Local Volatility

기호삼 한국재무학회 2006 한국재무학회 학술대회 Vol.2006 No.10

급첨 분포와 옵션 가격 결정

기호삼 ( Ho Sam Ki ),이미영 ( Mi Young Lee ),최병욱 ( Byung Wook Choi ) 한국재무관리학회 2004 財務管理硏究 Vol.21 No.2

왜도와 첨도를 고려한 옵션 가격의 결정

기호삼(Hosam Ki),최병욱(Byungwook Choi) 건국대학교 경제경영연구소 2004 商經硏究 Vol.29 No.1

The purpose of this study is to derive a European option pricing formula when the rate of return on the underlying asset follows a Gram-Chalier distribution instead of normal. This distribution explains well the volatility smile and furthermore the option prices calculated under the distribution are shown to be closer to the market option prices than that of Black-Scholes model(1973). We estimate the implied parameters of the new pricing formula such as volatility, skewness, and kurtosis, and conduct an in-sample test to verify the fitness of the pricing formula that we propose here.

바스켓 옵션의 가격결정을 위한 효율적인 수치적분법

기호삼 ( Hosam Ki ),반준화 ( Junhwa Ban ) 한국파생상품학회(구 한국선물학회) 2005 선물연구 Vol.13 No.1

장외파생상품의 거래상대방 익스포져(EAD) 측정방법

박병수,기호삼 예금보험공사 2008 金融安定硏究 Vol.9 No.1

In July 2005 the Basel Committee on Banking Supervision (BCBS) and the International Organization of Securities Commissions (IOSCO) added to the existing current exposure method (CEM) by publishing two new methodologies for measuring counterparty credit risk (CCR) of OTC derivatives transactions: the standardized method (SM) and the internal model method (IMM) In this study we measured banks’ counterparty exposures (Exposure at Default: EAD) in their OTC derivatives portfolio by using the three different models (SM, IMM and CEM), and made the following findings; Compared to the current exposure method, counterparty exposures were reduced by 12.04% when the internal model method was used: it resulted in a 24.94% decrease in interest rate swap and a 20.71% decrease in currency swap. However, the exposure decrease was comparatively insignificant for FX forwards and FX options. Employing the internal model method rather than the current exposure method provides incentives to banks such as reduced counterparty exposures and an enhanced BIS capital ratio. Moreover, the internal model method is deemed to be a more sophisticated model for the purpose of risk management of banks, and banks are encouraged to consider employing this model respond to the expected potential growth in the investment banking business. 바젤위원회(BCBS)와 국제증권감독기구(IOSCO)는 2005년 7월 장외파생상품의 거래상대방 신용리스크에 대하여 현행 BIS기준의 Current Exposure 방법 이외에 표준방법 및 내부모형법(IMM) 등의 측정방법을 제시하였다. 따라서 본 연구에서는 은행의 장외파생상품 포트폴리오에 대하여 거래상대방 익스포져를 표준방법, Current Exposure 방법, 내부모형법으로 측정하여 다음과 같은 연구결과를 얻었다. IMM으로 거래상대방 EAD를 측정하는 경우 Current Exposure 방법에 비해 익스포져가 12.04% 감소되는 것으로 나타났으며, 이자율스왑과 통화스왑은 각각 24.94%, 20.71% 감소되었으며, FX선도와 FX 옵션의 감소효과는 상대적으로 미미한 것으로 나타났다. 이상의 결과를 종합해 보면, IMM에 의한 거래상대방 EAD 측정방법은 현재 적용되고 있는 Current Exposure 방법에 비해 EAD가 감소되고 BIS비율이 제고되는 등 많은 인센티브가 있는 것으로 나타났다. 또한 IMM은 거래상대방 리스크관리를 위한 보다 정교한 모형으로 향후 IB 업무 확대에 따른 신용리스크 관리를 위해 적극적으로 고려할 필요가 있다고 판단된다.

K-ICS 2.0 무차익 DNS 금리충격 시나리오 산출 방법론의 이해와 검토

이상헌,기호삼 금융감독원 2019 금융감독연구 Vol.6 No.2

This study describes the process of calculating the arbitrage-free DNS (AFNS) interest rate shock scenario for measuring interest rate risk with the new K-ICS 2.0, which is a capital adequacy system evaluating and analyzing the risk and financial soundness of insurance companies under IFRS 17. The interest rate risk is particularly important due to its modeldependency compared to other risks, and it has considerable significance from a practical standpoint. In short, this study is about the calculation procedure of the interest rate shock scenario of K-ICS 2.0 and the estimation of AFNS and DNS models for the 4-sample period. Besides, the modifications of K-ICS 2.0 were reflected in the estimation process. As a result, we find that the AFNS model reduces the volatility of the interest rate shock more than the DNS model does. In particular, the purpose of the IAIS DNS shock generating algorithm is to eliminate the curvature effect and to identify two shocks in terms of level and slope directions, but an increased curvature effect has been caused. Therefore, twist shock is being humped or crossed at short maturity and is not conforming to its intuition and definition. Through this study, the partnership between financial supervisory authorities and insurance practitioners is expected to be achieved. In other words, the financial supervisory authority will be able to develop scenarios that are better suited to the situation of the insurance company. Also, the insurance practitioner is expected to access the methodology more easily while building the internal model based on the K-ICS.

Alternative numerical approaches to thejump-diffusion option valuation

최병욱,기호삼,이미영 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2

The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju [17]. The second approach is to modify the analytical methods of MacMillan [20] and Zhang [25] in a discrete time space. The third approach is to apply the simulation technique of Ib´a˜nez and Zapareto [14] to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.

신용등급 하락 조건부 채권의 가치평가

이상헌,기호삼 예금보험공사 2018 金融安定硏究 Vol.19 No.2

The purpose of this paper is to present a practical approach to do valuation of rating-triggered bond, which provides a higher-rated bond as collateral that allows the investors to exercise the right of early redemption when an issuer's credit rating falls below some predetermined threshold rating. The domestic rating-triggered bonds are classified into five categories and we stress that there are differences in calculating rating downgrade probability according to five categories in the process of valuation. Historical average transition matrix is used conveniently from credit rating companies for calculating the rating downgrade probability. Empirical valuation study shows that additional values from rating triggered clauses are not negligible. Therefore, it should include rating-triggered clauses in the process of the valuation of rating-triggered bond. It is expected that if default rates and rating downgrade probability are high when economic or credit condition gets worse, rating-triggered clauses will increase in value. Therefore it is necessary to consider rating-triggered clauses appropriately in the process of valuation. 본 연구는 발행자의 신용등급이 일정한 등급 이하로 하락할 경우 1) 높은 등급의 채권을 담보로 제공할 발행자의 의무 또는 2) 조기상환을 요구할 투자자의 권리가 발생하는 채권의 가치평가 방법을 실무적인 각도에서 제시한다. 국내에서 발행된 이와 같은 채권을 5가지 유형으로 분류한 후 평가과정에서 적용하는 전이행렬의 형태에 차이가 있음을 보여주었다. 또한 등급하락 확률을 계산하기 위해 신용평가사에서 제공하는 역사적 전이행렬을 사용하여 계산의 용이성을 확보하였다. 분석 결과 등급하락에 연계된 조건부 조항은 일정 부분 가치가 있는 것으로 평가되었다. 따라서 신용등급 하락 조건부 채권을 평가할 때 등급 하락 조건부 조항을 제외하고 일반채권과 동일한 방법으로 평가하는 것은 지양해야 할 것으로 보인다. 향후 경기 둔화 및 신용 상황 악화 등 금융불안이 발생하면 부도율 및 등급하락 확률이 상승하고 금리변동성이 높아지면 조건부 조항의 가치는 중첩적으로 높아질 것이다. 따라서 선제적인 채권 포트폴리오 위험관리를 위해 신용등급 하락 조건의 가치를 명시적으로 고려할 필요가 있다.

ISDA SIMM 개시증거금 모형과 구조화 금리 스왑

이상헌,기호삼 금융감독원 2020 금융감독연구 Vol.7 No.1

The purpose of this paper is to explain ISDA Standard Initial Margin Model (SIMM) and present the calculation of the initial margin of major interest rate structured swaps. From this quantitative analysis, we provide practical suggestions for soft landing of the initial margin regulation. We use Hull-White 1 and 2 factor model for vanilla swap, range accrual swap, and spread range accrual swap with issuer call options, which are major interest rate structured products of financial institution as hedging instruments. In order to sidestep some bias from selecting data sample and take market changes into account, data from 2014 to 2019 are used. Average ratios of initial margin to notional amount of each trades are estimated as 2.6%, 2.8%, 5.2% sequentially. In particular, it is important to include relevant maturity which reflect the major characteristics of trades. In particular, the SIMM initial margin using the Hull-White two-factor model sometimes showed a level of difficulty in coordination between counterparties. As such, the role of the financial supervisory authority is expected to increase in areas where coordination between theory and practice or among practices is necessary. In conclusion, we argue that it is necessary for detailed guidelines on the parameter estimation, sensitivity calculation, and reconciliation procedures which underlie the calculation of a stable and appropriate level of initial margin.

이표채 평균-분산 최적화 모형과 KTB 국고채 포트폴리오

이상헌,최건호,기호삼 성균관대학교 경영연구소 2021 자산운용연구 Vol.9 No.1

The purpose of this paper is to extend zero-coupon bond (ZCB) mean-variance portfolio optimization model to coupon bearing bond (CBB) counterpart and perform the empirical analysis for the efficient portfolio of KTB (Korean Treasury Bond). As KTB is issued as the semi-annual coupon bond, it is appropriate for CBB portfolio model to be used. We introduce the no arbitrage condition between CBBs and ZCBs as an additional constraint into an otherwise standard mean-variance bond optimization model. From the empirical analysis of KTB from 2006 to 2020, our finding is four-fold. First, the optimal CBB portfolio is similar to ZCB portfolio. Second, CBB portfolio is slightly different from the ZCB portfolio when considering target duration constraint. Third, the selection of maturities and introduction of strips result in the substitution effect between maturities. Fourth, from the perspective of financial institutions such as bank and insurance companies, some concentrated allocations (corner solutions) and the abrupt changes in weights are needed to be mitigated. The implication of our study is that it is appropriate to use this parsimonious CBB portfolio optimization model for strategic bond portfolio management.