FRM Part I · FRM Exam Part I · Binomial Trees
A stock is at USD 40 and in six months will be USD 44 or USD 36. A six-month European call has a strike of USD 40, and the risk-free rate is zero. What is the value of the call?
The call is worth USD 2.00. With a zero interest rate the risk-neutral up probability is 0.5, and the up payoff of 4 times 0.5 gives 2.00.
- AUSD 1.00
- BUSD 2.00Correct
- CUSD 2.50
- DUSD 4.00
Explanation
With r = 0, p = (1 - 0.9)/(1.1 - 0.9) = 0.5. Call payoff up = 4, down = 0. Value = 0.5 x 4 = 2.00. USD 4.00 ignores probability weighting.
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