing intervals compared to the
interval induced by the usual no-arbitrage price bounds. An extension allowing proportional transaction costs is also given. Numerical experiments
using S&P 500 options are given to demonstrate the practical applicability of the pricing scheme.
Keywords
Contingent ClaimPricing
Hedging
Sharpe Ratio
Martingales
Transaction Costs
Convex Programming