信用違約交換匯編

1、信用違約交換定義l信用違約交換(CDS)可視為一種金融資產(chǎn)保險(xiǎn)契約。當(dāng)債權(quán)人擔(dān)心手中握有倒帳風(fēng)險(xiǎn)的資產(chǎn)時(shí)(例如:公司債)可透過(guò)信用違約交換交易進(jìn)行避險(xiǎn)。l信用違約交換交易中，保護(hù)買(mǎi)方將定期支付一定費(fèi)用(稱為保費(fèi) credit spread)給保護(hù)賣方，而一旦出現(xiàn)違約，保護(hù)買(mǎi)方有權(quán)利將債券以面值賣給保護(hù)賣方，從而有效規(guī)避信用風(fēng)險(xiǎn),但票息的部分並未受到保護(hù)。契約明細(xì)範(fàn)例l回復(fù)率: 40%l到期年限:5年或10年l保費(fèi)(Credit spread):100bpl付息頻率:一季,半年,一年l參考實(shí)體:l本金:10 Million保護(hù)買(mǎi)方現(xiàn)金流量圖l年化保費(fèi):Sl回復(fù)率: Rl付息頻率:一季一次s0.2

2、5s 0.25該季僅須繳2/3保費(fèi)並且此後不需再繳保費(fèi)該季第二個(gè)月違約,領(lǐng)回本金(1-R):表示當(dāng)時(shí)要繳的保費(fèi)s 0.252/3信用違約交換定義l信用違約交換交易與保險(xiǎn)比較CDSInsurance付款時(shí)點(diǎn)保護(hù)期間期末保護(hù)期間期初償還金額本金 (1-回復(fù)率)保額全部承作機(jī)構(gòu)任何人皆可當(dāng)賣方 保險(xiǎn)公司交易地點(diǎn)OTC透過(guò)通路行銷次級(jí)市場(chǎng)可在次級(jí)市場(chǎng)交易量身訂做計(jì)算保費(fèi)的原理l模型設(shè)定:付保費(fèi)頻率:每季違約的時(shí)點(diǎn)發(fā)生在月底Pr(.):機(jī)率函數(shù)違約時(shí)點(diǎn): 保護(hù)時(shí)段:第 i 季,以 表示年化保費(fèi):S回復(fù)率: R現(xiàn)值: DFiT計(jì)算保費(fèi)的原理l保費(fèi)收取方式:年化保費(fèi)保護(hù)期間(違約時(shí)支付)。l保額提領(lǐng)方式本金

3、(1-回復(fù)率)(違約事件發(fā)生時(shí)領(lǐng)取)。l違約情境分析違約時(shí)點(diǎn)保護(hù)期間內(nèi)。違約時(shí)點(diǎn)超過(guò)保護(hù)期間。計(jì)算保費(fèi)的原理l不考慮發(fā)生機(jī)率的保費(fèi):違約時(shí)點(diǎn)超過(guò)保護(hù)期 S 0.25 。違約時(shí)點(diǎn)在保護(hù)期間內(nèi)(假設(shè)是第二個(gè)月) S 0.25 2/3 。( )iDF T1(2/12)iDF T計(jì)算保費(fèi)的原理l考慮發(fā)生機(jī)率的保費(fèi):Premium Leg 31111311/12Pr(1)/12/12)(/12)0.25Pr()(/12)kiiiiikkPLSTkTkDF TkSTDF Tk 折現(xiàn)折現(xiàn)保護(hù)期間保護(hù)期發(fā)生機(jī)率發(fā)間生機(jī)率外保護(hù)期間內(nèi)違約保護(hù)期間違約計(jì)算保費(fèi)的原理l不考慮發(fā)生機(jī)率的保額:違約時(shí)點(diǎn)超過(guò)保護(hù)期 0

4、。違約時(shí)點(diǎn)保護(hù)期間內(nèi)(假設(shè)是第二個(gè)月) (1-R) 。1(2/12)iDF T計(jì)算保費(fèi)的原理l考慮發(fā)生機(jī)率的保額:Default Leg 31111(/12)(1)Pr(1)/12/12)ikiiDF TkDLRTkTk 折現(xiàn)發(fā)生機(jī)率 保護(hù)期間內(nèi)違約可獲得賠償計(jì)算保費(fèi)的原理l繳費(fèi)頻率一季,5年 CDS 保費(fèi):Premium Leg 31201111311/12(/12)Pr(1)/12/12) 0.25(/12) Pr()ikiiiiikkDF TkPLSTkTkDF TkT 發(fā)生機(jī)保護(hù)期間保護(hù)折現(xiàn)率發(fā)生機(jī)率折現(xiàn)期間計(jì)算保費(fèi)的原理l繳費(fèi)頻率一季,5年 CDS 保額:Default Leg 31

5、201111(/12)(1)Pr(1)/12/12)ikiiiDF TkDLRTkTk 發(fā)生折現(xiàn)機(jī)率計(jì)算保費(fèi)的原理l合理保費(fèi) Premium (Credit spread) 31201111311/12(/12) Pr(1)/12/12) 0 .25(/12) Pr( ikiiiiikDLAkDF TkATkTkDTkSFT 保護(hù)期間保護(hù)期發(fā)生機(jī)現(xiàn)率間折現(xiàn)折其中) 發(fā)生機(jī)率計(jì)算保費(fèi)的原理lContinuous time model Notation 計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinu

6、ous time model計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time modellAccording to Stone-Weierstress theorem V(0.) can be uniformly approximated as close as a polynomial function on a compact interval.lThe hazard rate trend is not pronounc

7、ed and the value is usually smaller than 0.05.lThis implies that the higher degree of polynomial has not significant impact on value of function.lThus we suggest setting (.) to be affine function or even constant function on each subinterval for projected period.lFurthermore we assume that hazard ra

8、te function is piecewise constant.l In order to match the setting of hazard rate, we also assume that the instantaneous forward rates are piecewise constant. 計(jì)算保費(fèi)的原理lContinuous time model 計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time model()()()()( ,)( ,)( ,)( ,)( ,)( ,) ( ,)( , 1)( , )( , )b

9、bfuaaafbaP t u dQ t uP t a V t aeduP t a V tP t a V taaP t b V t beff計(jì)算保費(fèi)的原理lContinuous time modelIntegration ()()11()()()()1()()2by part() ( , )( , )( , ) ( , )()() ( , ) ( , )( , ) ( , )1()bbfu aiiaabfu afu aiafb auTP t u dQ t uP t a V t auTeduubuTP t a V t aeeduuaffaP t a V t aef2()(11)11( , ) (

10、, )( , ) ( , )()() ( , ) ( , )( ) ( , ) ( , ) ( ) iifb aiiP t a V t aP t b V t bfaTP t a V t ab TP t b V t bTbfTef計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time modellThe hazard rate term structure is regard as the risk factors which reflect P&L, analogous to the stock price is a factor causin

11、g the fluctuations in stock.lDespite a contract is endowed with several influencing factors, it is customary for a trader to make each contract effected by single risk factor.lThe traders replace hazard rate term structure with the average hazard rate. However, the practice quotes the spread (or pre

12、mium) available on the CDS market.lThus trader converts the spread into the implied hazard as a basis for pricing.計(jì)算保費(fèi)的原理lContinuous time modellIn order to facilitate the market liquidity, the available on the standard CDS market only 500bp and 100bp two coupon for contract. Consider a standard CDS

13、contract that coupon is c and the protection schedule as follows .l The cost (or market value) for the contract is defined by Default Leg minus Premium LeglHow do we define the Default Leg and Premium Leg for standard CDS contract?01 , ,.,NT TT計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time mod

14、el計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lContinuous time model計(jì)算保費(fèi)的原理lConclusionlIf the market Quote is equal to contract Coupon , the Upfront is zero.lIf the market Quote is higher than contract Coupon , the Upfront is positive. Hence, the implied hazard rate is increasing. On the contrary, if the ma

15、rket Quote is lower than contract Coupon , the Upfront is negative . Hence the implied hazard rate is decreasing.lThe Accrued Premium is the additional payment from the seller to buyer. Because of the agreement is owned by seller on the current protection period before the trade date.lThe Upfront is the market value for the remainder unrealized protection.lMark to Market =Upfront plus the Accrued Premium. ISDA 標(biāo)準(zhǔn)CDS契約明細(xì)l保護(hù)買(mǎi)方(protection buyer)l保護(hù)賣方(protection seller)l回復(fù)率(Recovery Rate): 40% 和 20%l標(biāo)準(zhǔn)保費(fèi)(Deal spread):5