• Title/Summary/Keyword: Option pricing

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

  • WATTANATORN, Woraphon;SOMBULTAWEE, Kedwadee
    • 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.

OPTION PRICING IN VOLATILITY ASSET MODEL

  • Oh, Jae-Pill
    • Korean Journal of Mathematics
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    • v.16 no.2
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    • pp.233-242
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    • 2008
  • We deal with the closed forms of European option pricing for the general class of volatility asset model and the jump-type volatility asset model by several methods.

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A numerical study on option pricing based on GARCH models with normal mixture errors (정규혼합모형의 오차를 갖는 GARCH 모형을 이용한 옵션가격결정에 대한 실증연구)

  • Jeong, Seung Hwan;Lee, Tae Wook
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.2
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    • pp.251-260
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    • 2017
  • The option pricing of Black와 Scholes (1973) and Merton (1973) has been widely reported to fail to reflect the time varying volatility of financial time series in many real applications. For example, Duan (1995) proposed GARCH option pricing method through Monte Carlo simulation. However, financial time series is known to follow a fat-tailed and leptokurtic probability distribution, which is not explained by Duan (1995). In this paper, in order to overcome such defects, we proposed the option pricing method based on GARCH models with normal mixture errors. According to the analysis of KOSPI200 option price data, the option pricing based on GARCH models with normal mixture errors outperformed the option pricing based on GARCH models with normal errors in the unstable period with high volatility.

NUMERICAL SOLUTIONS OF OPTION PRICING MODEL WITH LIQUIDITY RISK

  • Lee, Jon-U;Kim, Se-Ki
    • Communications of the Korean Mathematical Society
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    • v.23 no.1
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    • pp.141-151
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    • 2008
  • 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.

OPTION PRICING UNDER GENERAL GEOMETRIC RIEMANNIAN BROWNIAN MOTIONS

  • Zhang, Yong-Chao
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1411-1425
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    • 2016
  • We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

Recent Developments on Economic Valuation Method -CVA MAUA and Ral Option Pricing- (가치평가기법의 최근동향;CVM, MAUA 그리고 Real Option Pricing)

  • 허은녕
    • Journal of Korea Technology Innovation Society
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    • v.3 no.1
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    • pp.37-54
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    • 2000
  • 본 글에서는 최근 기술가치평가에 적용되고 있는 조건부가치평가법(Contingent Valuation Method) 다속성효용평가법(Multi-attribute Utility Assessment) 그리고 조건부청구권가치평가법(Real Option Pricing Method)의 세가지 가치측정기법들의 특징과 조요 관련 문헌들을 간략하게 정리하여 소개함으로서 관심있는 연구자들에게 유용한 정보를 제공하고자 한다. 소개하는 방법론들은 환경재화의 가치측정기법과 위험도가 높은 에너지프로젝트의 가치평가기법으로 개발된 기법들로서 신기술이 가지는 특징인 외부성 등의 비시장재적 특성과 높은 위험도에따른 투자가치를 반영할 수있어 기술 및 기업의 가치평가 사례연구에 응용할 수있다.

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An Option Pricing Model for the Natural Resource Development Projects (해외자원개발사업 평가를 위한 옵션가격 결정모형 연구)

  • Lee, In-Suk;Heo, Eunnyeong
    • Environmental and Resource Economics Review
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    • v.13 no.4
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    • pp.735-761
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    • 2004
  • As a possible alternative to Traditional Discounted Cash Flow Method, "Option Pricing Model" has drawn academic attentions for the last a few decades. However, it has failed to replace traditional DCF method practically due to its mathematical complexity. This paper introduces an option pricing valuation model specifically adjusted for the natural resource development projects. We add market information and industry-specific features into the model so that the model remains objective as well as realistic after the adjustment. The following two features of natural resource development projects take central parts in model construction; product price is a unique source of cash flow's uncertainty, and the projects have cost structure from capital-intense industry, in which initial capital cost takes most part of total cost during the projects. To improve the adaptability of Option Pricing Model specifically to the natural resource development projects, we use Two-Factor Model and Long-term Asset Model for the analysis. Although the model introduced in this paper is still simple and reflects limited reality, we expect an improvement in applicability of option pricing method for the evaluation of natural resource development projects can be made through the process taken in this paper.

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A COST-EFFECTIVE MODIFICATION OF THE TRINOMIAL METHOD FOR OPTION PRICING

  • Moon, Kyoung-Sook;Kim, Hong-Joong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.15 no.1
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    • pp.1-17
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    • 2011
  • A new method for option pricing based on the trinomial tree method is introduced. The new method calculates the local average of option prices around a node at each time, instead of computing prices at each node of the trinomial tree. Local averaging has a smoothing effect to reduce oscillations of the tree method and to speed up the convergence. The option price and the hedging parameters are then obtained by the compact scheme and the Richardson extrapolation. Computational results for the valuation of European and American vanilla and barrier options show superiority of the proposed scheme to several existing tree methods.

ASYMPTOTIC OPTION PRICING UNDER A PURE JUMP PROCESS

  • Song, Seong-Joo
    • Journal of the Korean Statistical Society
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    • v.36 no.2
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    • pp.237-256
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    • 2007
  • This paper studies the problem of option pricing in an incomplete market. The market incompleteness comes from the discontinuity of the underlying asset price process which is, in particular, assumed to be a compound Poisson process. To find a reasonable price for a European contingent claim, we first find the unique minimal martingale measure and get a price by taking an expectation of the payoff under this measure. To get a closed-form price, we use an asymptotic expansion. In case where the minimal martingale measure is a signed measure, we use a sequence of martingale measures (probability measures) that converges to the equivalent martingale measure in the limit to compute the price. Again, we get a closed form of asymptotic option price. It is the Black-Scholes price and a correction term, when the distribution of the return process has nonzero skewness up to the first order.