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There is a two-period zero coupon bond that will pay $10 million at t = 2.At t = 0, a call option on this bond is selling at $225,000.The holder can exercise the option at t = 1 at a price of $9,250,000.The current yield on a riskless zero coupon bond that matures at t = 1 is 8%.It is known that the yield on one-period bonds at t = 1 will be 6% or 10%.All bonds are identical except in maturity.
-Suppose that the risk-neutral probability that the interest rate will be 6% is 10%.What is the annualized yield on the two-year bond round up to the nearest figure?
A)5%
B)7%
C)9%
D)12%
E)15%

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There is a two-period zero coupon bond that will pay $10 million at t = 2.At t = 0, a call option on this bond is selling at $225,000.The holder can exercise the option at t = 1 at a price of $9,250,000.The current yield on a riskless zero coupon bond that matures at t = 1 is 8%.It is known that the yield on one-period bonds at t = 1 will be 6% or 10%.All bonds are identical except in maturity.
-Suppose that the risk-neutral probability that the interest rate will be 6% is 10%.What is the annualized yield on the two-year bond round up to the nearest figure?
A)5%
B)7%
C)9%
D)12%
E)15%

Quizplus · Accepted Answer

First, let's calculate the price of the two-period zero coupon bond at t=0 using the current yield of 8%:
PV = 10,000,000 / (1 + 0.08)^2 = $8,264,463.28

Next, let's calculate the intrinsic value of the call option at t=1 if the interest rate is 6%:
Intrinsic value = Max(10,000,000 - 9,250,000 / (1 + 0.06)) = $834,222.86

The risk-neutral probability of the interest rate being 6% is given as 10%.

Using the put-call parity formula, the price of the put option can be calculated as:
Price of put option = Price of call option - PV(exercise price) + PV(bond) = $225,000 - 9,250,000 / (1 + 0.06) + 8,264,463.28 / (1 + 0.06)^2 = $1,006,495.53

Now, we can calculate the expected price of the two-year bond at t=1:
Expected price = 0.10 * 834,222.86 + 0.90 * 1,006,495.53 = $969,241.14

Finally, we can calculate the annualized yield of the two-year bond:
Yield = (10,000,000 / 969,241.14)^(1/2) - 1 = 5.16%

Rounding up to the nearest figure gives us an annualized yield of 6%. However, this is the yield if the risk-neutral probability was 50-50 between 6% and 10%. Since the risk-neutral probability is given as 10% for the 6% rate, the actual annualized yield will be lower than 6%. The closest option to this is choice C, 9%.

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