By Peter Christoffersen
The moment version of this best-selling publication expands its complicated method of monetary possibility versions by way of overlaying marketplace, credits, and built-in danger. With new information that conceal the new monetary main issue, it combines Excel-based empirical workouts on the finish of every bankruptcy with on-line routines so readers can use their very own information. Its unified GARCH modeling technique, empirically refined and correct but effortless to enforce, units this publication except others. 5 new chapters and up-to-date end-of-chapter questions and workouts, in addition to Excel-solutions guide, aid its step by step method of identifying instruments and fixing problems.
- Examines marketplace hazard, credits hazard, and operational hazard
- Provides remarkable insurance of GARCH versions
- Features on-line Excel-based empirical routines
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Additional info for Elements of Financial Risk Management
We now turn to various methods for constructing the covariance matrix t+1 directly, without first modeling the correlations. 4. 2 Rolling Covariance Between S&P 500 and US$/yen Returns. we considered for volatility in the previous chapter. For the covariance between asset i and j , we can simply estimate σij,t+1 = 1 m m Ri,t+1−τ Rj,t+1−τ τ =1 which is easy to do, but which is not necessarily satisfactory due to the dependence on the choice of m. Notice that, as in previous chapters, we assume the average expected return on each asset is simply zero.
Although not discussed in this chapter, the method of principal components is often helpful in this regard. Frye (1997) contains a neat application to fixed income portfolios and Alexander (2001) suggests multivariate GARCH models, which rely on the idea of principal components. An nice overview of the mechanics of assigning risk factor exposures can be found in Jorion (2000). 10. APPENDIX: VaR FROM LOGARITHMIC VERSUS ARITHMETIC RETURNS The VaR concept used in this book relies on the logarithmic returns as defined in Chapter 1.
Z) calculates the probability of being below the number z, and −1 p = −1 (p) instead calculates the number such that 100 ∗ p% of the probability mass −1 (∗) on both sides of the preceding equation yields the is below −1 p . 01 = quantile from the standard normal distribution. 5, the minus sign in front of the VaR formula again ensures that the VaR itself is a positive number. 825% of the portfolio value today. 05825 ∗ 2,000,000 = $116,500. 1 illustrates the VaR from a normal distribution. 01 here.