I Description of KMV Model 2
1.1. 1st Stage: Estimation of the asset value and the volatility of asset return……………3
1.2. 2nd Stage: Calculation of the distance-to-default…………………………………………………..3
1.3. 3rd Stage: Derivation of the probabilities of default………………………..………………………5
II Intermediate conclusion 5
III Strentghs of KMV Model 5IV Weaknesses of KMV Model 6
Today,with the subprime’s crisis, risk management is a very important issue in financial markets. Moody’s bought the KMV Model.
KMV Model is a structural model inspired from Merton’s model. It is equivalent to an option model that evaluates the implied volatility of the company’s assets.
It relies on Black & Scholes valuation model (1973).
I Descriptionof KMV Model
KMV is a trademark of KMV Corporation that was founded in 1989. The KMV model calculates the Expected Default Frequency (EDF) based on the firm’s capital structure, the volatility of the assets returns and the current asset value. This model best applies to publicly traded companies for which the value of equity is market determined.
The translation of the public information intoprobabilities of default proceeds in 3 stages:
1.1. 1st Stage: Estimation of the asset value and the volatility of asset return
Financial models usually consider market values of assets, and not book values which only represent historical costs of the physical assets, net of their depreciation. The calculation of the market value of the firm’s assets and their volatility would be simple ifall the liabilities of the firm were traded and market-to-market every day.
Alternatively, KMV use the option pricing model to the valuation of corporate liabilities as proposed in “On the pricing of corporate debt: The risk structure of interest rates (Merton, R., 1974 in Journal of Finance 28, 449-470)”. According to this model, we assume that the firm’s capital structure is composed ofequity, short-term debt which is considered equivalent to cash, long-term debt which is assumed to be a perpetuity, and convertible preferred shares.
Figure 1: Firm’s structure capital
The estimation of the asset value and volatility of asset return usually requires the implementation of iterative techinique, with no analytical solution.
1.2. 2nd Stage: Calculation of the distance-to-defaultAccording to KMV, the default occurs when the asset value reaches a level somewhere between the value of total liabilities and the value of short-term debt. This point is named default point (DPT), and it is considered by KMV as the short-term debt plus half the long-term debt.
Figure 2: Default Point
The distance-to-default (DD) is the number of standard deviations between the mean ofthe distribution of the assets value and the default point (DPT).
Figure 3 : distance to default
E (V1) = expected asset value in 1 year
DPT = (short-term debt) + 1/2 (long-term debt)
S= volatility of asset returns
1.3. 3rd Stage: Derivation of the probabilities of default
The last stage consists as mapping the DD to the Expected Default Frequency (EDF), for a giventime horizon. Using a large sample of firms, we can draw the EDF as a function of the DD, as following:
Once we have the EDF for a given obligor, KMV uses a risk neutral valuation model to derive prices as a discounted expected value of future cash flows. The valuation of risky cash flows consists of (1) the valuation of the default-free component and (2) the valuation of the componentexposed to credit risk:
PV = Present Value of the cash flow
FV = Future Value (the obligation)
LGD = Loss Given Default, in percent
1 – LGD = recovery rate
i = the 1-year risk-free rate
Q = probability that the issuer defaults in 1 year, which is derived from EDF
II Intermediate conclusion
Variations in the stock price, the leverage ratio, and the asset volatility can all change...