Title: VaR
1VaR by example
- Zvi Wiener
- 02-588-3049
- http//pluto.mscc.huji.ac.il/mswiener/zvi.html
2Assets
- NIS TSAMUD Yen
- Deposit 1yr. 6 4,000
- Bonds 10yr. 5 2,000
- Credit 3yr. 15 8,000
Liabilities
Today L6
NIS TSAMUD Yen Saving 2yr. 4
1,800 Deposit 1mo. 11 8,200 Deposit 3mo.
L-2 3,000
Total (200) 200 4,000 (3,000)
3Assets
- NIS TSAMUD Yen
- Deposit 1yr. 6 4,000
- Bonds 10yr. 5 2,000
- Credit 3yr. 15 8,000
Liabilities
Today L6
NIS TSAMUD Yen Saving 2yr. 4
1,800 Deposit 1mo. 11 8,200 Deposit 3mo.
L-2 3,000
Total (200) 200 4,000 (3,000)
4Risk Factors
- USD/NIS exchange rate
- Yen/NIS exchange rate
- Inflation
- Real NIS interest rates (IR, 10 yr., 2 yr.)
- Nominal NIS IR (1mo., 10 yr.)
- USD IR, (1 yr.)
- Yen IR, (Libor 3 mo.)
5Fair Value
- For risk measurement we need not only the fair
value, but the fair value as a function of risk
factors in order to estimate the potential
profit/loss.
6Fair Value Function
7Fair Value Function
8Fair Value Function
9Sensitivity
- CPI
- USD
- Yen
- rnominal1mo
- rnominal3yr
- rreal2yr
- rreal10yr
- rUSD1yr
- rYen3mo
0.1 1 2 0.5 0.5 0.5 0.5 0.25 0.25
-8 40 -60 3 -103 17 -93 -10
2
10Risky Scenario
11Sensitivity
- CPI
- USD
- Yen
- rnominal1mo
- rnominal3yr
- rreal2yr
- rreal10yr
- rUSD1yr
- rYen3mo
0.1 1 2 0.5 0.5 0.5 0.5 0.25 0.25
-8 40 -60 3 -103 17 -93 -10
2
12Gradient Vector
- Direction of fastest decay (loss).
- Take the sensitivity vector and divide it by the
assumed changes in the risk factors.
13What if ...
- The sensitivity vector allows to estimate quickly
an impact of a certain market move on the value
of the portfolio. - Scalar multiplication of the gradient vector and
the hypothetical market change vector gives the
predicted loss/gain.
14Risk Management
- Swap Dollar Yen
- Two forward contracts
- Quanto option
- FRA (?)
- Fixed - floating swap