利用選擇權之權利金衡量選擇權調整信用價差

Abstract

在過去十幾年來，量化信用風險最基本的模型為Merton模型，由於公司整體價值為非交易資產，因此Merton模型在求算公司資產隱含波動度及違約率是奠基在長期經濟均衡的狀態。本研究在一個成熟資本市場的狀態下，假設一家公司的股市、債市及股票選擇權皆觀察得到市場價格，在Merton模型的經濟體中，由於資本市場存在市場區隔，會造成市場價格在Merton模型中產生了不均衡狀態，所以，本研究將萃取這不均衡的差異，定義隱含信用風險，來衡量一張債券在市場上所交易的信用價差及其模型求算的隱含信用風險的相對風險值，做為動態交易策略的參考。 本論文將先詳細介紹Merton及KMV模型，之後將股價及債券價格套入Merton模型中，再引入股票選擇權的隱含波動度，來計算債券預期損失做為隱含信用風險，再分別討論股價、債券價格及股價隱含波動度的變動對於隱含信用風險值的影響，並說明在市場上交易如何應用模型所得到的結果。 最後，為了更符合市場現實，本論文將放寬股價機率模型假設，利用市場所觀察到隱含波動度隨著執行價而歪斜的現象，推導出隱含的股價機率密度模型，再利用此模型去估算隱含信用風險，而且與原股價機率模型做一簡單的比較。

Over the past decade, Merton model plays a role of fundamental model to quantify the credit risk. As firm value is not traded asset, Merton model derives the asset implied volatility and default probability based on long-term economic equilibrium. Suppose we live in a mature capital market and all the market data from stock, bond and stock option can be observed. Due to market segmentation, the study extracts the un-equilibrium within the Merton model to define the implied credit risk measure. And we use this measure to tell the difference of credit spread of a corporate bond and model-derived credit risk as a reference of dynamic trading timing. In this study we introduce Merton model and KMV model first. Then substitute the stock and bond price for the model as well as incorporating the implied volatility from stock option. Reasonably, we can calculate the expected loss of the bond as implied credit risk. Furthermore, we make the scenario of the implied credit risk with respect to the stock price, bond price and the stock implied volatility and making a comment about applying the derived risk on the market. In the last part of the study, we make the relaxation on stock price probability density function to meet the volatility skew observed on the market. Then apply the new stock price density function on calculating the implied credit risk and compare with the risk from previous density function.