Marti G Subrahmanyam, Bin Gao, Jing-zhi Huang
ABSTRACT
In this paper, we propose an alternative approach for pricing and hedging
non-standard American options. In principle, the proposed approach applies
to any kind of American-style contract for which the payoff function has
a Markovian representation in the state space. Specifically, we obtain
an analytic solution for the value and hedge parameters of barrier options,
an important example of path-dependent options. The solution includes standard
American options as a special case. The analytic formula also allows us
to identify and exploit two key properties of the optimal exercise boundary
- homogeneity in price parameters and time-invariance - for American options.
In addition, some new put-call ``symmetry" relations are also derived.
These properties suggest a new, efficient and integrated approach to pricing
and hedging a variety of standard and non-standard American options. From
an implementation perspective, this approach avoids the current practice
of repetitive computation of option prices and hedge ratios. Our implementation
of the analytic formula for barrier options indicates that the proposed
approach is both efficient and accurate in computing option values and
option hedge parameters. In some cases, our method is substantially faster
than existing numerical methods with equal accuracy. In particular, the
method overcomes the difficulty that existing numerical methods have in
dealing with prices close to the barrier, the case where the barrier matters
most.
Subrahmanyam: (212) 998-0348 msubrahma@stern.nyu.edu
To request a copy of this paper click here
The Finance Department Working Paper Series has been generously sponsored
by