108156.pdf

250 Mathematics for Finance when it has just one price independent of the state, namely the face value. We are looking for a pro ...

Stochastic Interest Rates 251 We can see that the no-arbitrage conditions are satisfied: 0.84%< 0 .99%< 1 .25%, 0 .27%&l ...

252 Mathematics for Finance value of the following random cash flow: At time 2 we receive $20 in the state uu, $10 in the states ...

Stochastic Interest Rates 253 Proof Consider two bonds with maturitiesM≤Nand fix ann≤M. For each of the two bonds we have B(n, ...

254 Mathematics for Finance Figure 11.15 Data for Exercise 11.10 model the cash flow associated with the derivative security can ...

Stochastic Interest Rates 255 the consecutive values discounted by the appropriate short rates: n=0 n=1 n=2 0. 0005 0. 00041 & ...

256 Mathematics for Finance Example 11.10 Consider a fixed-coupon bond and a floating-coupon bond, both with annual coupons, tra ...

Stochastic Interest Rates 257 annual compounding): AB fixed 11 .40% 13 .40% variable LIBOR + 2% LIBOR + 3% In this case we say ...

258 Mathematics for Finance the fixed rate of 13.40% it was offered. This means a gain of $360 in each year on an $100,000 loan. ...

Stochastic Interest Rates 259 The price of the bond is reduced by the value of the caplet, that is, by 0.32773. For a caplet a ...

260 Mathematics for Finance we need a model of possible movements of bond prices for each maturity. The bond prices with differe ...

Stochastic Interest Rates 261 These problems can be avoided if some middle-of-the-road solution is adopted. Yet another altern ...

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Solutions....................................................... Chapter 1 1.1The value of the portfolio at time 0 is V(0) =xS(0 ...

264 Mathematics for Finance Use dealerAto change 1 dollar into 1. 58441 ∼= 0 .6312 pounds. Use dealerBto change 0.6312 pounds i ...

Solutions 265 1.7a) The payoff of a call option with strike price $90 will be C(1) = { 30 if stock goes up, 0 if stock goes down ...

266 Mathematics for Finance 1.9We need to find an investment intoxshares andybonds replicating the put option, that is, such tha ...

Solutions 267 2.3The timetsatisfies (1 +t× 0 .09)×800 = 830, which givest∼= 0 .4167 years, that is, 0. 4167 × 365 ∼= 152 .08 day ...

268 Mathematics for Finance 2.9The initial principalPsatisfies the equation (1 + 0.12)^2 P=1, 000. It follows thatP∼= 797 .19 do ...

Solutions 269 The capital repaid as part of thenth instalment is the difference between the outstanding balance of the loan afte ...