(使用股票價(jià)格計(jì)算違約機(jī)率)

1、20081017 paper reportR96072 黃源鱗20.6 Using Equity Prices to Estimate Default Probabilities(使用股票價(jià)格計(jì)算違約機(jī)率)o More up-to-dateo The value of the equity at time T as ET = max(VT-D,0) o This show that the equity is a call optiono So the Black-Scholes formula gives the value of the equity today asE0=V0N(d1)

2、- De-rTN(d2) - (20.3) where d1= ln(V0/D)+(r+v2/2)TvT d2= d1 - vTo The risk-neutral default probability is N(-d2) (seems N (d2) like the live probability (當(dāng)VTD) o To caculate N(-d2), we need V0 , 0 but we only know E 、E0 and equation(20.3)o From Itos Lemma , we can getEE0 = N(d1) VV0 -(20.4)dV / V =

3、uVdt+ VdZV -(1)dE / E = uEdt+ EdZE -(2) - dE = EvdV+ Evv(dV)2 + Etdt - dE = ( EvvV2V2 + VVEv + Et)dt + VVEvdZV -(3) 由(2)(3)比照係數(shù) - EE0dZE = VV0 EvdZV = VV0 N(d1) dZV EE0 = N(d1) VV0 (設(shè)dZE = dZV )Itos Lemao We can get V0 , 0 by equations (20.3) and (20.4) *o * To solve F(x,y)=0 and G(x,y)=0. we can us

4、e the Solver routine in Excel to find the values of x and y that minimize F(x,y)2 + G(x,y)2o * see also the keyword “ Mertons Model”20.7 Credit Risk in Derivatives Transactions (衍生性金融商品交易的信用風(fēng)險(xiǎn))o Because the claim that will be made in the event of a default is more uncertain o We can distinguish thre

5、e situations: o 1. Contract is a liability (負(fù)債)o 2. Contract is an asset o 3. Contract can become either an asset or a liabilityo Example o 1. a short option positiono 2. a long option positiono 3. a forward contractAdjusting Derivatives Valuations for Counterparty Default Risko The expected loss at

6、 ti:qi(1-R)Emax(fi,0) - uivi -(20.5)fi:the value of the derivative to the financial institutionqi:the risk-neutral default probabilityR:recovery rateui :qi(1-R) vi :the value today of the instrument o In case 1. fi is always negative , so the expected loss is zeroo In case 2. the max(fi ,0) if always fi . vi is the present value of fi, it always equals f020.8 Credit Risk Mitigation (減緩信用風(fēng)險(xiǎn))o Netting (類似貨品抵押)假如一家公司原持有 +10,+30,-25的契約 當(dāng)對方倒閉,此契約價(jià)值變 -10,-30,+25 若是沒有此條約,則損失會計(jì)為 -40, 但若是有此條約, 則損失會便-40+25=-15o Collateralization (類似保證金)當(dāng)契約價(jià)值隨市價(jià)改變時(shí),受益方需給另一方現(xiàn)值和原值的價(jià)差. (ex: $10 -