1. Current (annualised) US Treasury spot rates are as follows:

6 months	1 year	18 months	2 year
0.4%	0.5%	0.6%	0.66%

Assuming that Z-spread is equal to 55 basis points, calculate the bonds arbitrage free price. Show calculations.

1. If the bond is bought today at the arbitrage-free price and sold on 30 Sep 2017 at $101.10, what will be realised rate of return on bond. Show calculations.
2. From the US treasury spot rates above and assuming Z-spread of 55 basis points, calculate spot rates for this bond. Show calculations.
3. Using the bond-specific spot rates you have just calculated in Question 5, derive six-monthly forward rates, including six-months forward rate 6 month from now (_0.5f_0.5), six-month forward rate 12 months from now (₁f_0.5), and six-months forward rate 18 months from now (_1.5f_0.5) for the bond. Show calculations.
4. Estimate the bonds arbitrage free price using forward rates calculated in Question 6 and comment on comparability of spot rate and forward rate pricing. Show calculations.
5. There is another BHP Billiton 2.5 year semi-annual 2% coupon-paying bond in the market priced at $100.85. Using the bond-specific spot rates as calculated in Question 5 (for 0.5 year, 1 year, 1.5 year and 2 years), bootstrap 2.5-year spot rate for the bond. Show calculations.
6. Estimate the original bonds (displayed in Figure 1) Macaulay Duration and Convexity. Show calculations.

Hint: for semiannual coupon paying bonds you will be using the semiannual cash flows, yields and periods as inputs for your calculation of the Macaulay Duration and Convexity. You will need to convert the output of your calculations into the annualised (standard) form. To do that you should divide Macaulay Duration and Convexity based on the semiannual periods by 2 and 4 respectively to arrive with the final answer.

7. Estimate the original bonds (displayed in Figure 1) Approximate Modified Duration and Approximate Convexity by applying 12bp interest rate shock to annualised yield to maturity. Show calculations.
8. Assume the following interest rate tree

			2.18%
		1.82%
	1.34%		1.62%
0.95%		1.35%
	0.99%		1.20%
		1.00%
			0.89%
Current 6-month rate	6 months	12 months	18 months

1. Calculate value of the (option-free) bond using binomial model.
2. Assume the bond is callable on 30 Sep 2017 and 30 Mar 2018 at $100.40, calculate the value of the bond.
3. Calculate value of the call option and comment on who bears the cost of the call option.