What method of discounting do I use when computing option pricing with Binomial methods...

[sridhar]

Topic: Computing call option using 2-period binomial trees

David:

If a question on this topic says: ".A stock is priced at 40 and the periodic risk-free rate of interest is 8 percent. What is the value of a two-period European call option with a strike price of 37 on a share of stock using a binomial model with an up factor of 1.20 and a (risk-neutral) up probability of 67 percent?"

From this language, when we compute the PV of the call option say in Period 1 based on payoffs in Period 2 -- do we automatically use the continously compounding" interest rate or the annual interest rate.

That is, do we use the discount factor: exp (- 0.08*1) or 1/(1.08) -- I guess it doesn't matter if the answer choices are unambiguous regardless of which kind of interest rate we use. If the exam provides a choice based on annual compounding and I calculate using continous compounding -- can we be "safe" in assuming that my answer would be somewhat close to the choice provided in the exam.

In other words, should I stop being paranoid about such things

--sridhar

 

[David Harper CFA FRM]

Sridhar,

It's an understandable concern; as the FRM employs a variety of authors, we see different compound frequencies employed (Hull is always continuous, Tuckman is semiannual, and Jorion is sometimes annual). In regard to binomial trees specifically, John Hull has been assigned for several years and he is always continuous. Further, consistent with the Linda Allen reading, continuous compounding/discounting (i.e., being "time consistent" a.k.a., additive) is basically always a safe bet.

The question should say, but otherwise, I think you can take the following approach:

Unless specified (i.e., "use annual compounding"),

* Assume continuous
* Unless it's a bond problem, then assume semi-annual; Tuckman, being US-biased, uses semi-annual throughout. The fixed income chapters have been assigned to Tuckman for years, so this is the appropriate compound frequency for bond related problems (note this includes term structures, Chapter 9, which uses a binomial tree for options on bonds)

David