Pricing of convertible bonds with firm's default risk = 부도 위험이 있는 전환사채의 가격 산정

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Contingent convertible bonds (CoCos) are new hybrid asset classes that automatically convert into equities when the capital of the issuing firm falls below a specified level in financial distress. In this dissertation, we study new pricing methods of CoCos with capital-ratio triggers. First or all, we propose two dynamic models for pricing and managing risk of CoCo based on the empirical evidence or market variables. The capital-ratio model considers the joint dynamics of a capital-ratio and a stock price of the issuing bank, and the debt-equity model works on the joint dynamics of the debt amount and equity amount of the same bank. Using the optional sampling theorem and the stopping time distribution of the correlated geometric Brownian motion, we derive closed-form formulas for a fair price and price sensitivity for CoCo trading and risk management. We conduct a numerical simulation to verify the accuracy and efficiency of the theoretical results, and we perform comparison and check how the market parameters affect the prices of CoCo. We also propose two models for finding a theoretical price of CoCos taking account with default risk of an issuing bank. One setup considers an exogenous risk of the issuing bank. The default time is modeled by the first jump of a time-inhomogeneous Poisson process, which does not depend on endogenous structure of the firm. Assuming the total RWA amount to be a non-evolving random level, the capital-ratio is defined as the ratio of the equity and the total RWA amount. Another setup considers an embedded default risk of the issuing firm. Since the CoCo acts as a `buffer' against losses during times of distress, the conversion of CoCo is followed by the default. Once the capital-ratio drops below a certain level, the CoCo is converted into the equity and the capital-ratio is adjusted. If the adjusted capital-ratio falls into a certain lower level, then the issuing firm goes to default. The knock-out probability and the down-and-out call asset-or-nothing option pricing are used to derive the formula. We compare the theoretical results with those from Monte Carlo methods and analyze the price sensitivity of CoCo. Numerical tests show the efficiency and accuracy of our formula.
Choe, Geon Horesearcher최건호researcher
한국과학기술원 :수리과학과,
Issue Date

학위논문(박사) - 한국과학기술원 : 수리과학과, 2016.8 ,[iv, 68 p. :]


Contingent capital; CoCo bond; capital-ratio trigger; CET1 ratio; capital-ratio model; debt-equity model; two-dimensional geometric Brownian motion; 전환 자본; 코코 본드; 자본 비율 트리거; CET1 비율; 자본비율 모델; 부채자산 모델; 2차원 기하 브라운 운동

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