4.1.f. If q = periods/year under one frequency and m = periods/year under anotherfrequency, then:(1+Rm/m)^(mn) = (1+Rq/q)^(qn), such that(1+Rm/m)^m = (1+Rq/q)^qRm = [(1+Rq/q)^(q/m)-1]*mIn this case, we can covert 14% quarterly to semi-annual directly with:[(1+14%/4)^(4/2) – 1]*2 = 14.245%Discuss here in forum:Hull 4.2What is meant by LIBOR and LIBID. Which is higher?Answer:Licensed to Assel Mussagul at [email protected] Downloaded February 11, 2018.The information provided in this document is intended solely for you. Please do not freely distribute.
135LIBOR is the London InterBank Offered Rate. It is calculated daily by the British BankersAssociation and is the rate a AA-rated bank requires on deposits it places with other banks.LIBID is the London InterBank Bid rate. It is the rate a bank is prepared to pay on deposits fromother AA-rated banks. LIBOR is greater than LIBID.Hull 4.3The 6-month and 1-year zero rates are both 10% per annum. For a bond that has a life of 18months and pays a coupon of 8% per annum (with semiannual payments and one having justbeen made), the yield is 10.4% per annum. What is the bond’s price? What is the 18-monthzero rate? All rates are quoted with semiannual compounding.Answer:Suppose the bond has a face value of $100. Its price is obtained by discounting the cash flowsat 10.4%. The price is4/1.052 + 4/1.052^2 + 4/1.052^3 = 96.74If the 18-month zero rate is R, we must have4/1.05 + 4/1.05^2 + 104/ (1 + R/2)^3 = 96.74which gives R = 10.42%.Hull 4.4An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate thepercentage return per annum with:a) Annual compoundingb) Semiannual compoundingc) Monthly compoundingd) Continuous compoundingAnswers:a)With annual compounding the return is (1100/1000) – 1 = 0.1 or 10% per annum.b)With semi-annual compounding the return is R where 1000(1 + (R/2)^2 = 1100; i.e.,semi-annual R = 9.7618%c)With monthly compounding, R = 9.57% per annum.d)With continuous compounding, R = 9.53% per annum.The answers are also given in this spreadsheet.Licensed to Assel Mussagul at [email protected] Downloaded February 11, 2018.The information provided in this document is intended solely for you. Please do not freely distribute.
136Hull 4.5Suppose that zero interest rates with continuous compounding are as follows:Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters.Answers:The forward rates with continuous compounding are as follows:Qtr 2: 8.4%Qtr 3: 8.8%Qtr 4: 8.8%Qtr 5: 9.0%Qtr 6: 9.2%Licensed to Assel Mussagul at [email protected] Downloaded February 11, 2018.The information provided in this document is intended solely for you. Please do not freely distribute.
137Hull 4.6Assuming that zero rates are as in Problem 4.5 (above), what is the value of an FRA thatenables the holder to earn 9.5% for a 3-month period starting in one (1) year on a principal of$1,000,000? The interest rate is expressed with quarterly compounding.
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