IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
In a one-period binomial model a share priced at Rs 100 moves to Rs 120 or Rs 80. The one-period risk-free rate is 5% (simple, discrete). What is the risk-neutral probability of an up move?
The risk-neutral up probability is 0.625. It is the forward value of the share, 105, minus the down price 80, divided by the spread between up and down prices, 40, giving 25 over 40. It is not 0.5, which ignores interest.
- A0.50
- B0.5625
- C0.625Correct
- D0.70
- 0.5250
Explanation
q = (S(1+r) - Sd)/(Su - Sd) = (105 - 80)/(120 - 80) = 25/40 = 0.625. Using 0.5 ignores the interest rate. 0.5625 uses a mistaken numerator of 22.5.
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