Credit risk measurement: Developments over the last 20 years. R94723001 王思婷 R94723037 李雁雯 R94723042 許嘉津. Agenda. Introduction History of Credit Risk Measurement Fixed Income Portfolio Analysis – A new approach Conclusion. Introduction.
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– A new approach
(iii) More competitive margins on loans.
(iv) A declining value of real assets in many markets.
(v) A dramatic growth of off-balance sheet instrument with inherent default risk exposure, including credit risk derivatives.
- By taking advantage of its size, an FI can diversify considerable amounts of credit risk as long as the returns on different assets are imperfectly correlated
P = Xe-iT N(-d2) – SN(-d1)
d1 = ln(S/X)+(r+σ2/2)T , d2 = d1- σ√T
→ given S, σ, then P is computed.
Let S = A (value of asset)
X = B (debt)
V = value of a loan (from the prospective of FI)
put option P V=? Be-it
V = Be-iT – P , also
V = Be-kT
given B, T, i, A, σ,→ solve k = ?
Thus, FI should charge required yield, k, for the risky loan.
However, in real world, A and σ are unknown, then what?
-using OPM and stock price to calculate EDF
-Expected Default Risk (EDF) :
the probability that the MV of the firm’s asset (A) will fall below the promised payment on its S-T debt liability (B) in one year
When A and σA are unknown, use E and σE to estimate A and σA
The value of equity (E) is equivalent to hold a call option on the assets
E = h( A, σA, r, B, T)
σE = g(σA) → solve A and σA
Step 2: calculate distance to default(D)
D = (A-B)/ σA
Step 3: calculate EDF
Probability distribution of asset value (A) in one year
Distance to default
1. Is σE an accurate proxy of σA?
2. the efficacy of using a proxy analysis necessary for non-publicly traded equity companies
-the spreadsbetween Treasury strips and zero-coupon corporate bond reflect perceived credit risk exposures
p: the probability of not default (risk neutral probability)
γ: the proportion of the debt that is collectible on default
k: the interest rate of 1-yr zero-coupon corporate bond
i: the interest rate of 1-yr zero-coupon T-bond
p(1+k) + (1-p)γ(1+k) = (1+i)
→ solve p=? , 1-p=?
→This problem is mitigated when the measurement period of return is relative short, e.g., monthly or quarterly.
where EAR=Expected Annual Return
EAL=Expected Annual Loss
An alternative risk measurement approach
where X1 = working capital / total assets,
X2 = retained earnings / total assets,
X3 = EBIT / total assets, and
X4 = equity (book value)/total liabilities.
Thank you Instruments (cont.)！