(使用股票价格计算违约机率)
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d2= d1 - σv√T
The risk-neutral default probability is N(-d2) (seems N (d2) like the live probability (當VT>D))
To caculate N(-d2), we need V0 , σ0 but we only know σE 、E0 and equation(20.3)
From Ito’s Lemma , we can get
σEE0 = N(d1) σVV0 ----(20.4)
Ito’s Lema
dV / V = uVdt+ σVdZV ---(1) dE / E = uEdt+ σEdZE ---(2) -> dE = EvdV+ ½ Evv(dV)2 + Etdt -> dE = (½ EvvσV2V2 + σVVEv + Et)dt + σVVEvdZV ----(3) 由(2)(3)比照係數 ->
σEE0dZE = σVV0 EvdZV = σVV0 N(d1) dZV σEE0 = N(d1) σVV0 (設dZE = dZV )
We can get V0 , σ0 by equations (20.3) and (20.4) *
* To solve F(x,y)=0 and G(x,y)=0. we can use the Solver routine in Excel to find the values of x and y that minimize [F(x,y)]2 + [G(x,y)]2
In case 2. the max(fi ,0) if always fi .
vi is the present value of fi, it always equals f0
20.8 Credit Risk Mitigation (減緩信 用風險)
Netting (類似貨品抵押) 假如一家公司原持有 +10,+30,-25的契約 當對方倒閉,此契約價值變 -10,-30,+25 若是沒有此條約,則損失會計為 -40, 但若是有此條約, 則損失會便-40+25=-15
qi:the risk-neutral default probability R:recovery rate
ui :qi(1-R)
vi :the value today of the instrument
In case 1. fi is always negative , so the expected loss is zero
•
4、越是无能的人，越喜欢挑剔别人的 错儿。 02:01:4 902:01: 4902:0 1Tuesday, May 19, 2020
•
5、知人者智，自知者明。胜人者有力 ，自胜 者强。 20.5.19 20.5.19 02:01:4 902:01: 49May 19, 2020
Adjusting Derivatives’ Valuations for Counterparty Default Risk
The expected loss at ti: qi(1-R)E[max(fi,0)]
-> Σuivi
---(20.5)
fi:the value of the derivative to the financial institution
We can distinguish three situations: 1. Contract is a liability (負債) 2. Contract is an asset 3. Contract can become either an
asset or a liability
ຫໍສະໝຸດ Baidu
Example 1. a short option position 2. a long option position 3. a forward contract
ET = max(VT-D,0) This show that the equity is a call
option
So the Black-Scholes formula gives the value of the equity today as E0=V0N(d1) - De-rTN(d2) ---- (20.3) where d1= ln(V0/D)+(r+σv2/2)T σv√T
* see also the keyword “ Merton’s Model”
20.7 Credit Risk in Derivatives Transactions (衍生性金融商品交易的 信用風險)
Because the claim that will be made in the event of a default is more uncertain
20081017 paper report
R96072 黃源鱗
20.6 Using Equity Prices to Estimate Default Probabilities (使用股票價格計算違約機率)
More up-to-date The value of the equity at time T as
Collateralization (類似保證金)
當契約價值隨市價改變時,受益方需給另一 方現值和原值的價差. (ex: $10 -> $10.5
it can ask for $0.5 of collateral ) Downgrade Triggers (降級觸發)
當對方信用等級評比下降到某種等級,可以 規定馬上以市價直接清算掉此契約,不用等 到到期日
•
1、有时候读书是一种巧妙地避开思考 的方法 。20.5. 1920.5. 19Tues day, May 19, 2020
•
2、阅读一切好书如同和过去最杰出的 人谈话 。02:0 1:4902: 01:4902 :015/1 9/2020 2:01:49 AM
•
3、越是没有本领的就越加自命不凡。 20.5.19 02:01:4 902:01 May-20 19-May -20
The risk-neutral default probability is N(-d2) (seems N (d2) like the live probability (當VT>D))
To caculate N(-d2), we need V0 , σ0 but we only know σE 、E0 and equation(20.3)
From Ito’s Lemma , we can get
σEE0 = N(d1) σVV0 ----(20.4)
Ito’s Lema
dV / V = uVdt+ σVdZV ---(1) dE / E = uEdt+ σEdZE ---(2) -> dE = EvdV+ ½ Evv(dV)2 + Etdt -> dE = (½ EvvσV2V2 + σVVEv + Et)dt + σVVEvdZV ----(3) 由(2)(3)比照係數 ->
σEE0dZE = σVV0 EvdZV = σVV0 N(d1) dZV σEE0 = N(d1) σVV0 (設dZE = dZV )
We can get V0 , σ0 by equations (20.3) and (20.4) *
* To solve F(x,y)=0 and G(x,y)=0. we can use the Solver routine in Excel to find the values of x and y that minimize [F(x,y)]2 + [G(x,y)]2
In case 2. the max(fi ,0) if always fi .
vi is the present value of fi, it always equals f0
20.8 Credit Risk Mitigation (減緩信 用風險)
Netting (類似貨品抵押) 假如一家公司原持有 +10,+30,-25的契約 當對方倒閉,此契約價值變 -10,-30,+25 若是沒有此條約,則損失會計為 -40, 但若是有此條約, 則損失會便-40+25=-15
qi:the risk-neutral default probability R:recovery rate
ui :qi(1-R)
vi :the value today of the instrument
In case 1. fi is always negative , so the expected loss is zero
•
4、越是无能的人，越喜欢挑剔别人的 错儿。 02:01:4 902:01: 4902:0 1Tuesday, May 19, 2020
•
5、知人者智，自知者明。胜人者有力 ，自胜 者强。 20.5.19 20.5.19 02:01:4 902:01: 49May 19, 2020
Adjusting Derivatives’ Valuations for Counterparty Default Risk
The expected loss at ti: qi(1-R)E[max(fi,0)]
-> Σuivi
---(20.5)
fi:the value of the derivative to the financial institution
We can distinguish three situations: 1. Contract is a liability (負債) 2. Contract is an asset 3. Contract can become either an
asset or a liability
ຫໍສະໝຸດ Baidu
Example 1. a short option position 2. a long option position 3. a forward contract
ET = max(VT-D,0) This show that the equity is a call
option
So the Black-Scholes formula gives the value of the equity today as E0=V0N(d1) - De-rTN(d2) ---- (20.3) where d1= ln(V0/D)+(r+σv2/2)T σv√T
* see also the keyword “ Merton’s Model”
20.7 Credit Risk in Derivatives Transactions (衍生性金融商品交易的 信用風險)
Because the claim that will be made in the event of a default is more uncertain
20081017 paper report
R96072 黃源鱗
20.6 Using Equity Prices to Estimate Default Probabilities (使用股票價格計算違約機率)
More up-to-date The value of the equity at time T as
Collateralization (類似保證金)
當契約價值隨市價改變時,受益方需給另一 方現值和原值的價差. (ex: $10 -> $10.5
it can ask for $0.5 of collateral ) Downgrade Triggers (降級觸發)
當對方信用等級評比下降到某種等級,可以 規定馬上以市價直接清算掉此契約,不用等 到到期日
•
1、有时候读书是一种巧妙地避开思考 的方法 。20.5. 1920.5. 19Tues day, May 19, 2020
•
2、阅读一切好书如同和过去最杰出的 人谈话 。02:0 1:4902: 01:4902 :015/1 9/2020 2:01:49 AM
•
3、越是没有本领的就越加自命不凡。 20.5.19 02:01:4 902:01 May-20 19-May -20