Pricing Kernel-Based Option Valuation Approach: A New Perspective

류두진 ( Doo Jin Ryu ) 한국금융공학회 2012 한국금융공학회 학술발표회 Vol.2012 No.-

This study examines the empirical performance of three model-based option valuation approaches in the KOSPI200 options market. We evaluate the in-sample pricing, out-of-sample pricing and hedging performance of the approaches based on the specification of option pricing models directly (a pricing model-based approach), on the pricing kernels implied by the option pricing models (an implied pricing kernel-based approach), and on parametric pricing kernels which are independently structured to have their own explicit functional forms (a parametric pricing kernel-based approach). Two option pricing models, a GARCH option pricing model and a Black-Scholes (BS) option pricing model, and their implied pricing kernels are analyzed and two parametric pricing kernel specifications suggested by Rosenberg and Engle (2002) are compared in a unified framework which extends the GARCH process of Duan (1995) to reflect the dynamics of asymmetric volatility. We find that the empirical performance of the approaches related to the GARCH and Black-Scholes option pricing models is moderately improved when we estimate the structural parameters using options data (options-based estimation) compared to the model performances when estimating the parameters using only a time-series of underlying returns data (underlying returns-based estimation). With the estimates under the underlying returns-based estimation, the pricing modelbased option valuation approach outperforms the implied pricing kernel-based option valuation approach for both the GARCH and BS option pricing models. However, with the estimates under the options-based estimation, this relationship is reversed in pricing OTM options in the case of the GARCH option pricing model. Although the BS option pricing model is generally the worst performer with the estimates under the underlying returns-based estimation, it yields better performance for pricing ITM options and similar performance for hedging compared to the GARCH option pricing model with the estimates under the options-based estimation. The option valuation approach based on the parametric pricing kernel of which functional form is a Chebyshev polynomial performs best out of all approaches and methods considered in this study.

Pricing Kernel-Based Option Valuation Approach : A New Perspective

Doojin Ryu 한국재무학회 2011 한국재무학회 학술대회 Vol.2011 No.09

This study examines the empirical performance of three model-based option valuation approaches in the KOSPI200 options market. We evaluate the in-sample pricing, out-of-sample pricing and hedging performance of the approaches based on the specification of option pricing models directly (a pricing model-based approach), on the pricing kernels implied by the option pricing models (an implied pricing kernel-based approach), and on parametric pricing kernels which are independently structured to have their own explicit functional forms (a parametric pricing kernel-based approach). Two option pricing models, a GARCH option pricing model and a Black-Scholes (BS) option pricing model, and their implied pricing kernels are analyzed and two parametric pricing kernel specifications suggested by Rosenberg and Engle (2002) are compared in a unified framework which extends the GARCH process of Duan (1995) to reflect the dynamics of asymmetric volatility. We find that the empirical performance of the approaches related to the GARCH and Black-Scholes option pricing models is moderately improved when we estimate the structural parameters using options data (options-based estimation) compared to the model performances when estimating the parameters using only a time-series of underlying returns data (underlying returns-based estimation). With the estimates under the underlying returns-based estimation, the pricing modelbased option valuation approach outperforms the implied pricing kernel-based option valuation approach for both the GARCH and BS option pricing models. However, with the estimates under the options-based estimation, this relationship is reversed in pricing OTM options in the case of the GARCH option pricing model. Although the BS option pricing model is generally the worst performer with the estimates under the underlying returns-based estimation, it yields better performance for pricing ITM options and similar performance for hedging compared to the GARCH option pricing model with the estimates under the options-based estimation. The option valuation approach based on the parametric pricing kernel of which functional form is a Chebyshev polynomial performs best out of all approaches and methods considered in this study

채권선물옵션의 가격결정

안창모 ( Chang Mo Ahn ),정재욱 ( Jaewook Chung ) 한국금융공학회 2017 금융공학연구 Vol.16 No.2

본 논문은 이자율이 평균회귀확산과정 (mean-reverting diffusion process)을 따라 불확실하게 움직일 때 균형 채권현물가격, 채권선도가격, 채권선물가격, 채권선도 옵션가격, 채권선물 옵션가격의 폐쇄해를 제공한다. 이들 공식들은 블랙숄 (Black Scholes) 옵션공식과 일관성이 있어 쉽게 응용될 수 있다. 이들 공식은 현재가치화를 포함하고 있어 블랙숄 옵션공식과 다른 차이점이 있다. 본 논문의 중요한 기여는 채권선도가격이 채권선물가격보다 높은 한 채권선도옵 션가격이 채권선물옵션가격보다 높다는 것을 증명한 것이다. 일일결제 (the marking to market)에 의해 채권선물가격이 상응하는 채권선도가격 보다 저렴하기 때문에 채권선물옵션가격은 상응하는 채권선도옵션가격에 비해 저렴하다. We derive closed-form solutions for bond futures and forward prices and bond spot options, bond futures and forward options, when the instantaneous interest rates follow a mean-reverting diffusion process. The pricing formulas are consistent with the Black-Scholes option formula so that they can be easily applied. These formulas include the present value operator which makes them look different from the Black-Scholes formula. An important conclusion is that as long as the bond forward price is greater than the bond futures price, the bond forward call option price is greater than the bond futures call option price. Since the marking to market from the futures contract lowers the futures price compared to the forward price, the bond futures call option price is strictly lower than the corresponding bond forward call option price. This result is contrast to Ahn (1996a) which shows the numerical analysis that the currency futures option price is strictly greater than the corresponding currency forward option price since the currency futures price at the expiration date is greater than the corresponding currency forward price.

KOSPI200 옵션시장과 선물시장 간 가격발견 분석

이우백 ( Woo Baik Lee ),박종원 ( Jong Won Park ) 한국금융학회 2016 금융연구 Vol.30 No.2

본 논문은 개별 파생상품시장 간 상호 가격발견 기능과 결정요인을 KOSPI200 옵션시장과 선물시장을 대상으로 실증적으로 검증했다. 실증 분석에는 KOSPI200 옵션과 선물의 패리티로부터 유도한 합성선물가격과 실제선물가격으로 구성된 오차수정모형을 활용했다. 양 변수 간 선도. 후행 관계를 측정한 결과 합성선물이 실제선물을 일방적으로 선도하는 표본일의 비율은 전체표본의 57%로 합성선물이 실제선물의 가격발견을 지배적으로 주도하는 것으로 분석되었다. 반면실제선물은 합성선물에 독자적으로 선행하기보다 양방향적 관계에서 환류하는 경향이 강했다. 선도ㆍ후행 관계의 대안적인 지표로 Hasbrouck(1995)의 정보량을 도입하여 측정한 결과에서도 합성선물의 정보량은 66%로 실제선물의 값을 현저히 초과하여 역시 가격발견에서 우위에 있음이 확인되었다. 이와 같은 실증분석 결과를 볼 때 양 시장 간의 선도ㆍ후행관계는 결국 합성선물을 구성하는 옵션시장의 정보가 선물시장으로 유입되는 구조이며, 선물시장의 가격발견을 옵션시장이 주도하고 있음을 제시한다. 또한 선물시장에 대한 옵션의 가격발견 주도권을 머니니스와 유동성에 따른 표본으로 구분한 결과에서 선물시장의 가격발견의 대부분을 강하게 주도하는 옵션은 등가격옵션이지만, 외가격과 내가격으로 구성된 비등가격 옵션이 가격발견에 공헌하는 정도는 상대적으로 약한 것으로 파악되었다. 이 같은 연구 결과는 거래비용이 저렴하고 위험을 선호하는 투자자들이 집중하는 외가격 옵션에서 가격발견이 관찰된다는 일부 선행연구들의 실증 결과와는 대립된다. 이는 국내 옵션시장에서 외가격을 집중적으로 거래하는 투자주체는 개인투자자이며 이들은 외국인이나 국내 기관투자자에 비해 정보 수준에서 열위에 있으므로 투자손실을 입는다는 선행연구와 관련지어 생각해 볼 수 있다. 거래활동 측면에서도 유동성이 높은 옵션일수록, 가격발견을 주도하는 유동성 외부 효과가 존재하는 것으로 분석되었다. We examine price discovery the KOSPI 200 futures and options markets using the intraday data from Feb. 10, 2012 to June 13, 2001, There are many studies on price discovery among the individual derivatives products, however very few studies on the relationship between derivatives markets. There are many differential aspects in individual derivatives products and derivatives markets in trading strategy such as index arbitrage, informations types such as individual or market-wide, regulation such as program trading halts, and investor types. These motivate our study. KOSPI 200 futures and options markets are highest ranked markets among all index derivatives markets in the world in terms of trading volume. These markets provide a good opportunity to study price discovery and determinants between derivatives markets. Using the intraday data, we construct a Vector Error Correction Model (VECM) of KOSPI 200 actual futures prices and synthetic futures prices which are induced from option-futures parity. And the lead-lag relationship and ``information share`` of Hasbrouck (1995) are analyzed. We can replicate a synthetic futures position or option position from the put-call-futures parity, and this methodology is model free and is analyzed easily based on market prices. Key empirical results are summarized as follows: The result of the lead-lag relationship between synthetic futures and actual futures from VECM shows that synthetic futures price leads dominantly actual futures price, the sample which synthetic futures price lead actual futures price is 57% of total sample, but actual futures price shows an interactive feedback relationship rather than one way leading relationship to synthetic futures price. As an alternative measure we estimate ``information share`` of Hasbrouck (1995), the estimated value of synthetic futures is 66% which is markedly greater than that of actual futures. These results mean that price information generated in the options markets dominate the futures markets and price discovery in the futures market is lagged by the options market. These are very interesting, because that KOSPI 200 futures and options markets have a close market linkage via arbitrage mechanism and have developed a similar growth process. We can think that investors use a forecasting strategy of market directionality using market-wide information in futures market, however investors use a volatility forecasting strategy which include two-way directionality in options market and provide an information for futures price. Consequently options market can have superior to futures market in price discovery. Also investors can synthesize various cash flow positions using options products, these synthetic positions will be helpful for exploring the futures price. We analyze the initiative of options market in price discovery for the subsamples classified by option moneyness. The results show that the lead effect of options market strongly arise from at-the-money (ATM) options, but the contributions of out-of-the-money (OTM) and in-the-money options are weak. These results are contrary to existing studies on other countries, especially U.S.. Some studies report that price discovery effect of OTM options are significant, however in the KOSPI 200 options market many studies report that individual investors are noise traders who are inferior to foreign and institutional investors in information and have a speculative behaviour and loss from trading of low-cost OTM options. This means that the function of price discovery is activated in ATM options because of the trade participation of informed traders, however the price discovery is inferior in OTM options because of the trading behaviour of noise traders. And these imply that the efficacy of price discovery of options markets will be determined by information ability of investors and trading strategy. Finally, we analyze the initiative of options market in price discovery for the subsamples classified by option liquidity. The result shows that there are liquidity externalities which liquid options are more informative in price discovery. This means that in liquid markets, investors participate more actively in trading and this raises the market quality and so raise the price discovery.

Copula함수를 이용한 Digital Option의 가격결정에 관한 연구

정지훈 ( Ji Hoon Jung ),최양호 ( Yang-ho Choi ) 한국계리학회 2016 계리학연구 Vol.8 No.1

1973년 Black-Scholes 옵션가격결정 모형이 나온 이후 옵션에 대한 연구는 오늘날까지 급속도로 발전해 왔다. 옵션가격결정 모형은 광범위한 적용가능성을 가지고 있어 주식가치의 평가, 전환사채의 평가, 신주인수권 및 신주인수권부사채의 평가, 담보부채의 평가, 리스, 보험계약 등에 옵션가격결정 모형을 이용할 수 있다. 그러나 Black-Scholes 이론에 입각한 옵션가격결정 모형은 그 가정들이 비현실적인 부분들이 많고 또한, 오늘날 보험회사를 포함한 금융회사들의 파생상품과 같은 자산들로 구성된 포트폴리오에서 자산들 간의 종속성 문제들이 이슈가 되면서 많은 금융권의 회사들은 Copula를 이용하는 등 자산 간의 종속성 문제를 해결하려고 노력하고 있다. 본 논문에서는 옵션가격결정모형, Copula 등에 관한 이론을 고찰해 보고 MultidimensionalBlack-Scholes 옵션가격결정 모형과 Copula를 이용한 옵션가격결정 모형을 두 가지의 주식 데이터를 기초자산으로 하는 경우를 가정하여 Digital 옵션의 가치를 평가해 본다. 분석에 있어서는 R프로그램을 사용하였는데 그 중 본 논문의 분석에 적합한 BinaryOption,fitCopula, Copula패키지를 이용하여 분석을 진행하였다. 분석 결과 Copula를 이용하여 산출한 Digital 옵션가격이 Multidimensional Black-Sholes를 이용하여 산출한 Digital 옵션가격보다 크게 산출되었는데 이는 옵션가격을 결정할 때 Copula함수가 기초자산 간의 종속성을 더 잘 반영하였기 때문이라고 여겨진다. 본 연구의 한계로는 옵션가격결정 모형의 한계, 완전한 시장(Complete Market)을 가정하여 생기는 불완전한 시장(Incomplete Market)에서의 한계, 기초자산을 두 개라고 정하여 그 이상일 때 분석하기 어려운 한계 등이 있다. 본 연구의 타당성을 조금 더 확보하기 위해서는 보다 정확한 투입변수의 측정과 완전한 시장이 아닌 현실적인 불완전한 시장에서의 설명력이 높은 이론과 모형에 대한 연구가 필요할 것이다. Since Black-Scholes option pricing model was developed by F. Black and M. Scholes in 1973, rapid progress has been made in the studies of option until today. As the option pricing model has wide applicability, it can be used in evaluating various things such as stock values, convertible bonds, preemptive rights and bond with warrant, and collateralized debt and also in lease and insurance contracts. In addition, the option pricing model can be used in analyzing companies`` financial decision-making. By looking into the option pricing model, the multivariate option pricing model, and theories about Copula etc. and by applying the Multidimensional Black-Scholes option pricing model and the option pricing model using Copula to the stock market in the United States, this study carried out a comparative analysis on option prices using two types of option pricing models in the U. S. stock market. Especially, this research assessed the value of Digital option assuming the case of two underlying assets. The limitations of the present study include the limitation of Black-Scholes option pricing model, the limitation of analyzing Incomplete Market due to the assumption of Complete Market, and the limitation in analyzing the cases of more than two underlying assets. To ensure the validity of this study, there is a need to perform research including the measurement of more accurate input variables and studies on theories and models with better explanatory power in Incomplete Market which is more realistic than Complete Market.

The Stochastic Volatility Option Pricing Model: Evidence from a Highly Volatile Market

WATTANATORN, Woraphon,SOMBULTAWEE, Kedwadee Korea Distribution Science Association 2021 The Journal of Asian Finance, Economics and Busine Vol.8 No.2

This study explores the impact of stochastic volatility in option pricing. To be more specific, we compare the option pricing performance between stochastic volatility option pricing model, namely, Heston option pricing model and standard Black-Scholes option pricing. Our finding, based on the market price of SET50 index option between May 2011 and September 2020, demonstrates stochastic volatility of underlying asset return for all level of moneyness. We find that both deep in the money and deep out of the money option exhibit higher volatility comparing with out of the money, at the money, and in the money option. Hence, our finding confirms the existence of volatility smile in Thai option markets. Further, based on calibration technique, the Heston option pricing model generates smaller pricing error for all level of moneyness and time to expiration than standard Black-Scholes option pricing model, though both Heston and Black-Scholes generate large pricing error for deep-in-the-money option and option that is far from expiration. Moreover, Heston option pricing model demonstrates a better pricing accuracy for call option than put option for all level and time to expiration. In sum, our finding supports the outperformance of the Heston option pricing model over standard Black-Scholes option pricing model.

퍼지이론에 근거한 옵션가격결정모형의 실증적 고찰

강태훈(Tae-Hun Kang),이민규(Minkyu Lee) 한국산업경제학회 2016 산업경제연구 Vol.29 No.2

본 연구는 KOSPI 200 지수옵션시장을 대상으로 Qin and Li(2007) 모형(QL)의 유용성을 실증적으로 고찰하였다. Qin and Li(2007)는 주가수익률이 Zadeh(1965)의 퍼지집합이론에 근거한 기하Liu과정을 따른다는 가정 하에서 유럽형 옵션의 가치평가모형을 유도하였는데, 이는 Black and Scholes(1973)가 전통적인 확률이론에 근거한 기하브라운운동 하에서 유도한 모형(BS)과 대응될 수 있다. 그런데 실무에서는 BS의 체계적인 가격편의를 완화하기 위하여 상수변동성 대신에 주로 모수적인 변동성함수를 BS에 대입하여 사용(AHBS)하는 것으로 알려져 있다. 따라서 QL의 적합성과와 가격예측성과를 비교하기 위한 이론적이고 실무적인 기준모형으로 각각 BS와 AHBS를 이용하였다. QL과 BS, AHBS의 모수는 기초자산의 과거 시계열정보를 이용한 조건부변동성의 예측치와(나) 옵션시장가격에 내재된 정보로부터 추정하였기 때문에, 모형이 가정하는 기초자산의 확률과정과 변동성스마일의 고려여부, 모수추정자료와 방법에 따라 총 7가지 모형(BS_HR, BS_HU, BS_I, AHBS, QL_I, QL_IHR, QL_IHU)의 성과가 비교된다. 옵션가격의 예측에는 특정한 예측기간을 주관적으로 선택하지 않고, 분석표본의 결제월들 중에서 최소 거래일수가 12거래일이므로, 이를 기준으로 1거래일부터 11거래일까지의 모든 예측기간에 대하여 모형별 외표본성과를 비교하였다. 또한 모형별로 성과의 차이가 발생하는 이유를 옵션시장과 기초자산시장의 관련 변수들을 중심으로 살펴보았다. 분석결과, 퍼지이론에 근거한 QL_I는 AHBS보다 더 적은 모수를 이용하여 시장가격에 내재된 정보를 상대적으로 잘 반영할 수 있을 뿐만 아니라, BS보다 더 많은 모수를 가짐에도 시계열적으로 보다 안정된 예측오차를 가졌다. 그리고 QL_I는 머니니스와 잔존기간, 옵션유형에 상관없이 우수하지만 특히 풋옵션보다는 콜옵션을 이용한 의사결정에서 보다 유용하며, 내재모수의 시계열 불안정성이 증가할 수 있는 상황에서도 상대적으로 짧은 예측기간에서 콜옵션을 이용함으로써 보다 안정된 예측성과를 달성할 수 있는 것으로 확인되었다. This paper examines the improvement in the price forecasting of KOSPI 200 index options by using Qin and Li (2007)’s model (QL). Qin and Li (2007) formulated the european option pricing formula for fuzzy financial market which may be regarded as the fuzzy counterpart of Black and Scholes (1973) option pricing formula (BS). To investigate the usefulness of QL, the forecasting performance of QL are compared with those of BS and ad hoc approach of BS (AHBS) in which implied volatility are smoothed across strike prices. The option’s parameters are inferred by using the information implied in option market prices and (or) historical information from the underlying asset returns. And to make the concrete results, forecasting performance of the models are compared by looking at pricing errors into multiple forecasting periods and analysis of the determinants of the forecasting difference across models are examined based on underlying and option related effects on option pricing. It is found that QL based on fuzzy theory in which the option’s parameters are inferred by using the information implied in option market prices outperforms the other models in terms of effectiveness for in-sample pricing and out-of-sample pricing. Although this relative usefulness of QL remained unchanged regardless of the moneyness, maturity and type of options, QL is more relevant for the decision marking using call options. Summarizing all findings, QL is found to be a recommended option pricing model in KOSPI 200 index option market.

An Empirical Comparison of Option Valuation Approaches: The Case of KOSPI 200 Options

류두진 ( Doo Jin Ryu ) 한국금융공학회 2010 한국금융공학회 학술발표회 Vol.2010 No.2

This paper examines the empirical performance of two option valuation approaches: the pricing model-based option valuation approach, which is based on the direct specification of the option pricing models, and the implied pricing kernel-based option valuation approach, which is based on pricing kernels implied by option pricing models under the unified GARCH framework. In terms of parameter estimates obtained from the underlying returns-based estimation, the pricing model-based approach always outperforms the implied pricing kernel-based approach. However, in terms of parameter estimates obtained from the option-based estimation, the implied pricing kernel-based approach outperforms the pricing modelbased approach in pricing OTM options in the case of the GARCH option pricing model, and both of the option valuation approaches supported by the Black-Scholes option pricing model, which are generally poor performers, perform better than those option valuation approaches supported by the GARCH option pricing model in pricing ITM options and show similar performance in hedging.

콜옵션과 풋옵션 간의 정보수렴과정

강태훈(Tae Hun Kang) 한국증권학회 2016 한국증권학회지 Vol.45 No.3

본 연구는 제한된 차익거래 하에서 콜옵션과 풋옵션 간의 상호적인 정보수렴과정에 대한 가설을 실제 의사결정자의 관점에서 실증적으로 검증한다. 그리고 두 시장 간의 상호적인 정보수렴과정을 반영함으로써, 옵션의 시장가격을 보다 정확하게 예측할 수 있는가를 고찰한다. 본 연구에서 발견된 분석결과를 요약하면 다음과 같다. 첫째, 콜옵션시장(풋옵션시장)에서 더 강하게 영향을 미치는 정보는 적어도 3, 4거래일까지는 시간이 흐를수록 강도가 약해지면서 풋옵션시장(콜옵션시장)으로 지연되게 반영된다. 둘째, 콜옵션과 풋옵션시장 간의 상대적인 정보수렴속도를 비교한 결과, 본 연구의 분석기간인 2012년부터 2014년까지는 전반적으로, 콜옵션이 풋옵션시장보다 고유한 정보를 더 빠르게 수렴한 후에 이를 상대시장으로 흘려보내는 것으로 확인된다. 또한 정보를 더 빠르게 수렴할수록 시계열은 더 낮은 규칙성을 가질 것이므로, 이를 근사엔트로피로 측정한 결과에서도 콜옵션이 풋옵션보다 복잡성이 더 높았다. 셋째, 내재정보만을 이용하는 상이한 분석방법론으로 동일한 가설검정을 수행하더라도, 두 시장 간 정보수렴과정과 속도에 관한 일관된 결론이 확인되며, 벡터자기회귀모형의 추정결과 또한 이를 지지한다. 마지막으로 두 시장 간의 상호적인 정보수렴과정을 반영함으로써 향후 옵션의 시장가격을 보다 정확하게 예측할 수 있는가를 분석한 결과, 2거래일의 예측기간까지는 콜옵션과 풋옵션 간의 정보수렴과정을 이용함으로써 옵션가격 예측성과가 개선된다. 특히 두 내재정보를 가중평균하는 6가지의 상이한 방법들 중에는 예측기간이 한 거래일씩 증가할수록 단순히 가중치를 0.1로 감소시키는 방법도 포함되어 있으므로, 실무에서 자주 이용되는 AHBS보다 유용성과 편의성이 높을 것으로 기대된다. This study empirically tests some hypothesis about the information convergence processes between the call and put options market under limits to arbitrage, by using the methodology designed in terms of options market participants as well as econometric models, and then, analyzes whether considering the cross effects of implied informations into the information convergence processes can improve out-of-sample pricing performance. The major conclusions drawn from the empirical results are summarized as follows. First, the implied information reflected only in call (put) prices gradually have a decreased effect on a put (call) prices during three or four trading days. Second, the information convergence function of the call options market may be more efficient than the put options market. Specifically, the implied information reflected only in call (put) prices converge more quickly on the put options market before independent information of put options is fully reflected in call options prices. And, the degree of a complexity, irregularity and unpredictability in time series of the information implied in the call options prices, estimated by using the approximate entropy method proposed by Pincus (1991), is shown to be higher than those in put options prices. Third, the robustness testing which can control the effect of the decision errors be caused by variables except implied information in forecasted option prices reach the same conclusions about the information convergence processes between call and put options market. And the estimates of vector autoregression used to capture the linear interdependencies among volatilities implied in call and put options also support the hypothesis. Last, it is indeed useful to jointly model call and put implied volatilities, in which the cross effects of implied informations into the information convergence processes can be captured, to improve out-of-sample pricing performance up to two trading days, regardless of different weighting schemes of call and put implied volatilities. Especially, the simple scheme in which weighting are monotonically decreasing (increasing) in the forecasting days is not only more useful but also more easy to use than ad-hoc Black and Scholes model which is one of the most widely used option valuation procedures among practitioners.

Investigating the Theoretical and True Option Values with a Variety of Option Pricing Models : Based on the KOSPI 200 Stock Index Options

김규태,정수희 한국경영공학회 2010 한국경영공학회지 Vol.15 No.2

Abstract – Black and Scholes published the seminal paper "The Pricing of Option and Corporate Liabilities (8)" in 1973. The Black & Scholes model marked an epoch in trading options in an orderly market with well-defined contracts in 1973. An as the expiration date comes closer and closer thanks to their contribution, much research on valuing options has been actively conducted. For instance, Cox, Ross, and Rubinstein proposed a binomial lattice option pricing model in 1976. In Korea, the option market was introduced with the KOSPI 200 stock index option on the 7th day of July in 1997. Since then, the option market has been steadily growing. As the option market grows, it is required that the investors obtain an accurate option value. However, it is not easy to know the accurate option value in advance mainly due to the volatility of the options. In this paper, we will analyze the option pricing models to compare the theoretical option values with the option prices traded in a Korean option market. To provide theoretical option values, Black & Scholes model and binomial lattice option pricing model, which are most widely used, will be employed and a Monte Carlo simulation will be followed for the option price presumption and analysis. For the empirical analysis purpose, we will use the KOSPI 200 stock index option data from January to December in 2008 and 2009. The set of data was collected from a daily closing stock and option price list. For the comparison purpose, we will conduct a statistical analysis with the data collected to provide a validity test.