• Journal of the Korean Data and Information Science Society
• /
• 제24권4호
• /
• pp.669-677
• /
• 2013

본 연구에서는 다중자산 옵션 가격의 추정에 있어 자산의 수, 상관계수, 자산의 값들과 표준편차의 여러 조합에 대한 시뮬레이션을 통하여 저불일치 수열에 따르는 준난수 몬테칼로 방법들을 비교하였다. 결과적으로 준난수와 모로 역변환을 이용하는 것이 기본적인 몬테칼로 방법보다 정확하였으며 자산의 수와 관계없이 준난수 방법들 중 혼합법들이 더욱 효과적임을 알 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제26권4호
• /
• pp.343-352
• /
• 2022

We present the user-friendly graphical user interface design and implementation of Monte Carlo simulation (MCS) for computing option price of the four-underlying asset step-down equity linked securities (ELS) using the Android platform. The ELS has been one of the most important and influential financial products in South Korea. Most ELS products are based on one-, two-, and three-underlying assets. However, currently there is a demand for higher coupon payment from ELS products because of the increased interest rate in financial market. In order to allow the investors to have higher coupon payment, it is necessary to design a multi-asset ELS such as four-asset step-down ELS. We conduct the computational experiments to demonstrate the performance of the Android platform for pricing four-asset step-down ELS. Furthermore, we perform a comparison test with a three-asset step-down ELS.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제9권1호
• /
• pp.31-53
• /
• 2005

We analyze some real data and, from the background of analysis of data, we define a multi-dimensional jump-type asset model which is derived from short-sampling asset prices. We study some basic properties of this asset model.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제18권1호
• /
• pp.61-74
• /
• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제23권1호
• /
• pp.19-30
• /
• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제25권3호
• /
• pp.82-92
• /
• 2021

In this study, we present a fast option pricing method for four asset equity-linked securities (ELS) using Brownian bridge. The proposed method is based on Monte Carlo simulation (MCS) and a Brownian bridge approach. Currently, three asset ELS is the most popular ELS among multi-asset ELSs. However, four asset ELS emerged as an alternative to three asset ELS under low interest rate environment to give higher coupon rate to investors. We describe in detail the computational solution algorithm for the four underlying asset step-down ELS. The numerical tests confirm the accuracy and speed of the method.

• Journal of applied mathematics & informatics
• /
• 제38권5_6호
• /
• pp.439-461
• /
• 2020

A step-up option is a newly developed financial instrument that simultaneously provides higher security and profitability. This paper introduces two step-up options: step-up type1 and step-up type2 options, and derives the option pricing formulas using the Laplace transform. We assume that the underlying equity price follows a regime-switching model that reflects the long-term maturity of these options. The option prices are calculated for the two types of funds, a pure stock fund composed of risky assets only and a mixed fund composed of stocks and bonds, to reflect possible variety in the fund underlying asset mix. The impact of changes in the model parameters on the option prices is analyzed. This paper provides information crucial to product developments.