金融风险管理理论与实务.pptVIP

Antithetic variable technique uses twice the same sequence of random draws from t to T. It takes the original sequence and changes the sign of all their values Control variate technique a similar option has an analytical solution Quasi-random sequences create draws that are not independent but instead are designed to fill the sample space more uniformly many sources of financial risk V(ε) = E(εε‘)= R the matrix R is a symmetric real matrix, it can be decomposed into its so-called Cholesky factors (Cholesky factorization) construct the transformed variable ε = Tη V(ε) =E(εε) = E((Tη)(Tη)) = E(TηηT) = TE(ηη)T = TV(η)T = TIT = TT = R The covariance matrix, for instance, has dimensions N(N + 1)/2. A portfolio with 500 variables requires a matrix with 125,250 entries. In practice, the risk manager should simplify the number of risk factors. Principal component analysis (PCA) finds linear combinations of the risk factors that have maximal explanatory power. REAL DATA NORMAL AND LOGNORMAL DISTRIBUTIONS DISTRIBUTIONS WITH FAT TAILS TIME VARIATION IN RISK a sequence of past prices P0,P1,…,Pt, and the distribution of tomorrow‘s price, Pt + 1, should be inferred. whether the sequence of variables rt can be viewed as independent observations The hypothesis of efficient markets postulates that current prices convey all relevant information about the asset. random walk theory independent and identically distributed (i.i.d.) Rt,2=ln(Pt/Pt-2)=ln(Pt/Pt-1)+ ln(Pt-1/Pt-2) multiple-period expected return and volatility are μT= μT σT= σ sqrt(T) When successive returns are uncorrelated, the volatility increases as the horizon extends following the square root of time. Rt,2=ρRt-1+ut V(Rt+Rt-1)= σ 2 ×2(1+ ρ) ρ is called the autocorrelation coefficient, or the serial autocorrelation coefficient A positive value for ρ describes a situation where a movement in one direction is likely to be followed by another in the same direction. A negative value for ρ, by contrast, describes