• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.665-673
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• 2014

Power options have payoffs that are determined by the price of the underlying asset raised to some power. In this paper, power options are considered under a regime-switching model which can capture complex asset dynamics by permitting switching between different regimes. The pricing formulas for the Laplace transforms of power options are obtained. The prices of power options are calculated using the formulas and compared with the results of the Monte Carlo simulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.82-92
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• 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.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.11
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• pp.1-10
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• 2021

This paper compares the performance of Fama-French three-factor and five-factor models using a dataset of 20 Pakistani commercial banks for the period 2011 to 2020. We focus on an emerging economy as the findings from earlier studies on developed countries cannot be generalized in emerging markets. For empirical analysis, twelve portfolios were developed based on size, market capitalization, investment strategy, and growth. Subsequently, we constructed five Fama-French factors namely, R_M, SMB, HML, RMW, and CMA. The OLS regression technique with robust standard errors was applied to compare the predictive power of both the Fama-French models. Further, we also compared the mean-variance efficiency of the Fama-French models through the GRS test. Our empirical analysis provides three unique and interesting findings. First, both asset pricing models have similar predictive power to explain the expected portfolio returns in most cases. Second, our results from the GRS test suggest that there is no noticeable difference in the mean-variance efficiency of one asset pricing model over the other. Third, we find that all factors of both Fama-French models are statistically significant and are important for explaining the volatility of expected commercial bank returns in the context of Pakistan.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.659-673
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• 1998

In this paper we consider a security market whose asset price process is a vector semimartingale. The market is said to be fair if there exists an equivalent martingale measure for the price process, deflated by a numeraire asset. It is shown that the fairness of a market is invariant under the change of numeraire. As a consequence, we show that the characterization of the fairness of a market is reduced to the case where the deflated price process is bounded. In the latter case a theorem of Kreps (1981) has already solved the problem. By using a theorem of Delbaen and Schachermayer (1994) we obtain an intrinsic characterization of the fairness of a market, which is more intuitive than Kreps' theorem. It is shown that the arbitrage pricing of replicatable contingent claims is independent of the choice of numeraire and equivalent martingale measure. A sufficient condition for the fairness of a market, modeled by an Ito process, is given.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.59-73
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• 2009

A floating-strike lookback call option gives the holder the right to buy at the lowest price of the underlying asset. Similarly, a floating-strike lookback put option gives the holder the right to sell at the highest price. This paper will propose an outside floating-strike lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at some percentage of the lowest (or highest) price of the other underlying asset. In addition, this paper will derive explicit pricing formulas for these outside floating-strike lookback options. Sections 3 and 4 assume that the underlying assets pay no dividends. In contrast, Section 5 will derive explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples will be discussed.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.213-225
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• 2004

A fixed-strike lookback option is an option whose payoff is determined by the maximum (or minimum) price of the underlying asset within the option's life. Under the Black-Scholes framework, the time-t price of an equity asset follows a geometric Brownian motion. Applying the method of Esscher transforms, this paper will derive explicit pricing formulas for fixed-strike lookback call and put options, respectively. In addition, this paper will show a relationship (duality property) between the pricing formulas of the call and put options. Finally, this paper will derive explicit pricing formulas for the fixed-strike lookback options when their underlying asset pays dividends continuously at a rate proportional to its price.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.819-835
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• 2012

A floating-strike lookback call (or put) option gives the holder the right to buy (or sell) at some percentage of the lowest (or highest) price of the underlying asset. This paper will propose an outside lookback call (or put) option that gives the holder the right to buy (or sell) one underlying asset at its guaranteed floating-strike price that is some percentage times the smaller (or the greater) of a specific guaranteed amount and the lowest (or highest) price of the other underlying asset. In addition, this paper derives explicit pricing formulas for these outside lookback options. Section 3 and Section 4 assume that the underlying assets pay no dividends. In contrast, Section 5 derives explicit pricing formulas for these options when their underlying assets pay dividends continuously at a rate proportional to their prices. Some numerical examples are also discussed.

• Asia-Pacific Journal of Business
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• v.11 no.3
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• pp.199-215
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• 2020

Purpose - This article tries to test if the conditional consumption capital asset pricing model (CCAPM) with bank credit for household as a conditional variable can explain the cross-sectional variation of stock returns in Korea. The performance of conditional CCAPM is compared to that of multifactor asset pricing models based on Arbitrage Pricing Theory. Design/methodology/approach - This paper extends the simple CCAPM to the conditional version of CCAPM by using bank credit for household as conditioning information. By employing KOSPI and KOSDAQ stocks as test assets from the second quarter of 2003 to the first quarter of 2018, this paper estimates risk premiums of conditional CCAPM and a variety of multifactor linear models such as Fama-French three and five-factor models. The significance of risk factors and the adjusted coefficient of determination are the basis for the comparison in models' performances. Findings - First, the paper finds that conditional CCAPM with bank credit performs as well as the multifactor linear models from Arbitrage Pricing theory on 25 test assets sorted by size and book-to-market. When using long-term consumption growth, the conditional CCAPM explains the cross-sectional variation of stock returns far better than multifactor models. Not only that, although the performances of multifactor models decrease on 75 test assets, conditional CCAPM's performance is well maintained. Research implications or Originality - This paper proposes bank credit for household as a conditional variable for CCAPM. This enables CCAPM, one of the most famous economic asset pricing models, to conform with the empirical data. In light of this, we can now explain the cross-sectional variation of stock returns from an economic perspective: Asset's riskiness is determined by its correlation with consumption growth conditional on bank credit for household.

• International Journal of Highway Engineering
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• v.16 no.1
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• pp.75-89
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• 2014

PURPOSES : This study evaluates the economic value of national highway construction projects using Real Option Pricing Models. METHODS : We identified the option premium for uncertainties associated with flexibilities according to the future's change in national highway construction projects. In order to evaluate value of future's underlying asset, we calculated the volatility of the unit price per year for benefit estimation such as VOTS, VOCS, VICS, VOPCS and VONCS that the "Transportation Facility Investment Evaluation Guidelines" presented. RESULTS : We evaluated the option premium of underlying asset through a case study of the actual national highway construction projects using ROPM. And in order to predict the changes in the option value of the future's underlying asset, we evaluated the changes of option premium for future's uncertainties by the defer of the start of construction work, the contract of project scale, and the abandon of project during pre-land compensation stages that were occurred frequently in the highway construction projects. Finally we analyzed the sensitivity of the underlying asset using volatility, risk free rate and expiration date of option. CONCLUSIONS : We concluded that a highway construction project has economic value even though static NPV had a negative(-) value because of the sum of the existing static NPV and the option premium for the future's uncertainties associated with flexibilities.

• 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.