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Based on the theory of a wedge between the physical and risk-neutral conditional volatilities in Christoffersen, Elkamhi, Feunou, and Jacobs (2009), we develop a modification on the GARCH option pricing model with the filtered historical simulation proposed in Barone-Adesi, Engle, and Mancini (2008). The current conditional volatilities under the physical and risk-neutral measures are the same in the previous model, but should have been allowed to be different. Using extensive data on S&P 500 index options, our approach, which employs the current risk-neutral conditional volatility estimated from the cross-section of the option prices (in contrast to the existing GARCH option pricing models), maintains theoretical consistency under conditional non-normality as well as improves the empirical performances. Remarkably, the risk-neutral volatility dynamics are stable over time under this model. In addition, the comparison between the VIX index and the riskneutral integrated volatility validates our approach economically.

이 논문은 시뮬레이션 기법을 이용하여 콜 옵션 매도자가 직면하는 시장위험과 모델 위험 을 변동성이 추계적이고 거래가 비연속적인 시장에서 검토했다. 기초자산의 위험프리미 엄이 양(+)일 때 옵션 매도자는 평균적으로 큰 손실과 높은 시장위험에 직면하므로 동태적 델타헤지를 통한 위험관리를 수행하는 것이 일반적이다. 이 때 옵션 거래자는 불연속적인 금융시장과 같은 현실적인 제약이나 위험관리에서 사용되는 모델 자체의 비적격성으로 인해 발생하는 모델위험을 감수해야 한다. 본 연구에 따르면 추계적 변동성이 지배하는 금융시장에서 Black-Scholes 옵션 모형은 비적격한 모형임에도 불구하고, 완전히 적격 한 추계적 변동성 모형에 거의 필적하는 헤지성과를 내었다. 시뮬레이션 결과 모델 위험의 80~85%는 이산적 재조정 위험에서 발생했으며, 모델 비적격 위험이나 모수추정의 위험 의 비중은 상대적으로 덜 중요했다. 이 결과는 자산가격의 변화가 추계적 변동성으로 추동된다고 하더라도 Black-Scholes 모형이 여전히 효과적인 위험관리도구로 사용될 수 있다는 점을 시사한다

Using Monte Carlo simulation experiments, we examine the model risk of writing call option contracts when the underlying process driving security prices is characterized by stochastic volatility and trading occurs discretely. Simulations in this study reveal that discrete rebalacing risk is the main risk factor of total model risk while model misspecification risk and parameter estimation risk are relatively unimportant when single instrument hedge is utilized. These simulation results suggest that hedging based on the misspecified Black-Scholes model yields the hedging performance as good as that of the fully sprecified stochastic volatility model even when the true process driving security price movement is characterized by stochastic volatility. Hedging based on the Black-Scholes model is the simplest to implement. This may explain why the Black-Scholes formula is one of the best choices of option professionals even though it is widely accepted that the constant volatility assumption of the Black-Scholes model is violated in real world financial market. The results of this paper also suggest that for risk managers of financial institutions, the Black-Scholes option formular can be used as a viable risk management tool even under the financial markets characterized by stochastic volatilities.

In this paper, we proposed model for European option pricing using predicted cumulative probability distribution of hidden Markov Model. The Black-Scholes model is based on Gaussian distribution and the model's main shortfall is fat-tail problem. Because of fat-tail problem, the implied volatility surface is shaped skew, smirk or other forms. To correct model's drawback, we extract predicted cumulative distribution using hidden Markov Model and simulate the underlying price paths using Monte Carlo method. In the results, our model re ect current implied volatility surface suciently.

For the KOSPI 200 Index options, we examine the effect of extreme events for pricing options. We compare Black and Scholes(1973) model with Câmara and Heston(2008)’s options pricing model that allows for both big downward and upward jumps. It is found that Câmara and Heston(2008)’s extreme events option pricing models shows better performance than Black and Scholes(1973) model for both in-sample and out-of-sample pricing. Also downward jumps are more important factor for pricing stock index options than upward jumps. It is consistent with the empirical evidence that reports the sneers or negative skews in the stock index options market.

Black-Scholes 옵션 모형이 내가격 옵션을 과소평가하고, 외가격 옵션을 과대평가한다는 사실은 잘 알려져 있다. 이는 Black-Scholes 모형의 가정과는 달리 기초자산의 변동성이 잔여만기 동안 고정되어 있는 것이 아니라 추계적으로 변하기 때문인 것으로 추정된다. 이러한 점을 감안하여 Heston(1993)은 추계적 변동성 옵션 모형에 관한 패쇄형 해를 제안하였다. 그러나 추계적 변동성 모형은 추정해야 할 모수가 많고 복잡하여 옵션시장의 시장참여자들이 시장조성 과정에서 적극적으로 활용하기 어려운 단점이 있다. 추계적 변동성 모형과 별도로 Black-Scholes 옵션 모형의 비적격성을 개선하기 위한 또 다른 시도 중의 하나는 Black-Schole 모형에 비정규 왜도와 첨도를 추가한 Jarrow-Rudd 옵션 모형(1982)이다. Jarrow-Rudd는 기초자산의 가격이 로그노말 분포를 따른다는 Black-Scholes 옵션 모형의 엄격한 가정을 완화하여 주가수익률의 비정규성을 반영할 수 있는 옵션 모형을 제안하였다. 이 논문에서는 추계적 변동성이 지배하는 상황에서 초래되는 주가수익률의 비정규성을 Jarrow-Rudd 모형이 Black-Scholes 모형에 비해 얼마나 잘 반영하는 지를 옵션의 가격성과와 헤지성과 측면에서 시뮬레이션으로 분석하였다. Jarrow-Rudd 모형이 시뮬레이션의 대상으로 선택된 이유는 다음과 같다. 첫 째, Jarrow-Rudd 모형은 Black-Scholes 모형에 비해 추가적으로 추정해야 할 모수가 두 개 밖에 되지 않기 때문에 추계적 변동성 모형에 비해 간편하고 쉽게 활용이 가능하다. 둘 째, 금융자산의 분포가 종종 비정규 왜도와 첨도를 가진다는 사실이 잘 알려져 있는 바, 만약 이러한 현상이 변동성의 추계성에서 오는 것이라면 비정규 왜도와 첨도를 옵션 모형에 직접 반영한 Jarrow-Rudd 모형이 추계적 변동성 하에서 어떤 성과를 보이는 지를 검토하는 것은 매우 흥미로운 일이다. 이 연구의 결과는 다음과 같다. 변동성이 추계적인 경우 Jarrow-Rudd 모형은 Black-Scholes 모형의 가격성과를 크게 개선한다. 이는 기존의 연구(Jung 2003) 결과와 동일한 것이다. 그러나 시뮬레이션 결과 동태적 헤지 성과에서는 Jarrow-Rudd 모형이 Black-Scholes 모형을 의미 있게 개선하지는 못하는 것으로 나왔다. 장기의 과외가격 옵션의 경우 Jarrow-Rudd 모형의 헤지 성과가 Black-Scholes 모형에 비해 약간 나은 측면이 있으나 두 모형의 헤지 성과는 대체로 큰 차이를 보이지 않았다. 대체적으로 헤지성과는 어떤 옵션 모형을 사용했느냐 보다는 얼마나 자주 헤지포트폴리오를 재조정했느냐에 따라 더 민감하게 반응하였다. 전반적으로 이 연구의 결과는 비정규 왜도와 첨도를 조정한 Jarrow-Rudd 모형이 옵션 가격평가에서 Black-Scholes 모형을 대체할 수 있는 좋은 대안이 될 수 있으나 위험관리를 위한 헤지 수단으로는 오히려 간편한 Black-Sholes 모형이 선호될 수 있음을 시사한다. 한편 이 연구의 한계는 이 연구의 방법론으로 사용된 몬테카를로 시뮬레이션이 또 다른 모델 위험에 직면할 수 있다는 사실에 있다. 앞서 언급하였듯이 이 연구에서는 기초자산의 운동과정이 Heston(1993)이 가정하는 것과 동일한 과정을 따른다고 가정하였다. 그러나 실제 주가운동과정이 이와 다르게 움직일 가능성도 매우 크다. 이러한 관점에서 연구의 결론은 조심스럽게 해석되어야 할 필요가 있다. 모델위험에서 파생될 수 있는 이러한 문제는 시뮬레이션 대신 실제 옵션 자료를 사용하여 왜도와 첨도를 조정한 옵션 모형과 Black-Scholes 옵션 모형의 가격 및 헤지 성과를 비교하는 방법으로 검토될 수 있다. Corrado와 Su(1997), Kim(2006, 2008)은 이러한 실증연구를 통하여 이 논문과 유사한 결과를 얻었다. 그러나 그들의 연구에서는 이 논문과는 달리 헤지성과에 대한 비교를 단행하지는 않았다. 왜도와 첨도를 조정한 옵션 모형과 Black-Scholes 옵션 모형의 헤지성과 비교에 대한 실증연구를 통해 이 연구에서 검토하지 못한 부문에 대한 추가적인 이해를 구할 수 있을 것이다. 그러한 가능성은 추후의 후속연구에 남긴다.

It is well known that the volatility of asset returns is not constant, which has put forth the development of many option models incorporating a stochastic or GARCH process of volatility. Although these option models successfully reduce pricing and hedging errors of the Black-Scholes model, the complexity of the models often discourages market participants to utilize these models in pricing and hedging options. An alternative approach to adjust Black-Scholes model misspecification is to extend Black-Scholes model’s strict distributional assumption by adjusting non-lognormal skewness and kurtosis. This paper examines pricing and hedging performances of a skewness and kurtosis adjusted option model proposed by Jarrow and Rudd when volatility follows a stochastic process. Consistent with the previous research, the results of this study show that the skewness and kurtosis adjusted Jarrow-Rudd model reduces Black-Scholes pricing errors substantially especially for long-term, deep-in-the-money options. For hedging, however, improvements for the Jarrow-Rudd model over the Black-Scholes model are not virtually found. Overall, the study shows Jarrow-Rudd model could be a better alternative for the Black-Scholes model for option pricing but not necessarily for hedging. But considering the fact that Monte Carlo simulations employed in this study may subject to a model risk, the results of this simulation should be taken with caution.

This study evaluates GMDB(Guaranteed Minimum Death Benefit) put option of variable-universal life product with Black-Scholes option pricing model. The result is that first, life insurance company should prepare the contingency plan in regarding to investment risk of GMDB. Second, the fee for GMDB is divided by operating fund types. It means that the company consider volatility of underlying asset. According to analyzing GMDB rate as of reserve in equity fund type with between B-S model and Korean standard model, their rates are 42.14% and 2.539% respectively as of after 50years. Third, the company should establish the guide-line of standard for GMDB fee by progressing. At last, the company accumulate historical data of GMDB fee and update its data. and also, setting the internal networking to enact from market scenario formerly.

본 연구는 미니 KOSPI 200 옵션을 대상으로 최적 옵션가격결정모형을 찾는다. 옵션 가격결정모형으로는 Black and Scholes(1973) 모형, Ad-Hoc Black-Scholes 모 형, 확률 변동성(stochastic volatility)과 점프(jumps)를 고려한 모형을 비교한다. 연구 결과 미니 옵션 시장에서는 확률 변동성과 점프를 모두 고려한 모형이 내표본 및 외표본 가격결정에서 가장 우수한 성과를 보였고 헤징 성과에서는 2차항까지 포함 한 Ad-Hoc Black-Scholes 모형의 오차가 가장 작았다. 예측 기간을 1주일로 확장하 고, 월별로 성과를 검증한 경우에도 1일 예측과 일관된 결과를 보였고 각 모형들 간의 성과 차이는 통계적으로 유의하였다. 1차 항만을 고려한 Ad-Hoc Black-Scholes 모형의 가격결정 및 헤징 성과가 가장 우수했던 정규 옵션 시장을 대상으로 한 기존 연구들과 차별화된 결과를 확인하였다.

Mini KOSPI 200 options are derivatives based on the KOSPI 200 index, just like the regular KOSPI 200 options. While the contract terms, such as expiration dates and trading hours, are identical, mini options are structured to allow smaller investments by reducing the contract size to one-fifth (from a multiplier of 250,000 KRW to 50,000 KRW). This makes them accessible to smaller investors, aiming to increase retail participation. However, the question remains: have mini options successfully attracted retail investors as originally intended? As market data reveals, the share of retail investors in the mini options market is significantly lower than in the regular options market, contrary to the product’s initial purpose. Institutional investors, particularly securities firms, dominate the mini options market, contributing to its low liquidity. As a result, the liquidity premium in mini options leads to higher pricing compared to regular options with the same strike prices and expiration dates. This creates a barrier for retail investors, who generally prefer long positions and are sensitive to price disparities. Therefore, mini options have not achieved their goal of increasing retail participation and are instead primarily traded by institutional investors. The difference in liquidity and the composition of market participants leads to differing price determination mechanisms between mini and regular options. The distinct characteristics of the mini options market suggest that the optimal option pricing models suitable for regular options may not be applicable to mini options. The Black-Scholes (BS) option pricing model, introduced in 1973, has long been a fundamental tool in the options market, but its limitations have led to the development of many alternatives. The BS model, while advantageous for its simplicity and closed-form solution, fails to accurately reflect real-world variables like volatility and risk-free interest rates. Implied volatility, which is calculated based on option prices, tends to vary with strike prices and expiration times, a phenomenon known as the volatility surface, indicating that the BS model does not fully capture market realities. To overcome these limitations, various alternative models have been proposed, including stochastic interest rate models, stochastic volatility models, jump diffusion models, variance gamma models, and regime-switching models that assume sudden changes in volatility. GARCH models that assume conditional heteroscedasticity in the underlying asset are also used. Additionally, the Ad-Hoc Black-Scholes (AHBS) model is popular among market participants for estimating implied volatility using simple regression analysis. Previous research has shown that stochastic volatility models offer the greatest improvement over the BS model. Studies focused on the regular options market found that the AHBS model outperforms more mathematically complex models, including stochastic volatility models, in both pricing accuracy and hedging performance. Given that mini options display characteristics distinct from regular options, it is necessary to question whether the optimal pricing models used for regular options can still be applied effectively. This study aims to identify the optimal option pricing model for the mini KOSPI 200 options market. By comparing in-sample and out-of-sample pricing accuracy and hedging performance, we aim to recommend the most suitable model for participants in the mini options market. The models under consideration include the BS model, the AHBS model, and models that account for stochastic volatility and jumps. Through this comparison, we examine how differences in liquidity and the composition of market participants affect option pricing and hedging. The study suggests that markets with a high proportion of retail investors may favor simpler models like the BS model, while markets dominated by institutional investors might see better performance with more mathematically complex models. Given that the mini options market has a lower proportion of retail investors compared to regular options, it is expected that more sophisticated models that account for stochastic volatility and jumps will outperform simpler models like the BS model. This study provides several contributions to existing research. First, it is the first to explore the optimal options pricing model specifically for the mini KOSPI 200 options market. While mini options share many characteristics with regular options, their smaller contract sizes and different participantcomposition create unique market dynamics. The study shows that institutional investors play a larger role in the mini options market than in the regular options market, and that mini options have lower liquidity. These factors must be considered when selecting the optimal pricing model. Second, this research utilizes long-term data spanning 90 months, from the market’s inception to the present, offering a comprehensive view of the market’s evolution. Most previous studies focused on the early stages of the mini options market, where liquidity was insufficient. By incorporating a longer time frame, this study is able to capture the effects of market maturity and changes in volatility and liquidity over time. The results are as follows. Models that account for both stochastic volatility and jumps show the best performance in both in-sample and out-of-sample pricing tests. In terms of hedging performance, the AHBS model that includes both first-order and second-order strike prices performs the best. However, the differences in hedging performance across models are relatively small. When the forecasting period is extended to one week, the results remain consistent with the one-day forecast. Monthly performance also shows consistency, with statistically significant differences between the models' performance over the entire sample period. Compared to previous studies on the regular options market, which found that simpler AHBS models provided the best pricing and hedging performance, this study reaches different conclusions. The differences in liquidity and participant composition between the mini and regular options markets play a significant role in the selection of the optimal pricing model.

중국에서는 현재까지 예금보험제도가 없는 대신 묵시적인 예금보험제도가 존재하였다. 이런 예금보험제도는 금융시스템의 안정성에 대한 기여도가 있지만 장기적으로는 부작용이 생길 수 있다. 본 연구는 먼저 중국 상 장된 은행의 데이터를 가지고 Ronn & Verma 옵션평가모형을 이용하여 14개 은행의 예금보험료율을 추정하 였다. 주요한 연구결과는 다음과 같다. 첫째, 추정된 은행별 평균 예금보험료율을 살펴보면 국가소유은행은 0.0314%로서 주식제 상업은행 및 시티 상업은행의 0.1654%, 0.0630%보다 낮음을 알 수 있다. 둘째, 추정된 예금보험료율의 타당성을 평가하기 위하여, 추정된 예금보험료율과 Moody’s사의 신용등급의 관계를 추정한 결과 일부 기간에 높은 양의 상관관계로 추정되었는데 이는 은행의 채무불이행 위험을 어느 정 도 반영할 수 있다고 판단할 수 있다. 셋째, 추정된 예금보험료율과 수익성 지표인 ROA, 그리고 자본적정성지표인 BIS 자기자본비율과의 관계를 분 석한 결과 일부 기간에 예상대로 음의 상관관계가 나타났고, 자산 건전성을 나타내는 지표인 부실여신비율과 관계는 예상과 반대로 음의 상관관계가 나타났다. 이는 일부 기간에는 예금보험료율이 은행의 수익성, 자본적 정성 및 자산건전성과 유의적인 관련성이 존재할 수 있음을 의미한다.

The lack of deposit insurance in China is related to the fact that most of the banks in the country are State-owned and the government offer confidence to depositors. But under the “implicit deposit insurance system” it is impossible to provide a fair and efficient institution framework to tackle the great risks in Chinese banking system. The important issue in deposit insurance system is how to determine the deposit insurance premium. In this paper we use Ronn and Verma model(1986) to estimate Chinese 14 listed bank’s deposit insurance premium. In addition, in order to judge whether the estimation of deposit insurance premium rate is appropriate, we do the correlation analysis between the estimates and Moody’s credit ratings, capital variables such as ROA, BIS capital ratios , and Non-performing loan ratio. The results show that the estimated deposit insurance premium of listed banks are great different. And we find an significant relationship between the estimates and Moody’s credit ratings as well as capital variables in some period. It means that the estimated deposit insurance premium has an appropriate information about insured bank's default risk and can be relative with insured bank's profitability, capital adequacy and capital forbearance.

본 연구에서는 인근 택지지구의 기존주택을 대용변수로 활용한 이항옵션가격결정모형을 적용하여 최근에 판교신도시와 흥덕지구에 분양된 중대형 민영임대주택 분양권의 가치를 추 정하고 분양당첨의 손익을 분석하였다. 주요 분석결과로는 먼저 판교의 경우 중대형 민영임대주택의 분양당첨은 상당한 이익을 가져다 줄 수 있다는 것을 보여주었으나 흥덕의 경우 임대료선납이라는 부가조건에 의해서 겨우 손실을 면하는 것으로 나와 두 단지의 실제 청약경쟁률 결과와 어느 정도 부합되었다. 또 모수들의 변화에 대한 영향을 분석한 결과 판교의 경우 투자자들의 선호가 떨어지는 동 과 층에 당첨되더라도 어느 정도 수익이 보장될 가능성이 있으나 흥덕의 경우는 매우 취약 할 수 있다는 것을 알 수 있었다. 본 연구의 정책적인 함의로 중대형 민영임대주택 투자자들이 얻을 수 있는 미래의 시세차 익과 공급업체 측에서 추구하는 안정적인 초과임대수익 간의 적절한 균형을 모색하기 위하 여 분양권의 정확한 가치와 이에 따른 손익의 변화 등이 사전에 투자자들에게 충분히 알려 질 수 있는 제도적 장치가 필요하다는 것을 지적하였다 마지막으로 본 연구의 한계점을 제시하였다.

This paper investigate the value for a preemptive right on the private house for lease in Korea which were supplied at Pankyo and Heoungduk Area in February 2006 and May 2007. Using the price of the house in the neighborhood area, Bundang and Youngtong as proxy variable, we estimated the value of a preemptive right based on the binomial option pricing model. Major results are summarized as follows: (i) While a purchase of right for the case of Pankyo were profitable, the case of Heoungduk was'nt which was consistent with the historical competition results. (ⅱ) while the profitability for the Pankyo was stable across the variation of the parameters, Heoungduk was not. Finally, some policy implications and limitations of this paper were suggested.

본 연구는 대한민국에 주둔해 있는 주한미군의 운영유지를 위해 매년 지급하고 있는 방위비 분담금의 적정성을 검정한 연구이다. 주한미군의 역할과 가치를 위기상황에 대처하기 위한 풋옵션으로 정의하고, 풋옵션의 가격을 결정함으로써 주한미군의 전략적 가치를 추정하였다. 주한미군을 금융옵션이 아닌 실물옵션 개념으로 접근하여, 전쟁발생 이전의 한반도 경제규모를 “S(Spot Price)”으로, 개전 후 미군 증원 당시에 대한민국의 경제규모를 “K(Exercise Price)”로 정의하였다. K는 한반도 전쟁 시나리 오를 적용하여, S에서 동원령으로 인해 발생하는 산업 손실액, 남북경협자산 및 투자금의 동결 및 몰수 피해, 전쟁이후 민간과 군사분야의 피해율을 고려하여 추정하였다. 이후 블랙-숄즈 모형으로 도출된 풋 옵션 가격을 지급된 방위비 분담금 규모와 비교하여, 국방비 집행의 효율성을 판단하고, 미국과의 협상 을 위한 논리적 근거로 활용하고자 한다. 분석결과, 개전 후 미증원군이 한반도에 자동개입할 경우 전략적 가치의 범위는 2012년의 경우 9,000 억원~3조 9,800억 원으로, 2011년과 2012년에 방위비 분담금으로 지출한 8,125억 원과 8,361억 원은 실 물옵션 가격으로 적정함을 분석하였다. 연구결과로 제시된 적정 방위비 분담금의 범위가 넓어서, 연구의 현실성이 떨어진다고 볼 수 있으나, 비밀도 취급되는 한반도 전쟁시나리오를 엄격하게 적용시에는 보다 정확한 값을 얻을 수 있다. 개전 후 한반도 경제규모 변화율을 고려할 때, 미증원군의 전개시점이 빠를 수록 풋옵션의 적정가치는 급증하는 것으로 분석되었다. 지금까지 방위비 분담금에 대한 경제적 관점의 많은 연구가 있었으나 “적정한 방위비 분담금의 규모 는 얼마인가?”에 대한 연구는 협상 대상국인 미국을 설득할만한 수준으로 적당하지 않았다. 또한 감정적 이고 단편적인 비교로 인해 한반도의 안보의 특수성과 객관적인 접근법이 없었다. 본 논문은 한반도의 경제규모 변화를 실물옵션 기법으로 분석함으로써 합리성을 갖추고 전쟁시나리오에 따른 피해율을 반영 하여 현실을 정확히 반영하고자 노력하였다. 이는 실물옵션을 이용하여 방위비 분담금 규모를 추정한 최 초의 시도이다. 향후 진행될 방위비 분담금 특별협정(SMA. Special Measure Agreement) 간에 협상카 드로서 충분한 역할을 할 것으로 예상되며 분담금 지출에 대한 국가적 당위성과 예산사용의 합리성을 충분히 판단할 수 있는 근거가 될 것으로 기대된다.

The research is to estimate the validity of Korea’s annual contribution to the budget for maintaining the United States Forces Korea. Defining the put option as USFK’s role and value in order to confront crisis. It has estimated the strategic value(put premium) of the USFK by determining its price. Approaching the USFK as “Real Options” rather than “Financial Options”. We defined Korea’s economic scale prior to the wartime as “S(Spot price)” and after the breakout in time of US reinforcement as “K(Strike price)”. “K(Strike price)” is based on the Korea-U.S war scenario were calculated by considering loss of the civil and military sector. in this study, “K(Strike price)” is subtracted mobilization costs, investment costs, loss rate of the Korea from “S(Spot price)”. By comparing put option price approved by Black-Shoulds model with the amount of Korea’s budget contribution to the USFK. we try to evaluate the efficiency of National Defense expenses and to lay out a logical basis for negotiation with the United States. As a result, the interval of the strategic value is between 900 billion to 3.9trillion won in case of automatic intervention of US reinforcements, allowing Korea’s payments of 812billion and 836 billion won toward the USFK in 2011 and 2012 to be theoretically fairly valued as a Real Option price. The research can be lack of the reality because of the wide range of results, but we are able to get a more precise value by war scenario being kept secret. Considering the rate of change in Gross Domestic Product(GDP) after the wartime, the fair price of Put Option has been exponentially higher the sooner the US forces are augmented. Though there have been numerous studies on what would be the fair amount of the defense cost sharing in economical perspective, none of them yet succeeded in satisfying the palate of the United States. in other words, Most of the study was a lack of objectivity and rationality to appeal to the emotions or claims by simple comparison logic.This research endeavored to be rational by analysing the rate of change in GDP approached by the real option method and to be practical by reflecting the probability of damage according to the war scenario. It is the first attempt in estimating the contribution scale to the budget using the real options approach and is expected to play the satisfactory role for the future SMA(Special Measure Agreement) as the bargaining chip.

In recent years, financial industry has been growing rapidly. Especially the various products cause by financial engineering has been the major phenomenon of the development of financial market. If we call standard options, first generation options, then non-standard options can be called second generation options. Second generation options are exotic option. Option pricing method which used in this study were Closed-form formular assumed the log - normal price distribution and model followed underlying asset price distribution. In this study, Closed-form formular and Binomial model were programed by Excel Basic As a result of analysis. Binomial model is very convenient or speedy in exotic option which have special payoff pattern pricing.

Integrate the features of the geometric average in Asian option into level reset option, thus closed-form solution of geometric level reset options obtained through measure transformation and martingale pricing method. Numerical analysis results show that the geometric level reset call prices are increased with the increase of the number of level reset price, the risk hedge Δ value and the standard European call option are much closed, but there is no Δ jump phenomena of standard reset options.

The reconstruction of a volatility based on a Black-Scholes option pricing model is ill-posed. In order to overcome the ill-posedness, a homotopy perturbation inversion method is designed to solve the inverse problem. The proposed method is a modified version of the Landweber method. The reconstruction of a volatility is a nonlinear problem which is needed to be linearized. Hence, numerical experiments consist of the reconstruction of a policy parameter based on a Todaro model which is a linear inverse problem and the reconstruction of a volatility based on a Black-Scholes option pricing model in order to test the performance of the proposed method. Numerical examples show that the proposed method is more accurate and faster than the Landweber method.

In this paper, we derive the nonlinear equation for European option pricing containing liquidity risk which can be defined as the inverse of the partial derivative of the underlying asset price with respect to the amount of assets traded in the efficient market. Numerical solutions are obtained by using finite element method and compared with option prices of KOSPI200 Stock Index. These prices computed with liquidity risk are considered more realistic than the prices of Black-Scholes model without liquidity risk.

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

In this paper, we analyze offshore outsourcing contracts using the trinomial model, which is very useful in analyzing real options associated with offshoring projects. Earlier studies by Grenadier (1995) and Pashley, Krishnaswamy and Gilbert (1997) used the option pricing model to analyze lease contracts and debt contracts respectively. So far, however, no studies address offshore outsourcing contracts. Gopal, Mukhopadhyay, Krishnan, and Sivaramakrishnan (2003), Ethiraj, Kale, Krishnan, and Singh, (2004), Gopal and Koka (2010), and Gopal and Koka (2012) found through empirical studies a significant relationship between profits and type of contracts, and price and types of contracts respectively. But they do not provide a theoretical basis for their findings. In this paper we provide a theoretical basis for such a relationship employing the real options analysis using trinomial option pricing model.

In this paper, we investigate an efficient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.

In this paper, we propose a method to provide the distribution of option price under local volatility model when market-provided implied volatility data are given. The local volatility model is one of the most widely used smile-consistent models. In local volatility model, the volatility is a deterministic function of the random stock price. Before estimating local volatility surface (LVS), we need to estimate implied volatility surfaces (IVS) from market data. To do this we use local polynomial smoothing method. Then we apply the Dupire formula to estimate the resulting LVS. However, the result is dependent on the bandwidth of kernel function employed in local polynomial smoothing method and to solve this problem, the proposed method in this paper makes use of model averaging approach by means of bandwidth priors, and then produces a robust local volatility surface estimation with a confidence interval. After constructing LVS, we price barrier option with the LVS estimation through Monte Carlo simulation. To show the merits of our proposed method, we have conducted experiments on simulated and market data which are relevant to KOSPI200 call equity linked warrants (ELWs.) We could show by these experiments that the results of the proposed method are quite reasonable and acceptable when compared to the previous works.