 
Summary: On the valuation of constant barrier options under
spectrally one sided exponential Levy models
and Carr's approximation for American Puts
by
Florin Avram 1 , Terence Chan 2 and Miguel Usabel 3
Abstract: This paper provides a general framework for pricing options with a constant
barrier under spectrally onesided exponential Levy model, and uses it to implement
of Carr's approximation for the value of the American put under this model. Simple
analytic approximations for the exercise boundary and option value are obtained.
Keywords: American options; perpetual approximation; spectrally negative exponen
tial Levy process
1 Introduction
This paper develops Carr's \Erlang approximation" for the price of an American put option
under the spectrally negative exponential Levy model.
There has been lots of recent interest in mathematical nance (see for example [10])
towards extending results based on the exponential Brownian motion model to results based
on exponential Levy models. This is motivated by the superior ts to the data and hence
improved pricing formulas and hedging strategies provided by several special classes of Levy
models { see for example the hyperbolic model of Eberlein and Keller [9], the variancegamma
model of Madan [19] and the inverse Gaussian model of BarndorfNielsen [2]. Following
