Financial Derivatives B0300850
Assignment01
March14,2014
1.An interest rate is quoted as5%per annum with miannual compounding.What is the equivalent rate with(a)annual compounding,(b)monthly compounding,and(c)continously compounding.
2.The6-month,12-month,18-month,24-month zero rate are4%,4.5%,4.75%and5%,with miannual compounding.
(a)What are the rates with continuous compounding?
(b)What is the foreward rate for the6-month period beginning in18months?
(c)What is the value of a FRA that promis to pay you6%(compounded miannually)on a principal of$1million for the6-month period starting in18months?
3.What is the2-year par yield when the zero rates are as in Problem2?What is the yield on a2-year bond that pays a coupon equal to the par yield?
4.The following table gives the prices of bonds:
碑的组词Bond principal($)Time to maturity(years)Annual coupon1($)bond price($) 1000.500.098
100 1.000.095
内涵段子100 1.50 6.2101胆战心慌
100 2.008.0104
(a)Calculate zero rate for maturities of6months,12months,18months,and24months.
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(b)What are the foreward rate for the following periods:6months to12months,12months
瑞优羊奶1Half the stated coupond is assumed to be paid every six months.
to18months,abd18months to24months?
(c)What are the6months,12months,18months,and24months par yields for bonds that provide miannual coupond payment?早起的鸟儿
中国面积多大(d)Estimate the price and yield of a2-year bond providing a miannual coupond of7%per annum.
5.Portfolio A consists of a1-year zero-coupon bond with a face value of$2,000and a10-year zero-coupon with a face value of$5,000.The current yield on all bonds is10%per annum.
(a)Show that both portfolio have the same duration.
(b)Show that the percentage changes in the value of two portfolios for a0.1%per annum increa in yields are the same.
(c)What are the percentage changes in the value of the two portfolio s for a5%per annum increa in yields?
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