• The Journal of Asian Finance, Economics and Business
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• 제8권2호
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• pp.685-695
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• 2021

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.

• East Asian mathematical journal
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• 제33권1호
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• pp.23-36
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• 2017

We study an optimization problem for HARA utility function under a multi-scale Heston's stochastic volatility model. We investigate a practical strategy that do not depend on the incorporated factor which is unobservable in the market.

• 재무관리연구
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• 제26권3호
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• pp.227-246
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• 2009

옵션 모형에 관한 실증연구에서 모형의 적격성을 평가하는데 사용한 잣대는 옵션 모형으로 구한 이론적 가격과 시장옵션가격간의 가격괴리를 평가하거나 일정기간동안 정기적으로 재조정한 헤지포트폴리오의 성과를 비교하는 것이다. 기존의 연구에서는 기초자산의 변동성에 대한 Black-Scholes 모형의 엄격한 가정을 이완시킨 확률적 변동성 모형이 Black-Scholes 모형의 가격괴리를 크게 개선하고 있음을 밝히고 있으나 동태적 헤지성과에 대해서는 여러 연구가 일관된 결과를 도출하고 있지 못하고 있다. 이 연구에서는 시뮬레이션 기법을 이용하여 Heston의 확률적 변동성 모형의 가정이 완벽히 구현되는 상황을 재현하고 그 상황에서 Heston 모형과 Black-Schols 모형의 동태적 헤지성과를 비교하였다. 시뮬레이션 결과에 따르면 헤지수단으로 기초자산만을 사용하였을 경우 완전히 적격한 모형인 Heston 모형은 확률적 변동성을 감안하지 않은 Black-Scholes 모형에 비해 헤지위험을 크게 줄이지 못하는 것으로 나타났다. 이 결과는 동태적 헤지성과로 옵션모형의 적격성을 평가하는 데는 일정부문 한계가 있을 수 있다는 점을 시사한다. 한편 실무적인 측면에서 옵션거래에 대한 동태적 헤지수단으로 굳이 확률적 변동성 모형과 같은 복잡한 모형을 이용할 필요가 없다는 점을 내포한다.

• East Asian mathematical journal
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• 제34권1호
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• pp.1-16
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• 2018

We study an optimization problem for hyperbolic absolute risk aversion (HARA) utility function under two-factor Heston's stochastic volatility model. It is not possible to obtain an explicit solution because our financial market model is complicated. However, by using asymptotic analysis technique, we find the explicit forms of the approximations of the optimal value function and the optimal strategy for HARA utility function.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.180-193
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• 2023

Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

• 한국콘텐츠학회논문지
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• 제13권12호
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• pp.369-378
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• 2013

원-달러 장외 외환 시장은 1990년말 외환위기 및 2008년 서브프라임 위기때 극심한 변동성을 보였으므로 변동성 연구에 적합한 특성을 띤다. 본고는 ARCH 모형에 기반해 옵션 가격 결정 모형을 제시한 Duan, Heston and Nandi의 GARCH 모형으로 외환 옵션 시장에서 변동성의 특성이 옵션 가격에 반영되는 정도를 분석해 보았다. 2006년 5월부터 2013년 1월까지 원-달러 장외시장에서 거래되는 옵션 자료에 대해 본고는 세 가지 모형(Black and Scholes, Duan, Heston and Nandi)간의 설명력을 비교했다. 최우추정법으로 계산된 모수를 고정하고 전일 내재 변동성을 이용하여 당일의 이론 가격을 구해 오차를 계산하면 Duan 및 Black and Scholes 모형 모두 약 0.1% 수준을 보인다. 다만 Heston and Nandi는 상기 두 모형에 비해 큰 오차값을 가지며 또한 만기가 길어지면 설명력이 약해진다. 따라서 원-달러 외환 옵션시장의 경우 Duan 또는 Black and Scholes 모형을 이용하여 가치를 측정하는 것이 유용할 것으로 사료된다. 또한 정책적 시사점으로는 외환 현물 시장의 과거 변동성 평균이 14% 전후에서 형성되었으므로 내재 변동성 5%전후에서 외환 옵션 등을 매매하는 것은 매도자에게 대규모 손실을 초래할 수 있다.

• 대한수학회보
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• 제53권3호
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• pp.733-749
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• 2016

We aim to compute discretely monitored geometric Asian option prices under the Heston model. This method involves explicit formula for multivariate generalized Fourier transform of volatility process and their integrals over different time intervals using a recursive method. As numerical results, we illustrate efficiency and accuracy of our method. In addition, we simulate scenarios which show evidently practical importance of our work.

• 디지털융복합연구
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• 제7권1호
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• pp.73-80
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• 2009

In this study, the pricing performances of alternative simple option models are examined by creating a simulated market environment in which asset prices evolve according to a stochastic volatility process. To do this, option prices fully consistent with Heston[9]'s model are generated. Assuming this prices as market prices, the trading positions utilizing the Black-Scholes[4] model, a semi-parametric Corrado-Su[7] model and an ad-hoc modified Black-Scholes model are evaluated with respect to the true option prices obtained from Heston's stochastic volatility model. The simulation results suggest that both the Corrado-Su model and the modified Black-Scholes model perform well in this simulated world substantially reducing the biases of the Black-Scholes model arising from stochastic volatility. Surprisingly, however, the improvements of the modified Black-Scholes model over the Black-Scholes model are much higher than those of the Corrado-Su model.

• 대한산업공학회지
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• 제36권2호
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• pp.101-107
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• 2010

Among a variety of asset dynamics models in order to explain the common properties of financial underlying assets, parametric models are meaningful when their parameters are set reliably. There are two main methods from which we can obtain them. They are to use time-series data of an underlying price or the market option prices of the underlying at one time. Based on the Girsanov theorem, in the pure diffusion models, the parameters calibrated from the option prices should be partially equivalent to those from time-series underling prices. We call this phenomenon model consistency. In this paper, we verify that the two-state regime switching Black-Scholes model is superior in the sense of model consistency, comparing with two popular conventional models, the Black-Scholes model and Heston model.

• 대한수학회보
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• 제46권2호
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• pp.209-227
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• 2009

We examine a unified approach of calculating the closed form solutions of option price under stochastic volatility models using stochastic calculus and the Fourier inversion formula. In particular, we review and derive the option pricing formulas under Heston and correlated Stein-Stein models using a systematic and comprehensive approach which were derived individually earlier. We compare the empirical performances of the two stochastic volatility models and the Black-Scholes model in pricing KOSPI 200 index options.