金融工程課堂展示ppt課件

1、OPTIONS、FUTURES & OTHERDERIVATIVESSTUDENT PRESENTATIONTUTOR：PROF YE指點教師：葉永剛教授STUDENT NAME：HEHAO學生姓名：賀昊NO.：2003210507731. Extension of theTheoretical Framework for Pricing Derivatives;Martingales and Measures Chapter 192.Derivatives Dependent on a Single Underlying Variable3.Forming a Riskless Portfo

2、lio4.Market Price of Risk (Page 500)This shows that (m r )/s is the same for all derivatives dependent on the same underlying variable, qWe refer to (m r )/s as the market price of risk for q and denote it by l5.Differential Equation for (Equation 19.10, page 501)Using Itos lemma to obtain expressio

3、ns for m and s in terms of m and s. The equation m-ls=r becomes6.Risk-Neutral ValuationThe differential equation shows that q is like a stock price paying a dividend yield of r m + lsThis analogy shows that we can value in a risk-neutral world providing the drift rate of q is reduced from m to m ls7

4、.Extension of the Analysisto Several Underlying Variables(Equations 19.12 and 19.13, page 503)8.Derivatives Dependent on Commodity Prices (Page 506)For a commodity the futures price gives the expected value in the traditional risk-neutral world9.Martingales (Page 507)A martingale is a stochastic pro

5、cess with zero drfitA martingale has the property that its expected future value equals its value today10.Alternative Worlds11.A Key Result (Page 509) 12.Forward Risk NeutralityWe refer to a world where the market price of risk is the volatility of g as a world that is forward risk neutral with resp

6、ect to g.If Eg denotes a world that is FRN wrt g13.Aleternative Choices for the Numeraire Security gMoney Market AccountZero-coupon bond priceAnnuity factor14. Money Market Accountas the NumeraireThe money market account is an account that starts at $1 and is always invested at the short-term risk-f

7、ree interest rateThe process for the value of the account isdg=rgdtThis has zero volatility. Using the money market account as the numeraire leads to the traditional risk-neutral world15.Money Market Accountcontinued 16.Zero-Coupon Bond Maturing at time T as Numeraire 17.Forward PricesIn a world tha

8、t is FRN wrt P(0,T), the expected value of a security at time T is its forward price18.Interest RatesIn a world that is FRN wrt P(0,T2) the expected value of an interest rate lasting between times T1 and T2 is the forward interest rate19.Annuity Factor as the Numeraire20.Annuity Factors and Swap Rat

9、esSuppose that Sn,N is the swap rate corresponding to the annuity factor An,NIn a world that is FRN wrt the annuity factor, the expected swap rate equal the forward swap rate21.Extension to Several Independent Factors (Page 513)22.Extension to Several Independent Factorscontinued23.Applications(Sect

10、ion 19.7, page 514)Valuation of a European call option when interest rates are stochasticValuation of an option to exchange one asset for another24.Change of Numeraire(Section 19.8, page 517)25.Quantos(Section 19.9, page 518)Quantos are derivatives where the payoff is defined using variables measured in one currency and paid in another currencyExample: contract providing a payoff of ST K dollars ($) where S is the Nikkei stock index (a yen number)26.Diff SwapDiff swaps are