Penalty Methods For American Options With Stochastic Volatility (1998)
| Citations: | 53 - 18 self |
BibTeX
@MISC{Zvan98penaltymethods,
author = {R. Zvan and P. A. Forsyth and K.R. Vetzal},
title = {Penalty Methods For American Options With Stochastic Volatility},
year = {1998}
}
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Abstract
The American early exercise constraint can be viewed as transforming the two dimensional stochastic volatility option pricing PDE into a differential algebraic equation (DAE). Several methods are described for forcing the algebraic constraint by using a penalty source term in the discrete equations. The resulting nonlinear algebraic equations are solved using an approximate Newton iteration. The solution of the Jacobian is obtained using an incomplete LU (ILU) preconditioned PCG method. Some example computations are presented for option pricing problems based on a stochastic volatility model, including an exotic American chooser option written on a put and call with discrete double knockout barriers and discrete dividends.
