• The Journal of Asian Finance, Economics and Business
• /
• v.8 no.2
• /
• pp.685-695
• /
• 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.

• Korean Journal of Mathematics
• /
• v.16 no.2
• /
• pp.233-242
• /
• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.4
• /
• pp.249-273
• /
• 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].

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.55-60
• /
• 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.

• The Korean Journal of Financial Studies
• /
• v.3 no.1
• /
• pp.213-231
• /
• 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.

• East Asian mathematical journal
• /
• v.37 no.5
• /
• pp.567-576
• /
• 2021

In this paper, we deal with the pricing of vulnerable power exchange option. We consider the hybrid model as the credit risk model. The hybrid model consists of a combination of the reduced-form model and the structural model. We derive the closed-form pricing formula of vulnerable power exchange option based on the change of measure technique.

• Korean Journal of Mathematics
• /
• v.20 no.1
• /
• pp.47-60
• /
• 2012

We deal some analytic calculations for European option pricing by using the theory of elementary solution of generalized diffusion equation mainly.

• The Korean Journal of Financial Management
• /
• v.1 no.1
• /
• pp.133-149
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.2
• /
• pp.251-260
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.503-508
• /
• 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.