• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.620-627
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• 2003

The real option pricing theory has emerged as the new investment decision-making techniques superceding the traditional discounted cash flow techniques and thus has greatly received muck attention from academics and practitioners in these days the theory has been widely applied to a variety of corporate strategic projects such as a new drug R&D, an internet start-up. an advanced manufacturing system. and so on A lot of people who are interested in the real option pricing theory complain that it is difficult to understand the true meaning of the real option value. though. One of the most conspicuous reasons for the complaint may be due to the fact that there exit many different ways to calculate the real options value in this paper, we will present a replicating portfolio method. a risk-neutral probability method. a risk-adjusted discount rate method (quasi capital asset pricing method). and an opportunity cost concept-based method under the conditions of a binomial lattice option pricing theory.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.10-10
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• 2003

Option pricing theory developed by Black and Sholes depends on an arbitrage opportunity argument. An investor can exactly replicate the returns to any option on that stock by continuously adjusting a portfolio consisting of a stock and a riskless bond. The value of the option equal the value of the replicating portfolio. However, transactions costs invalidate the Black-Sholes arbitrage argument for option pricing, since continuous revision implies infinite trading, Discrete revision using Black-Sholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. Stochastic calculus serves as a fundamental tool in the mathematical finance. We closely look at the utility maximization theory which is one of the main option valuation methods. We also see that how the stochastic optimal control problems and their solution methods are applied to the theory.

• 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 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].

• 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.

• Journal of the Korean Society for Railway
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• v.10 no.2 s.39
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• pp.137-145
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• 2007

In traditional financial theory, the discount cash flow model(DCF or NPV) operates as the basic framework for most analyses. In doing valuation analysis, the conventional view is that the net present value(NPV) of a project is the measure of the present value of expected net cash flows. Thus, investing in a positive(negative) NPV project will increase(decrease) firm value. Recently, this framework has come under some fire for failing to consider the options of the managerial flexibilities. Real option valuation(ROV) considers the managerial flexibility to make ongoing decisions regarding the implementation of investment projects and the deployment of real assets. The appeal of the framework is natural given the high degree of uncertainty that firms face in their technology investment decisions. This paper suggests an algorithm for estimating volatility of logarithmic cash flow returns of real assets based on the Black-Sholes option pricing model, the binomial option pricing model, and the Monte Carlo simulation. This paper uses those models to obtain point estimates of real option value with the G7- HSR350X(high-speed train).

• International conference on construction engineering and project management
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• 2009.05a
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• pp.800-807
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• 2009

The limited public funds available for infrastructure projects have led governments to consider private entities' participation in long-term contracts for finance, construction, and operation of these projects to share risks and rewards between the public and the private. Because these projects have complicated risk evolutions, diverse contractual forms for each project member to hedge risks involved in a project are necessary. In light of this, Build-Operate-Transfer(BOT) model is considered as effective to accomplish Public Private Partnerships(PPPs) with a characteristic of an ownership-reversion. In BOT projects, the government has used such an incentive system as minimum revenue guarantee(MRG) agreement to attract the private's participation. Although this agreement turns out critical in success of BOT project, there still exist problematic issues in a financial feasibility analysis since the traditional capital budgeting theory, Net Present Value(NPV) analysis, has failed to evaluate the contingent characteristic of MRG agreement. The purpose of this research is to develop real option model based on option pricing theory so as to provide a theoretical framework in valuing MRG agreement in BOT projects. To understand the applicability of the model, the model is applied to the example of the BOT toll road project and the results are compared with that by NPV analysis. Finally, we found that the impact of the MRG agreement is significant on the project value. Hence, the real option model can help the government establish better BOT policies and the developer make appropriate bidding strategies.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1501-1509
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• 2011

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.721-733
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• 2011

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.753-755
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• 2005

The Black-Scholes (BS) option pricing model is a landmark in contingent claim theory and has found wide acceptance in financial markets. However, it has a difficulty in the use of the model, because the volatility which is a nonlinear function of the other parameters must be estimated. The more accurately investors are able to estimate this value, the more accurate their estimates of theoretical option values will be. This paper proposes a new model which is based on Particle Swarm Optimization (PSO) for finding more precise theoretical values of options in the field of evolutionary computation (EC) than genetic algorithm (GA)or calculus-based search techniques to find estimates of the implied volatility.