Optimal static quadratic hedging. Issue 9 (1st September 2016)

• Record Type: Journal Article
• Authors: Leung, Tim; Lorig, Matthew
• Is Part Of: Quantitative finance. Volume 16:Issue 9(2016)
• Page Start: 1341
• Page End: 1355
• Publication Date: 2016-09-01
• Subjects: Static hedging -- Leveraged ETF options -- Substitute hedging; C52 -- D81 -- G11 -- G13; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2016.1161229
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these expectations analytically in a general Markov diffusion market. To illustrate the versatility of our approach, we present several numerical examples, including hedging path-dependent options and options written on a correlated asset.