Replacting Callable Band

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AIMS: Using replicating portfolios develop and use an arbitrage argument to price a call option on a zero-coupon security. In addition: Explain why the option cannot be properly priced using expected discounted values. Explain the role of up-state and down-state probabilities in the option valuation.
Questions:

40.1 Assume the market six-month and one-year spot rates are 2.0% and 2.2%, respectively. Assume, per Tuckman’s two-step binomial interest rate tree (i.e., each step is six months), that the six months from now the six-month rate will be either 2.5% (+0.5%) or 2.0% (-0.5%) with equal probability. If a bond’s face value is $1,000, what is the market price of the bond (note: Tuckman assumes semi-annual compounding)?

* a. $968.45
* b. $964.63
* c. $978.36
* d. $982.12

40.2 What are the risk-neutral probabilities?

* a. p = 90.1% and 1-p = 9.9%
* b. p = 9.9% and 1-p = 90.1%
* c. p = 80.1% and 1-p = 19.9%
* d. p = 19.9% and 1-p = 80.1%

40.3 Use a replicating portfolio to determine the price of a call option, that matures in six months, to purchase the $1,000 face value bond at a strike price of $990. What is the market price of the call option?

* a. $0.25
* b. $1.25
* c. $3.25
* d. $9.25

40.4 What is the discounted expected value of the call option?

* a. $0.97
* b. $1.27
* c. $1.97
* d. $2.37

Answers:

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