Modeling and forecasting. Volatility - презентация, доклад, проект скачать

Нажмите для полного просмотра!

Modeling and forecasting. Volatility, слайд №1

Modeling and forecasting. Volatility, слайд №2

Modeling and forecasting. Volatility, слайд №3

Modeling and forecasting. Volatility, слайд №4

Modeling and forecasting. Volatility, слайд №5

Modeling and forecasting. Volatility, слайд №6

Modeling and forecasting. Volatility, слайд №7

Modeling and forecasting. Volatility, слайд №8

Modeling and forecasting. Volatility, слайд №9

Modeling and forecasting. Volatility, слайд №10

Modeling and forecasting. Volatility, слайд №11

Modeling and forecasting. Volatility, слайд №12

Modeling and forecasting. Volatility, слайд №13

Modeling and forecasting. Volatility, слайд №14

Modeling and forecasting. Volatility, слайд №15

Modeling and forecasting. Volatility, слайд №16

Modeling and forecasting. Volatility, слайд №17

Modeling and forecasting. Volatility, слайд №18

Modeling and forecasting. Volatility, слайд №19

Modeling and forecasting. Volatility, слайд №20

Modeling and forecasting. Volatility, слайд №21

Modeling and forecasting. Volatility, слайд №22

Modeling and forecasting. Volatility, слайд №23

Modeling and forecasting. Volatility, слайд №24

Modeling and forecasting. Volatility, слайд №25

Modeling and forecasting. Volatility, слайд №26

Modeling and forecasting. Volatility, слайд №27

Modeling and forecasting. Volatility, слайд №28

Modeling and forecasting. Volatility, слайд №29

Modeling and forecasting. Volatility, слайд №30

Modeling and forecasting. Volatility, слайд №31

Modeling and forecasting. Volatility, слайд №32

Modeling and forecasting. Volatility, слайд №33

Modeling and forecasting. Volatility, слайд №34

Modeling and forecasting. Volatility, слайд №35

Modeling and forecasting. Volatility, слайд №36

Modeling and forecasting. Volatility, слайд №37

Modeling and forecasting. Volatility, слайд №38

Modeling and forecasting. Volatility, слайд №39

Modeling and forecasting. Volatility, слайд №40

Modeling and forecasting. Volatility, слайд №41

Modeling and forecasting. Volatility, слайд №42

Modeling and forecasting. Volatility, слайд №43

Modeling and forecasting. Volatility, слайд №44

Modeling and forecasting. Volatility, слайд №45

Modeling and forecasting. Volatility, слайд №46

Modeling and forecasting. Volatility, слайд №47

Modeling and forecasting. Volatility, слайд №48

Modeling and forecasting. Volatility, слайд №49

Modeling and forecasting. Volatility, слайд №50

Modeling and forecasting. Volatility, слайд №51

Modeling and forecasting. Volatility, слайд №52

Modeling and forecasting. Volatility, слайд №53

Modeling and forecasting. Volatility, слайд №54

Modeling and forecasting. Volatility, слайд №55

Modeling and forecasting. Volatility, слайд №56

Modeling and forecasting. Volatility, слайд №57

Modeling and forecasting. Volatility, слайд №58

Modeling and forecasting. Volatility, слайд №59

Modeling and forecasting. Volatility, слайд №60

Modeling and forecasting. Volatility, слайд №61

Modeling and forecasting. Volatility, слайд №62

Modeling and forecasting. Volatility, слайд №63

Modeling and forecasting. Volatility, слайд №64

Modeling and forecasting. Volatility, слайд №65

Modeling and forecasting. Volatility, слайд №66

Modeling and forecasting. Volatility, слайд №67

Modeling and forecasting. Volatility, слайд №68

Modeling and forecasting. Volatility, слайд №69

Modeling and forecasting. Volatility, слайд №70

Modeling and forecasting. Volatility, слайд №71

Modeling and forecasting. Volatility, слайд №72

Modeling and forecasting. Volatility, слайд №73

Modeling and forecasting. Volatility, слайд №74

Modeling and forecasting. Volatility, слайд №75

Modeling and forecasting. Volatility, слайд №76

Modeling and forecasting. Volatility, слайд №77

Modeling and forecasting. Volatility, слайд №78

Modeling and forecasting. Volatility, слайд №79

Modeling and forecasting. Volatility, слайд №80

Содержание ▲

Вы можете ознакомиться и скачать презентацию на тему Modeling and forecasting. Volatility. Доклад-сообщение содержит 80 слайдов. Презентации для любого класса можно скачать бесплатно. Если материал и наш сайт презентаций Mypresentation Вам понравились – поделитесь им с друзьями с помощью социальных кнопок и добавьте в закладки в своем браузере.

Слайды и текст этой презентации

Слайд 1

Описание слайда:

Слайд 2

Описание слайда:

Outline Introduction: Why ARCH? ARCH Models Extensions: GARCH, T-GARCH, Q-GARCH, GARCH-M, Box-Cox GARCH Estimation Multivariate GARCH Models: Diagonal Vech, BEKK and CCC Application: Value-at-Risk (VaR) Appendix

Слайд 3

Описание слайда:

1. Introduction: Why ARCH?

Слайд 4

Описание слайда:

Слайд 5

Описание слайда:

Some example series: UST10Y

Слайд 6

Описание слайда:

Dow Jones

Слайд 7

Описание слайда:

U.S. Unemployment rate vs. stock market volatility, 1929-2010

Слайд 8

Описание слайда:

U.S. Realized Volatility (kernel based) 1997-2009

Слайд 9

Описание слайда:

Слайд 10

Описание слайда:

Слайд 11

Описание слайда:

Слайд 12

Описание слайда:

Слайд 13

Описание слайда:

Слайд 14

Описание слайда:

Skewness

Слайд 15

Описание слайда:

Kurtosis

Слайд 16

Описание слайда:

Слайд 17

Описание слайда:

Слайд 18

Описание слайда:

EViews Example – Daily S&P 500 Returns

Слайд 19

Описание слайда:

When we learn about GARCH(1,1)…

Слайд 20

Описание слайда:

We’ll be able to make squared residuals white noise

Слайд 21

Описание слайда:

Quality of TGARCH predictions: 1% quantiles, VaR(0.01), from August 1, 2007

Слайд 22

Описание слайда:

2. ARCH Models

Слайд 23

Описание слайда:

Слайд 24

Описание слайда:

Слайд 25

Описание слайда:

Слайд 26

Описание слайда:

Слайд 27

Описание слайда:

3. Extensions

Слайд 28

Описание слайда:

Слайд 29

Описание слайда:

Слайд 30

Описание слайда:

Слайд 31

Описание слайда:

I-GARCH If the coefficients of the GARCH model sum to 1, then the model has “integrated” volatility. This is similar to having a random walk, but in volatility instead of the variable itself. Model itself remains stationary (if constant variance model is stationary) Likelihood-based inference remains valid (Lumsdaine, 1996 Econometrica)

Слайд 32

Описание слайда:

Слайд 33

Описание слайда:

Слайд 34

Описание слайда:

Слайд 35

Описание слайда:

Слайд 36

Описание слайда:

Слайд 37

Описание слайда:

Слайд 38

Описание слайда:

Слайд 39

Описание слайда:

Слайд 40

Описание слайда:

Слайд 41

Описание слайда:

Слайд 42

Описание слайда:

Summing up (see Appendix for an expanded list)

Слайд 43

Описание слайда:

3. Estimation

Слайд 44

Описание слайда:

Maximum Likelihood

Слайд 45

Описание слайда:

Maximum Likelihood (continued)

Слайд 46

Описание слайда:

Optimization

Слайд 47

Описание слайда:

Multiple Solutions

Слайд 48

Описание слайда:

4. Multivariate models

Слайд 49

Описание слайда:

Слайд 50

Описание слайда:

Слайд 51

Описание слайда:

Слайд 52

Описание слайда:

Слайд 53

Описание слайда:

Слайд 54

Описание слайда:

Слайд 55

Описание слайда:

Слайд 56

Описание слайда:

An example of volatility “contagion’’

Слайд 57

Описание слайда:

5. Application: Value-at-Risk (VaR)

Слайд 58

Описание слайда:

VaR What is the most I can lose on an investment? VaR tries to provide an answer. It is used most often by commercial and investment banks to capture the potential loss in value of their traded portfolios from adverse market movements over a specified period. This potential loss can then be compared to their available capital and cash reserves to ensure that the losses can be covered without putting the firms at risk. VaR is applied widely in capital regulation (Basel)

Слайд 59

Описание слайда:

Value-at-Risk (VaR) VaR summarizes the expected maximum loss over a time horizon within a given confidence interval The VaR approach tries to estimate the level of losses that will be exceeded over a given time period only with a certain (small) probability For example, the 95% VaR loss is the amount of loss that will be exceeded only 5% of the time

Слайд 60

Описание слайда:

Value-at-Risk (VaR) - Continued The simplest assumption: daily gains/losses are normally distributed and independent. Calculate VaR from the standard deviation of the portfolio change, σ, assuming the mean change in the portfolio value is 0: 1-day VaR= N-1(X)σ, with X the confidence level. The N-day VaR equals sqrt(N) times the 1-day VaR.

Слайд 61

Описание слайда:

Measuring VaR with historical data

Слайд 62

Описание слайда:

Assuming a Normal distribution

Слайд 63

Описание слайда:

VaR with Normally Distributed Returns

Слайд 64

Описание слайда:

Portfolio VaR When we have more than one asset in our portfolio we can exploit the gains from diversification. There are gains from diversification whenever the VaR for the portfolio does not exceed the sum of the stand-alone VaRs (i.e., the VaRs on the single assets). The VaR for the portfolio equals the sum of the stand-alone VaRs if and only if the securities’ returns are uncorrelated.

Слайд 65

Описание слайда:

An Example Let us consider the following investment US$200 million invested in 5-year zero coupon US Treasury Examine VaR using a daily horizon Assume that the mean daily return is 0.01% Based on past several years of actual returns, the standard deviation is s = 0.295%.

Слайд 66

Описание слайда:

An Example (cont.)

Слайд 67

Описание слайда:

An Example of Portfolio VaR Two securities 30-year zero-coupon U.S. Treasury bond 5-year zero-coupon U.S. Treasury bond For simplicity assume that the expected return is zero Invest US$100 million in the 30-year bond Daily return volatility (std dev) s1 = 1.409% Invest US$200 million in the 5-year bond Daily return volatility (std dev) s2 = 0.295%

Слайд 68

Описание слайда:

An Example of Portfolio VaR 95% confidence level 30 year zero VaR 1.65 * 0.01409 * 100m = $2,325,000 5 year zero VaR 1.65 * 0.00295 * 200m = $974,000 Sum of individual VaRs = US$ 3.299m But US$3.299 million is not the VaR for the portfolio...why?

Слайд 69

Описание слайда:

VaR of the Portfolio Suppose the correlation between the two bonds is r12=0.88 Remember that Portfolio variance: (100*0.01409)2 + (200*0.00295)2 +2(100*0.01409)(200*0.00295) * 0.88 = 3.797 Portfolio standard deviation: sp = $1.948m Portfolio VaR = 1.65 * 1.948m = $3.214m This is different from the sum of VaRs

Слайд 70

Описание слайда:

The problem with Normality: Kurtosis Extreme asset price changes occur more often than the normal distribution predicts. Excess kurtosis (fat tails)

Слайд 71

Описание слайда:

Fat Tails and underestimation of VaR If we assume that returns are normally distributed when they are not, we underestimate the VaR

Слайд 72

Описание слайда:

Backtesting Model backtesting involves systematic comparisons of the calculated VaRs with the subsequent realized profits and losses. With a 95% VaR bound, expect 5% of losses greater than the bound Example: Approximately 12 days out of 250 trading days If the actual number of exceptions is “significantly” higher than the desired confidence level, the model may be inaccurate. Therefore, in additional to the risk predicted by the VaR, there is also “model risk”

Слайд 73

Описание слайда:

Relevance: Basel VaR Guidelines VaR computed daily, holding period is 10 days. The confidence interval is 99 percent Banks are required to hold capital in proportion to the losses that can be expected to occur more often than once every 100 periods At least 1 year of data to calculate parameters Parameter estimates updated at least quarterly Capital provision is the greater of Previous day’s VAR 3 times the average of the daily VAR for the preceding 60 business days plus a factor based on backtesting results

Слайд 74

Описание слайда:

Summing up A host of research has examined a. how best to compute VaR with assumptions other than the standardized normal b. How to obtain more reliable variance and covariance values to use in the VaR calculations. Here Multivariate GARCH models play an important role in assessing both portfolio risk and diversification benefits. We will see this in the forthcoming workshop