108156.pdf

210 Mathematics for Finance Figure 9.5 Decomposition of a target payoff into options and down price jumps. We also assume for si ...

Financial Engineering 211 is random and depends on the stock price after 20 days, KC= (S(20/365)−60)+−C C . To compute the exp ...

212 Mathematics for Finance 4.Options Combined with Risk-Free Investment.The risk can be ad- justed to an arbitrary level if opt ...

Financial Engineering 213 We shall build a simple model reflecting the analysts’s point of view. Addi- tional information obta ...

214 Mathematics for Finance The bull spread combined with risk-free will clearly be preferable to the other investments as it ha ...

10. Variable Interest Rates..................................... This chapter begins with a model in which the interest rates im ...

216 Mathematics for Finance 10.1 Maturity-Independent Yields............................... The present value of a zero-coupon u ...

Variable Interest Rates 217 As a consequence of Proposition 10.1, if the yield is independent of maturity and deterministic (t ...

218 Mathematics for Finance onebasis point, so here the rate drops by 100 basis points.) ThenB(6,12)∼= 0 .9692, which is more th ...

Variable Interest Rates 219 points on day 180,and remains at this level until the end of the year. If a bond is bought at the ...

220 Mathematics for Finance If the lifetime of our investment exceeds one year, we will be facing the problem of reinvesting cou ...

Variable Interest Rates 221 higher because so is the price at which we sell the bonds after three years. Year 0 1 2 3 Rate 12% ...

222 Mathematics for Finance hand, we do not gain in other circumstances. This is explained by the fact, that a certain parameter ...

Variable Interest Rates 223 Duration measures the sensitivity of the bond price to changes in the interest rate. To see this w ...

224 Mathematics for Finance If the duration of the bond is exactlyt,then d dy(P(y)e ty)=0. If the derivative is zero at some poi ...

Variable Interest Rates 225 Differentiating the last expression, we obtain d dy(PA(y)+PB(y)) = d dyPA(y)+ d dyPB(y) =−DA(y)PA( ...

226 Mathematics for Finance Exercise 10.12 Invest $1,000 in a portfolio of bonds with duration 2 using 1-year zero- coupon bonds ...

Variable Interest Rates 227 Example 10.8 The bond in Example 10.7 will have duration 4.23 ify=6%,and4.08 if y= 14%. Exercise 1 ...

228 Mathematics for Finance the face values ofB: $51, 376 .39, the market value ofA, selling at $101.46: $36, 682 .22. The resu ...

Variable Interest Rates 229 10.2 General Term Structure ................................... Here we shall discuss a model of b ...