Frequently Asked Questions In Quantitative Finance

282 Frequently Asked Questions In Quantitative Finance It follows that y=− lnZ T−t . Suppose that we have a coupon-bearing bond. ...

Chapter 5: Models and Equations 283 This is the slope of the price/yield curve. The quantity − 1 V dV dy is called theMacaulay d ...

284 Frequently Asked Questions In Quantitative Finance simplest of these assumes a deterministic evolution of a spot rate. The s ...

Chapter 5: Models and Equations 285 Writing this in terms of yieldsy(t;T)wehave Z(t;T)=e−y(t;T)(T−t) and so F(t;T)=y(t;T)+ ∂y ∂T ...

286 Frequently Asked Questions In Quantitative Finance Now move on to the second bond having maturity date T 2. We know the rate ...

Chapter 5: Models and Equations 287 the bond is significantly greater than the expiration of the option. The relevant formulæ ar ...

288 Frequently Asked Questions In Quantitative Finance The floorlet can be thought of in a similar way in terms of a put on the ...

Chapter 5: Models and Equations 289 In all of the spot rate models below we have dr=u(r,t)dt+w(r,t)dX as the real process for th ...

290 Frequently Asked Questions In Quantitative Finance witha,bandcbeing constant. As long asais suffi- ciently large this proces ...

Chapter 5: Models and Equations 291 Two-factor models In the two-factor models there are two sources of ran- domness, allowing a ...

292 Frequently Asked Questions In Quantitative Finance Hull and White The risk-neutral model dr=(η(t)−u−γr)dt+cdX 1 and du=−au d ...

Chapter 5: Models and Equations 293 rate,F, and its volatility,α, both of which are stochastic: dF=αFβdX 1 and dα=ναdX 2. There ...

294 Frequently Asked Questions In Quantitative Finance A multi-factor version of this results in the following risk-neutral proc ...

Chapter 5: Models and Equations 295 where the expectation is with respect to the risk-neutral process(es). The ‘present value’ h ...

296 Frequently Asked Questions In Quantitative Finance whereDis the amount of the debt, to be paid back at timeT. If we can hedg ...

Chapter 5: Models and Equations 297 If the yield on a risk-free, i.e. government bond, with maturityTisrthen its value is e−r(T− ...

298 Frequently Asked Questions In Quantitative Finance Heath, D, Jarrow, R & Morton, A 1992 Bond pricing and the term struct ...

Chapter 6 TheBlack–Scholes Formulæandthe Greeks ...

300 Frequently Asked Questions In Quantitative Finance I n the following formulæ N(x)= 1 √ 2 π ∫x −∞ e− 1 2 φ 2 dφ, d 1 = ln(S/K ...

Chapter 6: Black–Scholes and Greeks 301 Table 6.1:Formulæ for European call. Call Payoff max(S−K,0) ValueVSe−D(T−t)N(d 1 )−Ke−r( ...