• Management Science and Financial Engineering
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• v.19 no.1
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• pp.49-52
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• 2013

In this paper we provide a valuation formula for a variance swap with regime switching. A variance swap is a forward contract on variance, the square of realized volatility of the underlying asset. We assume that the volatility of underlying asset is governed by Markov regime-switching process with finite states. We find that the proposed model can provide ease of calculation and be superior to the models currently available.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.845-858
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• 2006

We present two approaches of the stochastic interest rate European option pricing model. One is a bond numeraire approach which is applicable to a nonzero value asset. In this approach, we assume log-normality of returns of the asset normalized by a bond whose maturity is the same as the expiration date of an option instead that of an asset itself. Another one is the expectation hypothesis approach for value zero asset which has futures-style margining. Bond numeraire approach allows us to calculate volatilities implied in options even though stochastic interest rate is considered.

• The Korean Journal of Financial Management
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• v.8 no.2
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• pp.165-208
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• 1991

This paper develops an intertemporal general equilibrium model of asset pricing with taxes under the noisy and the incomplete information structure and examines theoretically the stochastic behavior of general equilibrium asset prices in a one-good, production, and exchange economy in continuous time markets. The important features of the model are its integration of real and financial markets and the analysis of the effects of differential tax rates between ordinary income and capital gains. The model developed here can provide answers to a wide variety of questions about stochastic structure of asset prices and the effect of tax on them.

• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.237-256
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• 2007

This paper studies the problem of option pricing in an incomplete market. The market incompleteness comes from the discontinuity of the underlying asset price process which is, in particular, assumed to be a compound Poisson process. To find a reasonable price for a European contingent claim, we first find the unique minimal martingale measure and get a price by taking an expectation of the payoff under this measure. To get a closed-form price, we use an asymptotic expansion. In case where the minimal martingale measure is a signed measure, we use a sequence of martingale measures (probability measures) that converges to the equivalent martingale measure in the limit to compute the price. Again, we get a closed form of asymptotic option price. It is the Black-Scholes price and a correction term, when the distribution of the return process has nonzero skewness up to the first order.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.397-406
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• 2013

We present an improved binomial method for pricing European- and American-type Asian options based on the arithmetic average of the prices of the underlying asset. At each node of the tree we propose a simple algorithm to choose the representative averages among all the effective averages. Then the backward valuation process and the interpolation are performed to compute the price of the option. The simulation results for European and American Asian options show that the proposed method gives much more accurate price than other recent lattice methods with less computational effort.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.755-763
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• 2008

This paper approaches the problem of option pricing in an incomplete market, where the underlying asset price process follows a compound Poisson model. We assume that the price process follows a compound Poisson model under an equivalent martingale measure and it converges weakly to the Black-Scholes model. First, we express the option price as the expectation of the discounted payoff and expand it at the Black-Scholes price to obtain a pricing formula with three unknown parameters. Then we estimate those parameters using the market option data. This method can use the option data on the same stock with different expiration dates and different strike prices.

• 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.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.439-461
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• 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.

• Management & Information Systems Review
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• v.26
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• pp.1-26
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• 2008

Since Capital Asset Pricing Model(CAPM) was proposed in the early 1960s by William Sharpe(1964) and John Lintner(1965) researchers have investigated the validity of the model. The results of empirical researches do not show that expected returns of stocks seem to be determined solely by systematic risk of the stocks as precicted by CAPM. In this paper the relationship between transaction volume and expected returns of stocks was investigated. Empirical cross-sectional analysis about the data collected from Stock Market of Korea Exchange shows transaction volume and variability of stock returns play an important role in pricing assets. The well-known variables which were used traditionally to explain the differences of expected returns among stocks such as the size and beta of a stock seems to be unimportant in pricing assets.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.287-298
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• 2013

A standard deviation has been a starting point for a mathematical definition of risk. As a remedy for drawbacks such as subadditivity property discouraging the diversification, coherent and convex risk measures are introduced in an axiomatic approach. Choquet expectation and g-expectations, which generalize mathematical expectations, are widely used in hedging and pricing contingent claims in incomplete markets. The each risk measure or expectation give rise to its own pricing rules. In this paper we investigate relationships among dynamic risk measures, Choquet expectation and dynamic g-expectations in the framework of the continuous-time asset pricing.