2.2 Multiperiod Binomial Tree Models
2.2 Multiperiod Binomial Tree Models
Rating
Student: contains scenes of mild algebra or calculus that may require guid-
ance.
Section Starter Question
Suppose that you owned a 3-month option, and that you tracked the value of
the underlying security at the end of each month. Suppose you were forced
to sell the option at the end of two months. How would you determine a fair
price for the option at that time? What simple modeling assumptions would
you make?
Key Concepts
- A multiperiod binomial derivative model can be valued by dynamic
programming — computing the replicating portfolio and corresponding
portfolio values back one period at a time from the claim values to the
starting time.
Vocabulary
- The multiperiod binomial model for pricing derivatives of a risky secu-
rity is also called theCox-Ross-Rubenstein modelorCRR model
for short, after those who introduced it in 1979.
Mathematical Ideas
2.2 A binomial tree
The multiperiod binomial model hasN time intervals created by N + 1
trading timest 0 = 0,t 1 ,...,tN =T. The spacing between time intervals
is ∆ti = ti−ti− 1 , and typically the spacing is equal, although it is not
necessary. The time intervals can be any convenient time length appropriate
for the model, e.g. months, days, minutes, even seconds. Later, we will take
them to be relatively short compared toT.