108156.pdf

270 Mathematics for Finance The conditiong<rmust be satisfied or otherwise the series will be divergent. Using this formula a ...

Solutions 271 2.24The ratersatisfies er= ( 1+^012.^12 ) 12 . The solution isr∼= 0 .1194, about 11.94%. 2.25The frequencymsatisfi ...

272 Mathematics for Finance 2.30a) If the continuous compounding rate is 8%, then the price of the bond will be 5e−^0.^08 +5e−^2 ...

Solutions 273 Figure S.2 Coupon bond price versus time in Exercise 2.32 2.35By solving the equation (1 +r)−^1 =0. 89 we find tha ...

274 Mathematics for Finance 2.39Because the bond is trading at par and the interest rates remain constant, the price of the bond ...

Solutions 275 Figure S.4 Tree of price movements in Exercise 3.2 Figure S.5 Tree of price movements in Exercise 3.3 3.5The retur ...

276 Mathematics for Finance relation 1 +K(0,2) = (1 +K)^2 (assuming that 1 +K>0): Scenario K(0,2) K(1) =K(2) ω 1 17 .14% 8 .2 ...

Solutions 277 3.11Since the quarterly returnsK(1),K(2),K(3),K(4) are independent and iden- tically distributed, E(K(1)) =E(K(2)) ...

278 Mathematics for Finance 3.14Given the continuous risk-free rate of 14% and the time stepτ=1/12, we find the one-step return ...

Solutions 279 3.20By Condition 3.3 the random variablesS(1)/S(0) = 1+K(1) andS(2)/S(1) = 1+K(2) are independent, each taking thr ...

280 Mathematics for Finance Chapter 4 4.1We can use the formulae in the proof of Proposition 4.1 to find y(1) =^200 −^35.^24 × 1 ...

Solutions 281 This defines a predictable self-financing strategy. Its time 0 and time 1 value is 0. The value at time 2 will be ...

282 Mathematics for Finance 4.8The put option gives the right (but no obligation) to sell one share of stock for the strike pric ...

Solutions 283 5.2First we putK 2 (ω 2 )=xand compute Var(K 1 )=0. 001875 , Var(K 2 )=0.187 5x^2 +0. 015 x+0. 0003. The two secur ...

284 Mathematics for Finance 5.7First we findE(K 1 ) = 7% andE(K 2 ) = 23%. If the expected return on the portfolio is to beE(KV) ...

Solutions 285 5.13The weights in the portfolio with the minimum variance among all attainable portfolios with expected returnμV= ...

286 Mathematics for Finance 5.18The expected return on the portfolio can be expressed asKV=w 1 K 1 +···+ wnKnin terms of the exp ...

Solutions 287 You will be left with an arbitrage profit of 131 −120e (^1012) ×12% +1e 124 ×12% +2e 121 ×12%∼ = 1. 44 dollars. 6. ...

288 Mathematics for Finance 6.11The return on the index will be 3.37%. ForrF= 1% this gives the futures prices f(0,3)∼= 916 .97 ...

Solutions 289 7.6IfCE−PE<S(0)e−rdivT−Xe−rT, then at time 0 sell short e−rdivT of a share, write and sell a put, and buy a cal ...