• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.597-603
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• 2000

In this paper, we deal with the European Asian Arithmetical option and find the unique rational price associated with option and Asian arithmetical call-put parity.

• 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.

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

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

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1069-1075
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• 2000

In this paper, we deal with the European "Asian arithmetical option" and find the unique rational price associated with this option and Asian arithmetical call-put parity.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.569-574
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• 1999

In this paper we obtain relation between the heding prices in European and American option and apply to call option.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.87-100
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• 2009

Hedging strategy for European option of jump-type semimartingale asset model, which is derived from stochastic differential equation whose driving process is a jump-type semimartingle, is discussed.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.37-42
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• 2013

This paper suggests a numerical method for valuation of European and American options under the two L$\acute{e}$vy Processes, Normal Inverse Gaussian Model and the Variance Gamma model. The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the existing numerical method, the lattice-based method.

• 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.

• East Asian mathematical journal
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• v.34 no.3
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• pp.239-248
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• 2018

In this paper, we derive a closed-form formula of a second-order approximation for a European corrected option price under stochastic elasticity of variance model mentioned in Kim et al. (2014) [1] [J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)]. To find the explicit-form correction to the option price, we use Mellin transform approaches.

• 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).