市場指數型擔保債權憑證之評價－Implied Copula法之應用

Abstract

資產證券化源自於1970年代，隨著1997年東南亞金融危機及1998年韓國的金融危機，造成許多公司紛紛倒閉。金融機構因此產生許多因信用違約而損失的借款，故各類型信用衍生性金融商品逐漸在市場上出現，以供作信用違約避險之用。2006年末，美國產生次級房貸風暴造成金融泡沫化，可見信用違約問題對總體環境影響的重要性，也讓擔保債權憑證(Collateralized debt obligations, CDO)此商品在市場上更受到關注。金融市場主要是利用Gaussian copula/base correlation 模型來對CDO進行評價，但從前的評價模型所得到之結果容易錯估違約損失，無法真實反映市場報價的波動情況，且客製化CDO因契約型態不具標準化，更是難以評價。因此，本研究採用Hull & White (2006)提出的implied copula來評價市場指數型CDO，因為直接使用隱含在市場報價的資訊找到相對應的copula，所以違約相關性(default correlation)也就隱含在其中，不需計算出correlation也能進行評價。本研究選定CDX NA.IG此信用違約交換指數(Credit Default Swaps Index, CDS Index)為標的之合成型CDO分券進行實證分析，此合成型CDO分券為一種標準型分券，因其標的資產相同且規格ㄧ致。本評價模型利用市場上流通性佳的標準型CDO分券之市場報價，故可完全反應市場上的情況，進而將此資訊運用在流通性較差的客製化CDO分券評價，像是bespoke CDOs 和CDO squareds等。經實證結果指出，本評價方法透過標準型CDO分券報價確實可找出符合市場報價波動的資訊。此評價方法不僅結果較為真實，且用法容易明白，因此對於評價、交易和風險控管等都是一個相當實用的工具。因為此方法不允許市場上存在有套利的機會，故此評價方法比Gaussian copula/base correlation 方法評價之結果更可靠。

Asset Securitization originated in the 1970’s. As Southeast Asia and Korea’s financial crises struck the financial market, financial institutions could not collect debts because of the credit defaults caused by the bankrupt companies, and therefore Credit Derivatives were used to hedge credit risks. The Subprime Mortgage crisis which is an ongoing global economic problem started in the United States in late 2006 and began with the bursting of the housing bubble. It made major financial institutions face significant losses from investments in Mortgage Backed Securities (MBS) or Collateralized Debt Obligations (CDO). The recent market turmoil highlights the importance of the theme about credit default risks. For the various approaches to the valuation of CDO, the standard market model is Gaussian copula or base correlation. The market quotes observed through past models can not accurately match the actual volatility in the market because of wrong estimates of the extent of the default losses. For this reason, we use the implied copula approach which was first applied by Hull and White (2006). We no longer find the default correlations from the copula model, but imply them from the market quotes directly. In this paper, we chose CDX NA.IG to demonstrate how to value standardized CDO tranches. Standardization applies to both the composition of the reference pool and the structure of the tranches. We confirm that our model fits the market quotes exactly and make it clear to be used for pricing, trading, and risk management. It also enables non-standard credit derivatives, such as bespoke CDOs and CDO squareds, to be priced directly with market quotes for standardized CDO tranches. The spreads we find are more stable than those given by Gaussian copula or base correlation because we don’t permit any arbitrage.