IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
A share of an Indian company is priced at Rs 100. After one year it will be either Rs 120 or Rs 90. The continuously compounded risk-free rate is zero for simplicity. What is the risk-neutral probability of the up-move?
The risk-neutral up probability is 1/3, about 0.33. With a zero interest rate, q is (100 minus 90) divided by (120 minus 90). Weighting 120 by one-third and 90 by two-thirds returns the current price of Rs 100.
- A0.20
- B0.25
- C0.33Correct
- D0.50
- 0.67
Explanation
With r = 0, q = (S0 - Sd)/(Su - Sd) = (100-90)/(120-90) = 10/30 = 1/3. Check: (1/3)(120)+(2/3)(90)=40+60=100. The value 0.67 is the down-move probability.
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