부도위험채권의 가격결정에 관한 연구

Abstract

본 논문은 근래 국내 금융시장에서 관심이 증가하고 있는 부도위험이 있는 채권의 가격결정에 관한 연구이다. 제1장에서는 본 논문의 전체적인 요약과 구성에 대해 기술하였다. 부도위험채권의 가격결정의 이론적인 토대인 부도위험의 측정과 예측에 관한 선행연구들을 조사하여 정리하였고, 선행연구의 연장선상에서 제2장과 제3장의 연구방향과 공헌도에 대해 간략하게 정리하였다. 제2장에서는 몬테카를로 시뮬레이션(Monte Carlo Simulation, MCS)을 이용하여 옵션의 계속가치를 평가하기 위한 방법으로 Longstaff and Schwartz(2001)는 최소자승추정 몬테카를로 시뮬레이션(least square monte carlo simulation, LSMC)을 소개하였고, Huge and Rom-Poulsen(2007)은 LSMC의 옵션가치 추정오차를 감소시키는 방법(Extended LSMC)을 제안하여 더욱 발전시켰다. 본 장에서는 Hull and White(1990)와 Extended LSMC를 이용하여 조기상환조건이 있는 callable Range Accrual Note (CRAN)를 평가하는 방법을 제안하였다. 나아가 본 연구에서는 기초자산 가격과 계속가치를 추정하기 위한 각 단계에서 이들 추정대상의 설명력을 높일 수 있는 기저함수에 대해 분석한 후 기저함수의 선택에 따른 추정결과의 차이를 비교하였다. 기저함수에 대한 분석을 위해 CRAN을 고정금리채권과 지연디지털옵션의 포트폴리오로 정의하고, 각각의 해석 공식(analytic formula)을 이용하여 RAN의 기저함수로 상수항, 순간이자율, 그리고 Range를, 계속가치의 기저함수로는 상수항, RAN, 그리고 Range를 선택하여 그 추정결과의 차이를 분석하고 개선효과를 도출한다. 제3장에서는 Unified Ho and Lee(2009)모형을 이용하여 최근 관심이 증가하고 있는 신종자본증권의 가치평가에 대해 살펴본다. 신종자본증권은 주식과 채권의 특성을 함께 가진 유가증권으로 계약 조건에 따라 주식 또는 채권으로 분류될 수 있다. 신종자본증권의 손실흡수능력은 자본적 성격을 증가시키고, step-up 조항이나 조기상환옵션 등의 투자유인은 자본적 성격을 감소시킨다. 이러한 투자유인들은 조기상환채권(make-whole callable bond, MWCB)으로 분류하고 가격을 결정할 수 있다. UHL모형은 이자율위험과 신용위험을 함께 모형화할 수 있도록 GHL모형을 더욱 확장한 모형이다. 이자율위험에 대한 정보는 스왑/스왑션시장, 신용위험에 대한 정보는 CDS 스프레드의 시장부도확률(default probability from market)을 적용하였다. CDS는 선순위 무보증채권 또는 후순위채권을 준거자산으로 한 거래가 활발하여 일반 후순위채에 비해 변제순위가 앞서는 MWCB 가격결정에 적절하지 않을 수 있다. 한편, UHL모형을 이용하여 MWCB의 시장가격을 추종하는 내재부도확률(implied default probability from model)을 구할 수 있는데, 시장부도확률과 내재부도확률의 차이는 MWCB 가격결정 시 CDS시장에서 반영되지 않는 신용위험을 설명할 수 있다. MWCB 가격결정 시 UHL모형을 이용하는 것은 몇 가지 장점을 제공한다. 첫 번째, 무차익거래조건을 만족하는 모형의 특성에 의해 시장에서 형성된 가격에 부합하는 모형가격을 도출할 수 있다. 둘째, 시장가격에 적합하는 모형의 내재부도확률을 이용하여 동종 채권의 가격결정에 활용할 수 있다. 셋째, 과거 자료 또는 횡단면 자료를 이용하여 모형가격과 시장가격의 차이를 분석함으로써 시장의 가격결정 효율성에 대한 연구의 토대를 제공할 수 있다. |This dissertation has the essays on pricing defaultable bonds, which have been focused in Korea. Chapter 1 describes the abstract and construction of this dissertation. I search and summary the preliminary research to measure and model the credit risk as the theoretical background for pricing defaultable bonds and then based on them describe briefly the contribution of Chapter 2 and 3 in the point of academy and practice. Chapter 2 examines which basis functions are efficient to employ a combined method of Hull and White(1990) with the Monte Carlo simulation when I price a callable range note or a callable bond. I use the Huge and Rom-Poulson method which has modified the least squared Monte Carlo simulation proposed by Longstaff and Schwartz(2001) to reduce the estimation errors of the continuation value or the underlying assets. To use Monte carlo Simulation for pricing the early exercise premium, it is essential to accurately estimate the continuation value, because the investors will choose the higher value between the exercise and the continuation value at the possible early exercise dates. The main purpose of this paper is to analyze the estimation errors originating from the choice of the basis functions for the underlying asset and the continuation value estimation. I choose the callable bond and the callable range accrual note to show which basis functions are reliable to reduce the estimation errors. For this purpose, I replicate the callable range accrual note with a portfolio of a fixed rate bond and a delayed digital option. I use several basis functions such as a constant, the instantaneous interest rates, and the range in order to see which basis function is efficient for our purpose. I examine several combinations of the basis functions depending on which basis functions will be used for the underlying asset or the continuation value estimation. I show that the range which is an important determinant of the callable range accrual note is an effective basis function to accurately determine the underlying asset and the continuation value for the pricing of the callable range accrual note. Chapter 3 examines how to price hybrid securities, in recent years increasing an interest in, using Unified Ho and Lee(2009, UHL) model. Hybrid securities have the characteristic of bond and equity and can be classified to debt or equity in accordance with their contractual terms. The capacity to absorb losses increases the characteristic as equity but the investment incentives like as step-up or callable option decreases. The latter can be classified and priced as a make-whole callable bond(MWCB). UHL model is extend from Generalized Ho and Lee(2006, GHL) model in order to interest rate and credit risk at the same time. We can use interest rate swap and swaption market as the information of interest rate risk and market default probability from CDS spread as the information of credit risk. However, CDS with high trade activity has the senior subordinated or junior debt as the reference obligation and MWCB has lower credit quality than other subordinated debts because of the loss absorption mechanism. Therefore, the default probability from market can not explain appropriately the market price of MWCB. On the other hand, if we can get the implied default probability fitting the price of UHL model to the market price for MWCB, the difference means the credit risk not to be transferred from CDS market. Using UHL model in order to price MWCB provides several advantages. First, I can derive the model price fitting to the market by the characteristics of the model. Second, we can price other same bonds using the implied default probability. Last, analyzing the difference of model and market price using historical or panel data, we can get the theoretical fundamenta of other studies on market efficiency.; This dissertation has the essays on pricing defaultable bonds, which have been focused in Korea. Chapter 1 describes the abstract and construction of this dissertation. I search and summary the preliminary research to measure and model the credit risk as the theoretical background for pricing defaultable bonds and then based on them describe briefly the contribution of Chapter 2 and 3 in the point of academy and practice. Chapter 2 examines which basis functions are efficient to employ a combined method of Hull and White(1990) with the Monte Carlo simulation when I price a callable range note or a callable bond. I use the Huge and Rom-Poulson method which has modified the least squared Monte Carlo simulation proposed by Longstaff and Schwartz(2001) to reduce the estimation errors of the continuation value or the underlying assets. To use Monte carlo Simulation for pricing the early exercise premium, it is essential to accurately estimate the continuation value, because the investors will choose the higher value between the exercise and the continuation value at the possible early exercise dates. The main purpose of this paper is to analyze the estimation errors originating from the choice of the basis functions for the underlying asset and the continuation value estimation. I choose the callable bond and the callable range accrual note to show which basis functions are reliable to reduce the estimation errors. For this purpose, I replicate the callable range accrual note with a portfolio of a fixed rate bond and a delayed digital option. I use several basis functions such as a constant, the instantaneous interest rates, and the range in order to see which basis function is efficient for our purpose. I examine several combinations of the basis functions depending on which basis functions will be used for the underlying asset or the continuation value estimation. I show that the range which is an important determinant of the callable range accrual note is an effective basis function to accurately determine the underlying asset and the continuation value for the pricing of the callable range accrual note. Chapter 3 examines how to price hybrid securities, in recent years increasing an interest in, using Unified Ho and Lee(2009, UHL) model. Hybrid securities have the characteristic of bond and equity and can be classified to debt or equity in accordance with their contractual terms. The capacity to absorb losses increases the characteristic as equity but the investment incentives like as step-up or callable option decreases. The latter can be classified and priced as a make-whole callable bond(MWCB). UHL model is extend from Generalized Ho and Lee(2006, GHL) model in order to interest rate and credit risk at the same time. We can use interest rate swap and swaption market as the information of interest rate risk and market default probability from CDS spread as the information of credit risk. However, CDS with high trade activity has the senior subordinated or junior debt as the reference obligation and MWCB has lower credit quality than other subordinated debts because of the loss absorption mechanism. Therefore, the default probability from market can not explain appropriately the market price of MWCB. On the other hand, if we can get the implied default probability fitting the price of UHL model to the market price for MWCB, the difference means the credit risk not to be transferred from CDS market. Using UHL model in order to price MWCB provides several advantages. First, I can derive the model price fitting to the market by the characteristics of the model. Second, we can price other same bonds using the implied default probability. Last, analyzing the difference of model and market price using historical or panel data, we can get the theoretical fundamenta of other studies on market efficiency.