Topic 3: Models Flashcards
What is the difference between EXOgenous and ENDOgenous variable?
EXO: determined outside a model and thus taken as a given
ENDO: determined inside a model, takes on the value the model prescribes
Normative vs Positive
Normative:
- aims to describe how participants and prices SHOULD behave
- thus if any deviation, potential mispricing. assumes actual prices converge towards normative model
- factors of rational financial decisions
e.g. arb-free models like put call parity
Positive:
- how it ACTUALLY behaves like technical trading
Theoretical vs Empirical
Theoretical: SIMPLE and not practical for complex securities
Empirical: COMPLEX securities. Observations of historical data but require variables to be constant to change in predictable ways.
Applied vs Abstract
Applied: Real World
Abstract: Theoretical
Cross Sectional vs Time Series
Cross: relationship across variables at a SINGLE POINT in time
Time Series: behaviour across time
Vasciek Model means
Mean-reverting; Short term to trend towards long term
i.e. Next = Current + Factor(Long Term - Current) + Vol of Change of Interest Rate
*Unbiased Expectations Theory for term structure = all credit-risk free bonds expected to earn same rate of return.
Cox Ingersoll and Ross Model is a variant of the Vasciek model. In what way>
Variance of short term rate is proportional to short term rate. When rates approach 0, vol approaches 0.
Arbitrage-Free Model, e.g. Ho and Lee
Assumes short term rates follow normally distributed process.
Uses binomial pricing in current zero coupon bond prices
Describe BDT Binomial
Models 1yr Spot Rates
- at each rate, next year has 2 possible rates with 0.5 probability
- Tree Calibrated to:
1) LEVELS: Returns of 2yr zero
2) SPREADS: between up and down = implied rate vol
BDT Short Term Rate
r upper = r lower x e ^ 2vol
What is Adverse Selection and Akerlof? How to reduce effects of adverse selection?
Adverse Selection: Asymmetric Info before financial transaction is complete, i.e. borrowers expose lenders to credit risk
Akerlof: Markets for LEMONS
- In the presence of asymmetric information between buyer and seller, quality of goods decline
Define Moral Hazard and how to reduce effects of moral hazard?
Assumes more risk to the detriment of other party. E.g. after taking insurance, person takes more risks, or after taking loan, borrower invests in riskier projects
- Restrict loan proceeds
- Limit size of loan to risky borrowers
- Monitor behaviour etc.
Describe the 3 types of credit risk modelling approaches
- Structural: S+P = B+C
- Reduced-form
- Empirical
Merton Model: Strengths and Weaknesses
STRENGTHS
- intuitive and basis for more complex models
WEAKNESSES
- parameters not readily observable, e.g. market value of firm, vol
- Model predicts very low credit spread for short term debt, contradict empirical data
Merton’s EQUITY VALUE
Max (A - K,0)
Merton’s Risky DEBT Value
K - Max (K-A,0)
Altman Model: X1 to X5
Working Capital / Total Assets
Retained Earning / Total Assets
EBITDA / Total Assets
Equity Value / BV of Liability
Sales / Total Assets
The credit spread generated by the Merton model DECLINES when which of the following variables INCREASES?
- debit maturity
- asset volatility
- leverage
- risk-free interest rate
Risk-Free Rate
Increases in all of the other inputs of the Merton model (i.e., debt’s maturity, assets’ volatility, and firm’s leverage) result in an increase in the credit spread (and in the probability of default).
Assumptions of Merton Structural Credit Risk Model
- Only equity and bonds
What is the default trigger in Merton vs KMV Model?
Merton: assets < face value of zero coupon bond
KMV: assets < all of short term debt + part of long term debt (weighted). This is based on assuming that short-term debt has to be serviced sooner than long-term debt and thus is more time-sensitive.
Company has Altman Z score of 1.6. Which of the following best describes the financial health of the company?
Altman Z-score default-based categories
Z < 1.81: Default group
1.81 ≤ Z ≤ 2.99: Gray zone
Z > 2.99: Non-default group
Which of the following credit risk models take a firm’s default as exogenous?
1. Reduced
2. Structural
3. Empirical
Reduced form