• Title, Summary, Keyword: option pricing

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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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VALUATION FUNCTIONALS AND STATIC NO ARBITRAGE OPTION PRICING FORMULAS

  • Jeon, In-Tae;Park, Cheol-Ung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.14 no.4
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    • pp.249-273
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    • 2010
  • Often in practice, the implied volatility of an option is calculated to find the option price tomorrow or the prices of, nearby' options. To show that one does not need to adhere to the Black- Scholes formula in this scheme, Figlewski has provided a new pricing formula and has shown that his, alternating passive model' performs as well as the Black-Scholes formula [8]. The Figlewski model was modified by Henderson et al. so that the formula would have no static arbitrage [10]. In this paper, we show how to construct a huge class of such static no arbitrage pricing functions, making use of distortions, coherent risk measures and the pricing theory in incomplete markets by Carr et al. [4]. Through this construction, we provide a more elaborate static no arbitrage pricing formula than Black-Sholes in the above scheme. Moreover, using our pricing formula, we find a volatility curve which fits with striking accuracy the synthetic data used by Henderson et al. [10].

A PROBABILISTIC APPROACH FOR VALUING EXCHANGE OPTION WITH DEFAULT RISK

  • Kim, Geonwoo
    • East Asian mathematical journal
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    • v.36 no.1
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    • pp.55-60
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    • 2020
  • We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for modeling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumulative function via a change of measure technique and a multidimensional Girsanov's theorem.

A SPECIFICATION TEST OF AT-THE-MONEY OPTION IMPLIED VOLATILITY: AN EMPIRICAL INVESTIGATION

  • Kim, Hong-Shik
    • The Korean Journal of Financial Studies
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    • v.3 no.1
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    • pp.213-231
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    • 1996
  • In this study we conduct a specification test of at-the-money option volatility. Results show that the implied volatility estimate recovered from the Black-Scholes European option pricing model is nearly indistinguishable from the implied volatility estimate obtained from the Barone-Adesi and Whaley's American option pricing model. This study also investigates whether the use of Black-Scholes implied volatility estimates in American put pricing model significantly affect the prediction the prediction of American put option prices. Results show that, at long as the possibility of early exercise is carefully controlled in calculation of implied volatilities prediction of American put prices is not significantly distorted. This suggests that at-the-money option implied volatility estimates are robust across option pricing model.

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The Pricing of Corporate Common Stock By OPM (OPM에 의한 주식가치(株式價値) 평가(評價))

  • Jung, Hyung-Chan
    • The Korean Journal of Financial Management
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    • v.1 no.1
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    • pp.133-149
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    • 1985
  • The theory of option pricing has undergone rapid advances in recent years. Simultaneously, organized option markets have developed in the United States and Europe. The closed form solution for pricing options has only recently been developed, but its potential for application to problems in finance is tremendous. Almost all financial assets are really contingent claims. Especially, Black and Scholes(1973) suggest that the equity in a levered firm can be thought of as a call option. When shareholders issue bonds, it is equivalent to selling the assets of the firm to the bond holders in return for cash (the proceeds of the bond issues) and a call option. This paper takes the insight provided by Black and Scholes and shows how it may be applied to many of the traditional issues in corporate finance such as dividend policy, acquisitions and divestitures and capital structure. In this paper a combined capital asset pricing model (CAPM) and option pricing model (OPM) is considered and then applied to the derivation of equity value and its systematic risk. Essentially, this paper is an attempt to gain a clearer focus theoretically on the question of corporate stock risk and how the OPM adds to its understanding.

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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.

COMPARISON OF NUMERICAL METHODS FOR OPTION PRICING UNDER THE CGMY MODEL

  • Lee, Ahram;Lee, Younhee
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.503-508
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    • 2016
  • We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

Decision-Making of Consumers with Higher Pain of Payment: Moderating Role of Pain of Payment When Payment Conditions Differ

  • Koh, Geumjoung;Sohn, Young Woo;Rim, Hye Bin
    • Science of Emotion and Sensibility
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    • v.21 no.4
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    • pp.3-10
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    • 2018
  • The present study explores two relationships: first, between number of payment and payment option preference, and second, total sum and payment option preference, with pain of payment as a mediator variable. The analyses revealed that consumers who feel higher pain of payment preferred the pennies-a-day pricing to the aggregate pricing when the per-payment price is low. Consumers who experience higher pain of payment prefer to pay in small frequent installments because they feel the small per-payment price can be comparable to daily expense. Consumers who experienced higher pain of payment preferred aggregate pricing to pennies-a-day pricing when the per-payment price was high. When the per-payment price is high, it is no longer comparable to daily expense, thus leading to greater pain of payment among consumers. The study discusses the implications for mechanism of pain of payment on payment option preference.