• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.93-106
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• 2021

In this paper, an efficient hybrid numerical method for solving two-asset option pricing problem is presented based on the Crank-Nicolson and the radial basis function methods. For this purpose, the two-asset Black-Scholes partial differential equation is considered. Also, the convergence of the proposed method are proved and implementation of the proposed hybrid method is specifically studied on Exchange and Call on maximum Rainbow options. In addition, this method is compared to the explicit finite difference method as the benchmark and the results show that the proposed method can achieve a noticeably higher accuracy than the benchmark method at a similar computational time. Furthermore, the stability of the proposed hybrid method is numerically proved by considering the effect of the time step size to the computational accuracy in solving these problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.121-137
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• 2022

In this paper, we investigate an efficient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.181-202
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• 2017

In this paper, we develop a mobile platform for pricing equity linked securities(ELS) using Monte Carlo simulation. Mobile phone or smartphone is an important part of most people's lives and has become an everyday item at the present day. Moreover, importance of technologies for anytime and anywhere is increasing daily. Thus, we construct a mobile computing environment for pricing ELS instead of desktops or laptop computers. We provide a detailed Java programming code and a process manual to easily follow up all processes of this paper.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.409-424
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• 2021

In this paper, we investigate a pricing model for mortgage-backed securities (MBSs) of a pay-through type of collateral mortgage obligation (CMO), embedded call options, which can be exercised by the intermediary, and pass-through MBSs. We suggest a prepayment-risk-neutral pricing model, applying a reduced-form prepayment rate model, and then compute and investigate the appropriate prices and spreads in the coupon rates between CMOs and PT MBSs. We believe that this study contributes in that it provides a sophisticated pricing model for MBSs, especially to the financial markets which are not advanced enough to finance with a simple type of MBSs.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.513-533
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• 2004

We present the pricing and hedging method for options with general payoffs in the presence of transaction costs. The convexity of the payoff function-gamma of the options- is an important issue under transaction costs. When the payoff function is convex, Leland-style pricing and hedging method still works. However, if the payoff function is of general form, additional assumptions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payoff is convex as in Leland 〔11〕 and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. 〔10〕, Avellaneda and Paras 〔1〕. We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payoff into difference of two options each of which has a convex payoff. This method is consistent with a scheme of separating out the seller's and buyer's position of an option. In this paper, we first present a simple linear valuation method of general payoff options, and also propose in the last section more efficient hedging scheme which costs less to hedge options.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.459-479
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• 2007

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.83-96
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• 2011

This work proposes a binomial method for pricing the cliquet options, which provide a guaranteed minimum annual return. The proposed binomial tree algorithm simplifies the standard binomial approach, which is problematic for cliquet options in the computational point of view, or other recent methods, which may be of intricate algorithm or require pre- or post-processing computations. Our method is simple, efficient and reliable in a Black-Scholes framework with constant interest rates and volatilities.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.285-294
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• 2008

A new Monte Carlo method is presented to compute the prices of barrier options on stocks. The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers. It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods.

• Korean Journal of Construction Engineering and Management
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• v.11 no.6
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• pp.54-64
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• 2010

A firm decides to go to the project based on its investment analysis. However, the cash flows generated from the real project can not be always coincident with what expected as it follows uncertain behavior and the asymmetric payoff caused by the managerial flexibilities involved in the real asset affects the project value. Amongst various managerial flexibilities entailed in most of the real assets, although investment delay has been known to enhance the project value thanks to its ability to provide new market information to management, the related research to select the time to invest have been just few. Therefore, this research aims to show the theoretical framework to decide when to invest reflecting the behaviors of increasing project value and loss recovery cost due to investment delay with option pricing, related financial economic, and variational theories.

• The Korean Journal of Financial Management
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• v.20 no.1
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• pp.279-304
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• 2003

This study presents some empirical results on variable rate deposit insurance premium in Korea. The study estimates deposit insurance premium for all insured financial institutions in Korea using Ronn and Verma(1986) model which is based on Merton(1977)'s option pricing model. The sample period is 1995-2001 and the study includes trend analysis and cross-sectional analysis for premium estimation. The study also includes the correlation analysis between the estimates and profitability and capitalvariables such as BIS capital ratios, ROE and ROA. The results show that the estimates differ across financial institutions and sample periods. Thus it supports that each deposit premium should reflect its own risks. It also supports the necessity for the system of variable rate deposit insurance premium.