IAI Actuarial Core Principles · Economic Modelling · Binomial option-pricing model
Two investors disagree about the real-world probability that a share will rise in a one-period binomial model, one believing 0.7 and the other 0.4. Both accept the same share prices, up and down values and risk-free rate. Which statement about the no-arbitrage price of a call option on the share is correct?
The no-arbitrage price is identical for both investors. It is fixed by replication, equivalent to discounting expected payoff under the risk-neutral probability, which depends only on prices, up and down factors and the risk-free rate, not on beliefs or risk aversion.
- AThe investor with 0.7 should value it higher, since the up-move is more likely
- BThe price is the average of the two investors' expected payoffs
- CThe price is the same for both, as it depends only on the risk-neutral probabilityCorrect
- DThe price depends on each investor's risk aversion
- The price cannot be determined without the real-world probability
Explanation
The call can be replicated by shares and cash, so its arbitrage-free price depends only on the replicating portfolio cost, equal to the discounted expected payoff under q. Real-world probabilities and risk preferences do not enter.
Did you get it right without looking?
One question tells you little. A timed set on Binomial option-pricing model shows your real accuracy, how long you take and where you lose marks.
More Binomial option-pricing model questions
- In a binomial tree, the holder of an American put compares, at each node, the value from exercising now with the value from continuing. Whic…
- Which statement about the no-arbitrage argument used to price options in the binomial model is correct?
- In a binomial model for a non-dividend-paying share with a positive interest rate, which statement correctly explains why an American put ma…
- A share is priced at Rs 100. In one period it moves to either Rs 125 or Rs 80, and the risk-free rate is 10% for the period. A one-period Am…
- 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). Wh…
- 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 ra…