• The Journal of Asian Finance, Economics and Business
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• v.8 no.2
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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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• v.33 no.1
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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.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.227-246
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• 2009

This study examines the dynamic hedging performances of the Black-Scholes model and Heston model when stock prices drift with stochastic volatilities. Using Monte Carlo simulations, stock prices consistent with Heston's(1993) stochastic volatility option pricing model are generated. In this circumstance, option traders are assumed to use the Black- Scholes model and Heston model to implement dynamic hedging strategies for the options written. The results of simulation indicate that the hedging performance of a mis-specified Black-Scholes model is almost as good as that of a fully specified Heston model. The implication of these results is that the efficacy of the dynamic hedging performances on evaluating the specifications of alternative option models can be limited.

• East Asian mathematical journal
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• v.34 no.1
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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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• v.27 no.3
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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.

• The Journal of the Korea Contents Association
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• v.13 no.12
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• pp.369-378
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• 2013

The Korean Won-Dollar exchange markets showed radical price movements in the late 1990s and 2008. Therefore it provides good sources for studying volatility phenomena. Using the GARCH option models, I analysed how the prices of foreign exchange options react volatilities in the foreign exchange spot prices. For this I compared the explanatory power of three option models(Black and Scholes, Duan, Heston and Nandi), using the Won-Dollar OTC option markets data from 2006 to 2013. I estimated the parameters using MLE and calculated the mean square pricing errors. According to the my empirical studies, the pricing errors of Duan, Black and Scholes models are 0.1%. And the pricing errors of the Heston and Nandi model is greatest among the three models. So I would like to recommend using Duan or Black and Scholes model for hedging the foreign exchange risks. Finally, the historical average of spot volatilities is about 14%, so trading the options around 5% may lead to serious losses to sellers.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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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.

• Journal of Digital Convergence
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• v.7 no.1
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.36 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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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.