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65 RISK FEBRUARY 2001 next, yields exact prices up to rounding errors to European-style op-
 

Summary: 65 RISK FEBRUARY 2001
Strap
next, yields exact prices up to rounding errors to European-style op-
tions and extends to barrier, American-style and Bermudan options. Our
model of lines yields exact solutions to the VG model for path-depen-
dent options with payout contingent on information on the lines only,
such as discretely monitored barrier and Bermudan options and special
values of one of the VG parameters. American-style options are priced
only approximately as the exercise boundary is piecewise constant in this
scheme. The case of a general VG model is within reach of Richardson
extrapolation methods.
In the following, we review the financial interpretation of the method
of lines in terms of randomised maturity options as developed by Carr
(1998), introduce the proposed model of lines that is appropriate for VG
models, discuss barrier and Bermudan options, and elaborate on extrap-
olation methods. We refer the reader to Albanese, Jaimungal & Rubisov
(2000) for a more thorough discussion of implementation details.
Jumps and the method of lines
The method of lines is an approximation scheme for solving quite gener-
al partial differential equations (PDEs). In contrast to lattice pricing mod-

  

Source: Albanese, Claudio - Department of Mathematics, King's College London
Jaimungal, Sebastian - Department of Statistics, University of Toronto

 

Collections: Mathematics