ABSTRACT
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
Appendix 20.A: Feasibility of the Initialized Non-Recombining Tree . . . . . . . . 445
Appendix 20.B: Feasibility of the Initialized Non-Recombining Tree
Assuming Time Dependent rf, d and Dt . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Appendix 20.C: Formulas Adjusted for Time Dependent rf, d and Dt. . . . . . . . 448
C ALIBRATING A TREE, OTHERWISE KNOWN AS CONSTRUCTING an implied tree, meansfinding the stock price and/or associated probability at each node in such a way that the tree reproduces the current market prices for a set of benchmark instruments. The
main benefit of calibrating a model to a set of observed option prices is that the calibrated
model is consistent with today’s market prices. The calibrated model can then be used to
price other more complex or less liquid securities, such as Over The Counter (OTC)
options whose prices may not be available in the market.
