Static Hedging of Barrier Options with a Smile: An Inverse Problem

Let L be a parabolic second order differential operator on the domain ¯ Π = [0, T ] × ℝ. Given a function u : ℝ → R and ^x > 0 such that the support of of u is contained in (−∞, −ˆx], we let ˆy : ¯ Π → E be the solution to the equation: Lˆy= 0, ^ y| {0}× ℝ = u. Given positive bounds 0

[1]  Leif B. G. Andersen,et al.  Static Replication of Barrier Options: Some General Results , 2000 .

[2]  P. O. Shorygin.  On the Controllability Problem Arising in Financial Mathematics , 2000 .

[3]  Leonard Rogers,et al.  Robust Hedging of Barrier Options , 2001 .

[4]  L. Hörmander.  Linear Partial Differential Operators , 1963 .

[5]  Brian Davies,et al.  Partial Differential Equations II , 2002 .

[6]  Lagrange principle for problems of optimal control of ill-posed or singular distributed systems , 1992 .

[7]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[8]  P. Carr,et al.  Static Hedging of Timing Risk , 1999 .

[9]  P. Carr,et al.  Static Hedging of Exotic Options , 1998 .

[10]  A. Friedman.  Partial Differential Equations of Parabolic Type , 1983 .

[11]  J. Lions,et al.  Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles , 1968 .

[12]  Static versus Dynamic Hedging of Exotic Options: An Evaluation of Hedge Performance via Simulation , 2002 .

[13]  D. Liu.  European Option Pricing with Transaction Costs , 2000 .

[14]  Local exact controllability of the?two-dimensional Navier-Stokes equations , 1996 .

[15]  Emanuel Derman,et al.  STOCHASTIC IMPLIED TREES: ARBITRAGE PRICING WITH STOCHASTIC TERM AND STRIKE STRUCTURE OF VOLATILITY , 1998 .

[16]  David Hobson,et al.  Robust hedging of the lookback option , 1998, Finance Stochastics.

[17]  K. Toft.,et al.  How Well Can Barrier Options Be Hedged by a Static Portfolio of Standard Options , 1998 .

[18]  Oleg Yu. Imanuvilov,et al.  On approximate controllability of the Stokes system , 1993 .

[19]  Andrew Chou,et al.  Static Benefits Breaking Barriers , 1997 .

[20]  Nassim Nicholas Taleb,et al.  Dynamic Hedging: Managing Vanilla and Exotic Options , 1997 .

[21]  Walter Schachermayer,et al.  Pricing, No-Arbitrage Bounds and Robust Hedging of Installment Options , 2000 .

[22]  R. Douady.  CLOSED FORM FORMULAS FOR EXOTIC OPTIONS AND THEIR LIFETIME DISTRIBUTION , 1999 .

[23]  Robert Lattès,et al.  Méthode de quasi-réversibilbilité et applications , 1967 .

[24]  P. Carr,et al.  Hedging Complex Barrier Options , 2002 .

[25]  Espen Gaarder Haug.  Barrier Put-Call Transformations , 1999 .

[26]  L. Levidow,et al.  How Biotechnology Regulation Separates Ethics from Risk , 1997 .

[27]  Andrew Chou,et al.  A uniform approach to static replication , 1998 .

[28]  Daniel Tataru,et al.  Carleman estimates and unique continuation for solutions to boundary value problems , 1996 .

[29]  E. Fernández-Caraa,et al.  Local exact controllability of the Navier – Stokes system ✩ , 2004 .

[30]  Emanuel Derman,et al.  Static Options Replication , 1995 .

[31]  Marco Avellaneda,et al.  Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model , 1996 .