Old Exam question question - Exam 6, 2002, Question 3.

[jlwallis2]

Exam 6, 2002, Question 3.

This question has come up as a review question in my study manual (CSM).

You are given the following information:
i) All options have nine months to expiry
ii) All options have a strike price of 49.
iii) Current stock price is $50.
iv) Volatility is 30%
v) The risk-free rate with continuous compounding is 5% per annum.

Using the binomial option pricing model and a three-month step, calculate the cost of a European put.

I'm fine with answering this, except for one point. MacDonald states:

u=e^[(r-delta)h+sigma(sqrt(h))]

but the solution for this question states:
u=e^[sigma(sqrt(h))]

What am I missing? Why would the forward price be ignored in this calculation.. or is it that delta is assumed to equal r?

(Note: r is the risk-free rate with continuous compounding
delta is the stock's continuous dividend yield,
sigma is volatility and h is the time period.)

[Abraham Weishaus]

Perhaps the textbook used for the course at the time used the Cox binomial tree.

The tree based on forward prices is McDonald's preferred method, but is not the only binomial tree available.

I think CSM should've mentioned in the question that the Cox tree is to be used, since in the context of the current syllabus this cannot be taken for granted.

[Actuarialsuck]

This is discussed in ASM I believe, depends what you center around.

If it's r \, - \, \delta then u \, = \, e^{(r \, - \, \delta)h \, + \, \sigma \sqrt{h}}

If it's 1 then u \, = \, e^{\sigma \sqrt{h}} (C - R - R)

If it's r \, - \, \delta \, - \, \frac{1}{2} \sigma^{2} then u \, = \, e^{(r \, - \, \delta \, - \, \frac{1}{2} \sigma^{2})h \, + \, \sigma \sqrt{h}} (lognormal / J - R)

IIRC...

[jlwallis2]

Ah yes, now I remember this stuff.

Thanks.