信用違約交換的交易實務 主講人 蔡宏彬

信用違約交換定義 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。 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 回復率: 40% 到期年限:5年或10年 保費(Credit spread):100bp 付息頻率:一季,半年,一年 參考實體: 本金:10 Million

保護買方現金流量圖 年化保費:S 回復率: R 付息頻率:一季一次 s×0.25 s ×0.25 該季僅須繳2/3保費並且此後不需再繳保費 :表示當時要繳的保費 s ×0.25×2/3

信用違約交換定義 信用違約交換交易與保險比較 CDS Insurance 付款時點 償還金額 保額全部 承作機構 保險公司 交易地點 OTC 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 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: τ 保護時段:第 i 季,以 表示 年化保費:S 回復率: R 現值: DF

計算保費的原理 保費收取方式: 保額提領方式 違約情境分析 年化保費×保護期間(違約時支付)。 本金×(1-回復率)(違約事件發生時領取)。 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 不考慮發生機率的保費: S ×0.25 × 。 違約時點超過保護期 違約時點在保護期間內(假設是第二個月)

計算保費的原理 考慮發生機率的保費:Premium Leg

計算保費的原理 不考慮發生機率的保額: 違約時點超過保護期 0 。 違約時點保護期間內(假設是第二個月) (1-R)× 。

計算保費的原理 考慮發生機率的保額:Default Leg

計算保費的原理 繳費頻率一季,5年 CDS 保費:Premium Leg

計算保費的原理 繳費頻率一季,5年 CDS 保額:Default Leg

計算保費的原理 合理保費 Premium (Credit spread)

計算保費的原理 Continuous time model Notation

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model According to Stone-Weierstress theorem V(0.) can be uniformly approximated as close as a polynomial function on a compact interval. The hazard rate trend is not pronounced and the value is usually smaller than 0.05. This implies that the higher degree of polynomial has not significant impact on value of function. Thus we suggest setting λ(.) to be affine function or even constant function on each subinterval for projected period. Furthermore we assume that hazard rate function is piecewise constant. 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 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model The hazard rate term structure is regard as the risk factors which reflect P&L, analogous to the stock price is a factor causing the fluctuations in stock. Despite a contract is endowed with several influencing factors, it is customary for a trader to make each contract effected by single risk factor. The traders replace hazard rate term structure with the average hazard rate. However, the practice quotes the spread (or premium) available on the CDS market. Thus trader converts the spread into the implied hazard as a basis for pricing.

計算保費的原理 Continuous time model In 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 contract that coupon is c and the protection schedule as follows . The cost (or market value) for the contract is defined by Default Leg minus Premium Leg How do we define the Default Leg and Premium Leg for standard CDS contract?

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Continuous time model

計算保費的原理 Conclusion If the market Quote is equal to contract Coupon , the Upfront is zero. If the market Quote is higher than contract Coupon , the Upfront is positive. Hence, the implied hazard rate is increasing. On the contrary, if the market Quote is lower than contract Coupon , the Upfront is negative . Hence the implied hazard rate is decreasing. The 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. The Upfront is the market value for the remainder unrealized protection. Mark to Market =Upfront plus the Accrued Premium.

ISDA 標準CDS契約明細 保護買方(protection buyer) 保護賣方(protection seller) 回復率(Recovery Rate): 40% 和 20% 標準保費(Deal spread):500bp 和 100bp 報價方式:保費(Done Spread) 或 Upfront 到期日:每年的3/20,6/20,9/20,12/20 報價年限: 5Y 和 10Y

ISDA 標準CDS契約明細 Up front =0 Done Spread Deal Spread 100-Upf Accrued+Principal

ISDA 標準CDS契約明細 Up front <0 Done Spread Done Spread 本金100的 Upfront 本金=Notional 的 Upf Accrued+Principal

ISDA 標準CDS契約明細 Upfront >0 Done Spread 本金100的 Upfront 100-Upf 本金=Notional 的 Upf Accrued+Principal

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