信用违约交换汇编

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保險契約。當債權人擔心手中握有倒帳風險的資產時(例如:公司債)可透過信用違約交換交易進行避險。l信用違約交換交易中，保護買方將定期支付一定費用(稱為保費 credit spread)給保護賣方，而一旦出現違約，保護買方有權利將債券以面值賣給保護賣方，從而有效規避信用風險,但票息的部分並未受到保護。契約明細範例l回復率: 40%l到期年限:5年或10年l保費(Credit spread):100bpl付息頻率:一季,半年,一年l參考實體:l本金:10 Million保護買方現金流量圖l年化保費:Sl回復率: Rl付息頻率:一季一次s0.2

2、5s 0.25該季僅須繳2/3保費並且此後不需再繳保費該季第二個月違約,領回本金(1-R):表示當時要繳的保費s 0.252/3信用違約交換定義l信用違約交換交易與保險比較CDSInsurance付款時點保護期間期末保護期間期初償還金額本金 (1-回復率)保額全部承作機構任何人皆可當賣方 保險公司交易地點OTC透過通路行銷次級市場可在次級市場交易量身訂做計算保費的原理l模型設定:付保費頻率:每季違約的時點發生在月底Pr(.):機率函數違約時點: 保護時段:第 i 季,以 表示年化保費:S回復率: R現值: DFiT計算保費的原理l保費收取方式:年化保費保護期間(違約時支付)。l保額提領方式本金

3、(1-回復率)(違約事件發生時領取)。l違約情境分析違約時點保護期間內。違約時點超過保護期間。計算保費的原理l不考慮發生機率的保費:違約時點超過保護期 S 0.25 。違約時點在保護期間內(假設是第二個月) S 0.25 2/3 。( )iDF T1(2/12)iDF T計算保費的原理l考慮發生機率的保費:Premium Leg 31111311/12Pr(1)/12/12)(/12)0.25Pr()(/12)kiiiiikkPLSTkTkDF TkSTDF Tk 折現折現保護期間保護期發生機率發間生機率外保護期間內違約保護期間違約計算保費的原理l不考慮發生機率的保額:違約時點超過保護期 0

4、。違約時點保護期間內(假設是第二個月) (1-R) 。1(2/12)iDF T計算保費的原理l考慮發生機率的保額:Default Leg 31111(/12)(1)Pr(1)/12/12)ikiiDF TkDLRTkTk 折現發生機率 保護期間內違約可獲得賠償計算保費的原理l繳費頻率一季,5年 CDS 保費:Premium Leg 31201111311/12(/12)Pr(1)/12/12) 0.25(/12) Pr()ikiiiiikkDF TkPLSTkTkDF TkT 發生機保護期間保護折現率發生機率折現期間計算保費的原理l繳費頻率一季,5年 CDS 保額:Default Leg 31

5、201111(/12)(1)Pr(1)/12/12)ikiiiDF TkDLRTkTk 發生折現機率計算保費的原理l合理保費 Premium (Credit spread) 31201111311/12(/12) Pr(1)/12/12) 0 .25(/12) Pr( ikiiiiikDLAkDF TkATkTkDTkSFT 保護期間保護期發生機現率間折現折其中) 發生機率計算保費的原理lContinuous time model Notation 計算保費的原理lContinuous time model計算保費的原理lContinuous time model計算保費的原理lContinu

6、ous time model計算保費的原理lContinuous time model計算保費的原理lContinuous time model計算保費的原理lContinuous time model計算保費的原理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. 計算保費的原理lContinuous time model 計算保費的原理lContinuous time model計算保費的原理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計算保費的原理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計算保費的原理lContinuous time model計算保費的原理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.計算保費的原理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計算保費的原理lContinuous time model計算保費的原理lContinuous time mod

14、el計算保費的原理lContinuous time model計算保費的原理lContinuous time model計算保費的原理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 標準CDS契約明細l保護買方(protection buyer)l保護賣方(protection seller)l回復率(Recovery Rate): 40% 和 20%l標準保費(Deal spread):5