Download Measure of Market Risk

Risk Management
Bank Risks
¾ Market Risk. The risk in reducing the value of the Bank’s positions due
to changes in markets.
¾ Credit Risk. The risk in reducing the value of the Bank’s assets due to
changes in the credit quality of the counterparties.
™ Counterparty deafult is an extreme case, but losses can also occur
when a counterparty’s credit quality decreases.
™ Credit risk is an issue even when the bank holds only payment
obligations.
¾ Liquidity Risk. The risk of losses because of travel-time delays of
assets.
¾ Operational Risk.
™ Fraud.
™ Model risk (using the wrong pricing model, for instance)
™ Human Factor
¾ Legal and Regulatory Risk.
™ Transactions that are voided due lack of appropriate licenses.
™ Changes in Tax Laws
G-30 Policy recommendations
¾ General Policies:
“Policies governing derivatives use should be
clearly defined, including the purposes for which
these transactions are to be undertaken. Senior
management should approve proceedures and
controls to implement these policies, and
management at all levels should enforce them”
G-30 Policy recommendations
Market Risk Policies.
¾ Mark-to-market
¾ Market valuation methods (e.g., derivatives should priced
at mid-market levels, taking into account funding costs,
administrative costs, etc.)
¾ Identifying revenue sources
¾ Measuring market Risk (VaR)
¾ Stress simulations
¾ Investment and funding forecasts
¾ Independent market risk management
¾ Practices by end users
¾ Measuring credit exposure
G-30 Policy recommendations
Credit Risk Policies.
¾ Aggregate credit exposures, taking into account
netting agreements.
¾ Independent credit risk management
¾ Master agreements
¾ Credit enhancements
Recommended bibliography
¾ P. Jorion “Value at Risk”. Irwin (1996).
¾ Croughy, Galai and Mark “Risk Management”,
McGraw Hill (2000)
Measure of Market Risk
Value-at-Risk (VaR)
It is the loss that the portfolio will experience under
distress.
¾ The loss is taken over a time horizon: a day, a
month, sometimes even one year.
¾ “Distress” is quantified by a percentile of the P&L
function, usually 95% or 99%.
VaR is a measure of risk which has several
drawbacks, as we will see next, but it is an
accepted industrial standard, after J.P.Morgan
introduced their RiskMetrics document in 1994. It
is now part of the implementation of the Bassel
convention of 1991.
VaR drawbacks
¾ It is not sub-additive: the VaR of a portfolio with
several components can be larger or smaller than
the VaR of each of its components.
¾ Difficult to calculate:
™Sampling methods are ineffective, as most of
the elements of the sample are irrelevant.
™The quantile function is very unstable, unrobust at the tail.
Three calculation methods
¾ Historical
¾ Monte-Carlo
¾ Analytic.
VaR calculation: general framework
Step 1: generate
scenarios
Step 3: computer
P&L statistics
Step 2: evaluate
P&L under each
scenario
The answer
MonteCarlo VaR
¾ Scenarios are generated
taking random samples
from probability
distributions.
¾ Pros:
™it can fit any given
distribution in an
adequate manner
™It is not hostage to
historical events: it can
come up with new
ones
MonterCarlo VaR: Cons
Most scenarios
generated are useless,
as they fall under the
quantile
The few meaningful
may not reconstruct the
tail of the distribution
adequately.
MonteCarlo VaR: more cons
10,000 draws
How may scenarios
to take?
1000 draws
100 draws
Historical VaR
Yield Curves
Step 1: select historical
scenarios
6.00%
18-Sep-00
5.80%
19-Sep-00
20-Sep-00
21-Sep-00
5.60%
5.40%
22-Sep-00
25-Sep-00
26-Sep-00
5.20%
27-Sep-00
28-Sep-00
12/1/2028
12/1/2026
12/1/2024
12/1/2022
12/1/2020
12/1/2018
12/1/2016
12/1/2014
12/1/2012
12/1/2010
12/1/2008
12/1/2006
12/1/2004
12/1/2002
5.00%
12/1/2000
% yield
6.20%
Time at Maturity
Step 2: evaluate
P&L under each
scenario
Step 3: compute
P&L statistics