14 research outputs found
A New Algorithm for Monte Carlo for American Options
2000 Mathematics Subject Classification: 91B28, 65C05.We consider the valuation of American options using Monte
Carlo simulation, and propose a new technique which involves approximating
the optimal exercise boundary. Our method involves splitting the boundary
into a linear term and a Fourier series and using stochastic optimization in
the form of a relaxation method to calculate the coefficients in the series.
The cost function used is the expected value of the option using the the
current estimate of the location of the boundary. We present some sample
results and compare our results to other methods
Using Monte Carlo Methods to Evaluate Sub-Optimal Exercise Policies for American Options
∗This research, which was funded by a grant from the Natural Sciences and Engineering Research Council of Canada, formed part of G.A.’s Ph.D. thesis [1].In this paper we use a Monte Carlo scheme to find the returns
that an uninformed investor might expect from an American option if he
followed one of several näıve exercise strategies rather than the optimal
exercise strategy. We consider several such strategies that an ill-advised
investor might follow. We also consider how the expected return is affected
by how often the investor checks to see if his exercise criteria have been met
Critical Layer Analysis of Stuart Vortices in a Plane Jet
Asymptotic techniques are used to model quasi-steady-state vortices in the plane (Bickley) inviscid jet. A nonlinear critical layer analysis is used to find a family of steady-state
finite amplitude two-dimensional vortices which are based on the Stuart vortex
Some Nonlinear Vortex Solutions
We consider the steady-state two-dimensional motion of an inviscid
incompressible fluid which obeys a nonlinear Poisson equation. By seeking
solutions of a specific form, we arrive at some interesting new nonlinear
vortex solutions
On the optimal exercise boundary for an American put option
An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying PDE, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit
Asymptotic analysis of American call options
American call options are financial derivatives that give the holder the right but not the obligation to buy an underlying security at a pre-determined price. They differ from European
options in that they may be exercised at any time prior to their expiration, rather than only at expiration. Their value is described by the Black-Scholes PDE together with a constraint that
arises from the possibility of early exercise. This leads to a free boundary problem for the optimal exercise boundary, which determines whether or not it is beneficial for the holder to
exercise the option prior to expiration. However, an exact solution cannot be found, and therefore by using asymptotic techniques employed in the study of boundary layers in fluid
mechanics, we find an asymptotic expression for the location of the optimal exercise boundary and the value of the option near to expiration
On the optimal exercise boundary for an American put option
An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying PDE, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit
On the optimal exercise boundary for an American put option
An American put option is a derivative financial instrument that
gives its holder the right but not the obligation to sell an
underlying security at a pre-determined price. American options
may be exercised at any time prior to expiry at the discretion of
the holder, and the decision as to whether or not to exercise
leads to a free boundary problem. In this paper, we examine the
behavior of the free boundary close to expiry. Working directly
with the underlying PDE, by using asymptotic expansions, we are
able to deduce this behavior of the boundary in this limit