Question #10 - Reading 31 Valuation of Contingent Claims

Reading: Reading 31 Valuation of Contingent Claims

PDF File: Reading 31 Valuation of Contingent Claims.pdf

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Shared Context

in five months is a 4.6% T-Bond currently priced at $1,002.33 (full price) per $1,000 par. The CTD paid its last coupon four months ago, and its conversion factor is 1.13. The risk free rate is 2.99%. Peter Wang, one of your colleague, knew of your interest in derivative products advises you to consider interest rate options and swaptions. Wang makes the following comments: Comment 1: An investor having a long position in a call option on a bond has the same position as if he is long an interest rate floor. Comment 2: A borrower of a floating rate loan can create an interest rate collar by buying an interest rate cap and selling an interest rate floor and the cap sets the maximum interest rate payable by the borrower. Comment 3: A payer swaption is the right to enter into a specific swap at some date in the future as the fixed-rate payer. A payer swaption becomes more valuable if an equivalent swap at the market rate is higher than the strike rate.

Question

Which of the following is closest to the no-arbitrage price of the 5-month T-Bond futures contract?

Answer Choices:

A. $867.20

B. $877.47

C. $976.02

Explanation

The no-arbitrage price for T-Bond futures is given by the formula: QFP = {(full price) × (1 + Rf)T – AIT – FVC)(1 / CF) The full price of the bond = clean price + accrued interest. Since the bond pays semi- annual coupons, and four months have passed since the last coupon, there are two months until the next coupon. Accrued interest (AI) = (days since last coupon / days between coupons) × $ semiannual coupon. In this question we have not been told days but instead have months. AIT in the formulae represents the accrued interest at the maturity of the futures contract. Given the last coupon was 4 months ago the next coupon of $23 will be in two months' time. At the maturity of the futures contract in five months we will be 3 months through the coupon period, hence: AIT = (3 months / 6 months) × $23 = $11.5 The next coupon will be in two months' time (four months' ago, plus six months) and will equal $23. FVC in the above formula is this coupon compounded up to the futures maturity, three months later, so FVC = $23 × 1.02993 / 12 = $23.17. Thus, QFP = [($1,002.33 × 1.02995 / 12) – $11.5 – $23.17] / 1.13 = $867.20

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