|
Activity Number:
|
68
|
|
Type:
|
Contributed
|
|
Date/Time:
|
Sunday, August 6, 2006 : 4:00 PM to 5:50 PM
|
|
Sponsor:
|
Section on Risk Analysis
|
| Abstract - #306351 |
|
Title:
|
Partial Hedging Using Malliavin Calculus
|
|
Author(s):
|
Lan Nygren*+ and Lakner Peter
|
|
Companies:
|
Rider University and New York University
|
|
Address:
|
567 Grant Street, Newtown, PA, 18940,
|
|
Keywords:
|
contingent claim ; partial hedging ; Malliavin calculus ; lookback option ; convex duality ; shortfall risk
|
|
Abstract:
|
We consider the problem of partial hedging of derivative risk when the investor's attitude towards the shortfall is captured by a general convex loss function. We derive the dual problem from the Legendre-Fenchel transform of the loss function and interpret the optimal strategy as the perfect hedging strategy for a modified claim. However, computation of the hedging strategy for this modified claim requires other tools than the well-known "delta" hedging technique since the associated optimal wealth process is usually too complicated to possess an analytic expression. We show how the Malliavin calculus approach can be used to derive the hedging strategy for the modified claim. The advantage of this probability based hedging approach is illustrated in a couple of explicitly worked out examples.
|
