• 대한수학회지
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• 제38권5호
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• pp.1031-1046
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• 2001

The paper studies the evolution of the financial markets and pays the basic attention to the role of financial innovations (derivative securities) in this process. A characterization of both complete and incomplete markets is given through an identification of the sets of contingent claims and terminal wealths of self-financing portfolios. the dynamics of the financial system is described as a movement of incomplete markets to a complete one when the volume of financial innovations is growing up and the spread tends to zero (the Merton financial innovation spiral). Namely in this context the paper deals with the problem of pricing risks in both field: finance and insurance.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권1호
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• pp.79-84
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• 2020

In this article, we implement a recently developed fast Monte Carlo simulation (MCS) for pricing equity-linked securities (ELS), which is most commonly issued autocallable structured financial derivative in South Korea, on the mobile platform. The fast MCS is based on Brownian bridge technique. Although mobile platform devices are easy to carry around, mobile platform devices are slow in computation compared to desktop computers. Therefore, it is essential to use a fast algorithm for pricing ELS on the mobile platform. The computational results demonstrate the practicability of Android application implementation for pricing ELS.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1073-1080
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• 2008

Reverse convertible fund is a method of investment assuring both profit and stability in an unstable stock market, and shares characteristics of a hedge fund and derivative securities. This study analyzes empirically whether reverse convertible funds can indeed serve as a new method in variable stock market environment to provide high profit with low risks especially in the Korean stock market.

• Communications for Statistical Applications and Methods
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• 제29권1호
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• pp.85-101
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• 2022

Derivative-linked securities (DLS) is a type of derivatives that offer an agreed return when the underlying asset price moves within a specified range by the maturity date. The underlying assets of DLS are diverse such as interest rates, exchange rates, crude oil, or gold. A German 10-year bond rate-linked DLS and a USD-GBP CMS rate-linked DLS have recently become a social issue in Korea due to a huge loss to investors. In this regard, this paper accounts for the payoff structure of these products and evaluates their prices and fair coupon rates as well as risk measures such as Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). We would like to examine how risky these products were and whether or not their coupon rates were appropriate. We use Hull-White Model as the stochastic model for the underlying assets and Monte Carlo (MC) methods to obtain numerical results. The no-arbitrage prices of the German 10-year bond rate-linked DLS and the USD-GBP CMS rate-linked DLS at the center of the social issue turned out to be 0.9662% and 0.9355% of the original investment, respectively. Considering that Korea government bond rate for 2018 is about 2%, these values are quite low. The fair coupon rates that make the prices of DLS equal to the original investment are computed as 4.76% for the German 10-year bond rate-linked DLS and 7% for the USD-GBP CMS rate-linked DLS. Their actual coupon rates were 1.4% and 3.5%. The 95% VaR and TVaR of the loss for German 10-year bond rate-linked DLS are 37.30% and 64.45%, and those of the loss for USD-GBP CMS rate-linked DLS are 73.98% and 87.43% of the initial investment. Summing up the numerical results obtained, we could see that the DLS products of our interest were indeed quite unfavorable to individual investors.

• 대한수학회보
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• 제55권4호
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• pp.1241-1261
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• 2018

We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order H which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.

• 지능정보연구
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• 제3권1호
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• pp.1-12
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• 1997

파생금융상품이란 주식이나 채권과 같은 기준자산에 대해서 발행되는 2차 금융상품으로써 기존의 재무이론에서는 수리적 모형에 기반을 둔 가격결정모형을 이용하여 가치를 평가하였다. 그러나 이러한 전통적인 가격결정모형은 복잡한 현실세계를 단순화시키기 위한 제반 가정을 요구하기 때문에 이러한 가정이 현실에 부적합한 경우에는 모형가격이 실제가격으로부터 커다란 괴리를 갖게 된다. 본 연구에서는 전통적인 가격결정방법의 단점을 극복할 수 있는 자료 의존적인 인공신경망기법을 제시하고 대표적인 파생금융상품인 국내 전환사채의 가격결정에 적용해 봄으로써 그 가능성을 제시하였다. 인공신경망기법을 전환사채의 가격결정에 적용한 결과 전통적 가격결정방법에 비해 평균절대오차를 70%정도 줄일 수 있다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권4호
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• pp.277-293
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• 2016

We develop an efficient numerical method for pricing the Derivative Linked Securities (DLS). The payoff structure of the hybrid DLS consists with a standard 2-Star step-down type ELS and the range accrual product which depends on the number of days in the coupon period that the index stay within the pre-determined range. We assume that the 2-dimensional Geometric Brownian Motion (GBM) as the model of two equities and a no-arbitrage interest model (One-factor Hull and White interest rate model) as a model for the interest rate. In this study, we employ the Monte Carlo simulation method with the Compute Unified Device Architecture (CUDA) parallel computing as the General Purpose computing on Graphic Processing Unit (GPGPU) technology for fast and efficient numerical valuation of DLS. Comparing the Monte Carlo method with single CPU computation or MPI implementation, the result of Monte Carlo simulation with CUDA parallel computing produces higher performance.

• 인터넷정보학회논문지
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• 제10권1호
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• pp.123-134
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• 2009

CRM(Customer Relationship Management)은 비즈니스 환경에서 기업의 이익과 경쟁적 우위를 차지할 수 있도록 하는 새로운 비즈니스 전략이다. 최근, 금융 산업은 자본시장통합법 시행을 앞두고(2009년) 금융 IT 산업 및 서비스에 대한 질적 양적 성장을 요구하고 있다. 이에 따라 증권, 보험, 은행, 선물, 자산운용사, 투신사들은 파생상품 및 서비스의 향상을 위해 노력하고 있다. 본 논문에서는 CRM 센터에서 증가하는 인바운드 고객 채널을 효율적으로 관리하기 위한 방안으로 대용량 채널 통합을 위한 채널 서버 모델을 제안하고 설계 구현하였다. 제안한 채널 서버 모델은 다양한 인바운드 채널 서비스를 통합 관리하고 표준화 하였다. 제안한 모델은 금융 서비스를 지원하는 뱅킹시스템, 증권사, 보험 등에서 인바운드 고객을 효율적으로 응대할 수 있다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.231-249
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• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권2호
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• pp.159-168
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• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.