AIM: Relate the difference between true and risk-neutral probabilities to interest rate drift.
AIM: Relate the difference between true and risk-neutral probabilities to interest rate drift.
42.1 Assume a binomial interest rate tree where the six-month rate either jumps up 50 basis points or jumps down 50 basis points. The real-world (or “true”) probabilities are 50% and 50% for each up- and down-state. If the interest rate drift is +20 basis point under risk-neutral probabilities, what is the risk-neutral probability of an up-state (p)?
* a. 50%
* b. 60%
* c. 70%
* d. 80%
42.2 Which of the following is MOST essential to the argument that contingent claims can be valued with risk-neutral pricing?
* a. The no-arbitrage price is invariant to investor risk preferences
* b. The no-arbitrage price accounts for investor risk preferences
* c. Investors are risk-neutral in the imaginary world
* d. The discount rate impounds investor risk aversion
42.3 In regard to the valuation of contingent claims (derivatives) by risk-neutral pricing, each of the following is true EXCEPT for:
* a. Expected discounted value will equal arbitrage price
* b. We must assume the growth (return) on the underlying equals the risk-free rate
* c. The risk-free discount rate is appropriate
* d. The derivative price is the same in the imaginary world (risk-neutral investors) and the real world
Answers:
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42.1 Assume a binomial interest rate tree where the six-month rate either jumps up 50 basis points or jumps down 50 basis points. The real-world (or “true”) probabilities are 50% and 50% for each up- and down-state. If the interest rate drift is +20 basis point under risk-neutral probabilities, what is the risk-neutral probability of an up-state (p)?
* a. 50%
* b. 60%
* c. 70%
* d. 80%
42.2 Which of the following is MOST essential to the argument that contingent claims can be valued with risk-neutral pricing?
* a. The no-arbitrage price is invariant to investor risk preferences
* b. The no-arbitrage price accounts for investor risk preferences
* c. Investors are risk-neutral in the imaginary world
* d. The discount rate impounds investor risk aversion
42.3 In regard to the valuation of contingent claims (derivatives) by risk-neutral pricing, each of the following is true EXCEPT for:
* a. Expected discounted value will equal arbitrage price
* b. We must assume the growth (return) on the underlying equals the risk-free rate
* c. The risk-free discount rate is appropriate
* d. The derivative price is the same in the imaginary world (risk-neutral investors) and the real world
Answers:
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