FRM Part I · FRM Exam Part I · Binomial Trees
When a binomial tree is used to value options on a futures contract, what growth rate is assumed for the futures price in a risk-neutral world?
The futures price is assumed to have zero expected growth in a risk-neutral world. A futures contract costs nothing to enter, so it needs no drift to earn the risk-free return, and the up probability is (1 - d)/(u - d).
- AZeroCorrect
- BThe risk-free rate r
- CThe risk-free rate minus the convenience yield
- DThe risk-free rate minus the dividend yield
Explanation
Entering a futures contract costs nothing, so in a risk-neutral world its expected return is zero and the futures price is a martingale. This gives p = (1 - d)/(u - d). The rate r applies to a non-dividend stock, and r - q applies to an index or currency, not to a futures price.
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