We introduce two day-count conventions: - T^{A}(t,T) = 30/360 in years. It measures the distance...
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We introduce two day-count conventions: - T^{A}(t,T) = 30/360 in years. It measures the distance between dates t and T as thirty times the number of entire months comprised between the two dates plus the actual number of residual days, all divided by 360. - T^{S}(t,T) = ACTUAL/90 is the quarter-based equivalent of the ACTUAL/360 convention. It thus measures the distance between dates t and T as the number of days comprised between the two times divided by 90. At time t=1/1/2013, we observe under T^{S}, the following term structure of semiannually compounded spot rates quoted per quarter (p.q.=0.25 years): R_{T1}(t)=1.0% p.q, R_{T2}(t)=1.5% p.q.,R_{T3}(t)=2.1% p.q., with maturities: T1= 1/7/2013, T2= 1/1/2014, T3= 1/1/2015. (Remark: here, time unit = 1 quarter, day count convention =T^{S}, compounding rule = discrete, with Delta = 0.5 years). a) Show that 1 actual quarter may be strictly greater than 1 quarter as measured by T^{S}. Then, calculate all: b) spot LIBORs, c) forward LIBORs d) forward monthly compounded rates, each quoted per annum (p.a.) under the day-count convention T^{A}
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