货币时间价值与利率期限结构清华大学绝金融工程PPT学习教案

1、会计学1 货币时间价值与利率期限结构清华大学货币时间价值与利率期限结构清华大学 绝金融工程绝金融工程 2 第1页/共38页 3 第2页/共38页 4 Four basic factors 第3页/共38页 5 第4页/共38页 6 第5页/共38页 7 01 00 11 max ( )( ) . (1) u cu c st ceb cer b 第6页/共38页 8 01 10 000 100 ()(1)( ) () ()()1 1(1/1) ( )() u cru c orfor ccdc u cc ucdc r u cu cc 00 00 ()1 (1/1) () c ucdc r u cc

2、 Relative risk aversion coefficient Thus, the real interest rate is given by 第7页/共38页 9 Time 0 Time 1 01 (,)c c 2 u 1 u 0 e 1 e - (1+RC) Investment opportunity set 21 uu b b(1+r) 第8页/共38页 10 Time 0 Time 1 01 (,)c c b (1+r)b 2 u 1 u 0 e 1 e 21 uu - (1+RC) 第9页/共38页 11 0 0012 max() . . (1)1. T t t t T

3、t ttt Eu c s tcebbb cerbtT 1 ( ,.) T bb 1 ( ,.) T ee 1 ( ,.) T cc 第10页/共38页 12 Yield to Maturity (YTM) YTM varies with different financial instruments, because the exposure of financial instruments are quite different and the required risk premiums differ from each other. Risk-free interest varies w

4、ith terms . Its called the term structure of interests. Risk-free interests ? ? No! Yes! 第11页/共38页 13 Compound interest interest earned on interest already earned )1ln( * rr Continuously compounding r simple rate of return annually m times of interest payments annually r m 1 compounding rate of inte

5、rest payments annually m r r m m m 11 1 m Let r r m e m m r lim 111 Continuously compounding 第12页/共38页 14 Basic financial risks: Risk-free security: Substitute in reality: Treasury 第13页/共38页 15 ntr t , 1, Zero-coupon rates set Bills are zero coupon while notes and bonds have coupons. Zero-coupon rat

6、es set can be obtained by conversion. 第14页/共38页 16 1 year 10% 0A 2 years 1,00 0 1,00 0 910.50 982.10 %83. 9 50.910 50.9101000 1 r 2 2 2 21 )1 ( 1100 %83. 91 100 )1 ( 1001000 1 100 10.982 rrr %08.11 2 r B 第15页/共38页 17 Shapes of Yield Curve upwardflat downwar d Some theories for the shapes of yield cu

7、rve Unbiased expectations theory Liquidity preference theory Market segment theory Preferred habitat theory 第16页/共38页 18 115$%)151 (100$F . One years risk-free rate A mini case: 100$ 0 S %5 f r . What is one years forward price of this stock? ? 第17页/共38页 19 Position Immediate Cash Flow Cash Flow in

8、the Future Replicating Stock Using risk-free bond and forward contract Suppose forward price F = $106 per share Short sell $100 risk- free bond Short sell one stock forward at $106 per share Buy one stock at $100 per share +$100 $105 0106 S1 $100S1 Net Cash Flow0$1 Arbitrage Stock forward price = $1

9、05 per share 第18页/共38页 20 Forward price of a risky asset is not the expectation of the future spot price of the asset. Proposition! 第19页/共38页 21 nBuy spot e -qT of the asset and reinvest income from the asset in the asset. nShort a forward contract on one unit of the asset. 第20页/共38页 22 0T Se- qT F

10、Se-qT=Fe-rT F=Se(r-q)T 第21页/共38页 23 Forward interest rates are the expectation of future risk-free spot interest rates. 0123n Zero-coupon rates & forward interest rates )1)(1 ()1 ( 211 2 2 frr )1 ()1)(1)(1 ()1 ( 132211nn n n fffrr 第22页/共38页 24 Zero-coupon rates, discount factors & forward interest r

11、ates v rt t t 1 1 v r t t t 1 1 f v v m j j j 1 1, r t v t t 1 1 1 r v t t t 1 1 v01 v v f m j j j 1 1 1 Discount factors t v Forward rates j f Zero- coupon rates tr 第23页/共38页 25 第24页/共38页 26 第25页/共38页 27 Buyin g an FRA Floating rate deposit Starting t1 ending t2 Fixed rate Loan Starting t1 ending t

12、2 = + 第26页/共38页 28 第27页/共38页 29 Swap Price Interest rate swap 02nt1 102nt Cash Flow of Buyer Cash Flow of Seller 第28页/共38页 30 Interest Rate Swap Quotation for LIBOR 第29页/共38页 31 Pricing Par Bonds 0 )1 ()1 ( 1 0 n n t t r Par r iPar PNPV Par i Par iPar i P0 Par 0 1 2 n t ParPthenriIf 0 , 第30页/共38页 32

13、 Zero-coupon pricing technique 0 1 2 . n t Par Par Par*i Par*i Par*i Pa r 0 1 2 n tPar*f1 Par*f 2 Par*f n Par 0 1 2 n t Par*i Par*i Par*i Par*f 1 Par*f 2 Par*f n Investment Cash Flow Financing Cash Flow n n n t t t r Par r iPar ParNPV )1 ()1 ( 1 0 n t t t n n r r i 1 )1( 1 )1( 1 1 第31页/共38页 33 Furth

14、er illustration of composition & decomposition 0 1 2 n t Par*f 1 Par*f2 Par*f n Pa r Pa r 0 1 2 n t Par*f 1 Par*f2 Par*f n + 0 1 2 n t Pa r Pa r = 0 NPV = 0 0 1 2 n t Pa r Pa r = Decompositio n of finance cash flow 第32页/共38页 34 第33页/共38页 35 102nt 1 2 3 第34页/共38页 36 Currency Swap 0 1 2 . n t P1 P1 i1 i1 i1 0 1 2 . n t P2 P2 i2 i2 i2 Fixed interest rate currency swap 0 1 2 . n t P1 i1 i1 i1 P2 i2 i2 i2 第35页/共38页 37 第36页/共38页 38 Summary of Chapter Two 1. Time Value of Money Term Structure o