Given instruments in the following table

(a) Extract the semiannual discount factors for 10 years using the bootstrap method with linear and log-linear interpolation in discount factors.

(b) On the same graph, plot the semiannual zero-coupon yields (Formula 2.8 with \(w=0\) ) for \(6 \mathrm{~m}, 1 \mathrm{y}, \ldots, 10 \mathrm{y}\) maturities for linear and \(\log\)-linear interpolation methods.

(c) Using the discount factor curve from the log-linear interpolation, compute the price of a 5 -year, \(1 \%\) semiannual coupon bond and convert the price using Formula 2.5 to a semiannual yield. Do the same with a semiannual coupon rate of \(8 \%\) to observe the coupon effect on yields.

Hint: See Table 2.5

Table  2.5

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Instrument 6m (182 day) T-Bill 2y Treasury 3y Treasury Sy Treasury 7y Treasury 10y Treasury Semiannual Market coupon rate yield 0% 0.75% 1.375% 1.40% 2.125% 2.00% 2.5% 3% 3.25% Market price 99.62083% 99.95086% 100.36222% 2.50% 100% 2.90% 100.62942% 3.20% 100.42501%