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Consider the Treasury bond futures prices on p. 3. These prices are quoted as percent of par value for a $100,000 bond so the settlement price for the Dec futures contract (139-02) implies a price of 139 2/32% of par, or $139,062.50. Assume that the expiration date is December 31 and calculate the number of days to expiration. Find the riskless interest rate (p. 5) that most closely corresponds to the futures contract period. Consider the cost of carry model for bond futures: F0 = S0 e(r - y)T (3) where r and y are the continuously compounded interest rate and coupon yield. Treasury bond futures are based on a 6% coupon bond which pays semiannual coupons; therefore, the annualized and continuously compounded coupon yield is ln(1.03)2 = 0.0591.
a. Assume that the spot price of the underlying Treasury bond is $100,000. What should be the Dec 2022 futures price?
b. Given that the actual futures price is different than the one you computed in part a, the spot bond price must not be $100,000. What is the spot bond price that sets the futures price in equation (3) equal to the actual futures price?
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