• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.251-265
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• 2021

This paper discusses the pricing of autocallable structured product with knock-in (KI) feature using the exit probability with the Brownian Bridge technique. The explicit pricing formula of autocallable ELS derived in the existing paper handles the part including the minimum of the Brownian motion using the inclusion-exclusion principle. This has the disadvantage that the pricing formula is complicate because of the probability with minimum value and the computational volume increases dramatically as the number of autocall chances increases. To solve this problem, we applied an efficient and robust simulation method called the Brownian Bridge technique, which provides the probability of touching the predetermined barrier when the initial and terminal values of the process following the Brownian motion in a certain interval are specified. We rewrite the existing pricing formula and provide a brief theoretical background and computational algorithm for the technique. We also provide several numerical examples computed in three different ways: explicit pricing formula, the Crude Monte Carlo simulation method and the Brownian Bridge technique.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.207-217
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• 1996

The problem of detecting change with independent data is considered. The asymptotic distribution of the sample change process with the sample Fourier coefficients is shown as a Brownian Bridge process. We suggest to use dynamic statistics such as a sample Brownian Bridge and graphs as statistical animation. Graphs including change PP plots are given by way of illustration with the simulated data.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.473-481
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.683-693
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• 2008

In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.417-427
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• 1997

In this paper the parameter change problem in the stationary time series is considered. We propose a cumulative sum (CUSUM) of squares-type test statistic for detection of parameter changes in the AR(1) process. The proposed test statistic is based on the CUSIM of the squared observations and is shown to converge to a standard Brownian bridge. Simulations are performed to evaluate the performance of the proposed statistic and a real example is provided to illustrate the procedure.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1197-1211
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• 2011

The actual power performance of historical structural change tests are compared under various alternatives. The tests of interest are F, CUSUM, MOSUM, Moving Estimates and empirical distribution function tests with both recursive and ordinary least-squares residuals. Our comparison of the structural tests involves limiting distributions under the hypothesis, the ability to detect the alternative hypotheses under one or double structural change, and smooth change in parameters. Even though no version is uniformly superior to the other, the knowledge about the properties of those tests and connections between these tests can be used in practical structural change tests and in further research on other change tests.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.753-763
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• 2002

When there is one change-point in the hazard rate model, a change-point estimator with the partial score process is suggested and compared with the previously developed estimators. The limiting distribution of the partial score process we used is a function of the Brownian bridge. Simulation study gives the comparison of change-point estimators.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.895-906
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• 2015

Diffusion is a mathematical tool to explain the fluctuation of financial assets and the movement of particles in a micro time scale. There are ongoing statistical trials to develop an estimation method for diffusion models based on likelihood. When we estimate diffusion models by applying the maximum likelihood estimation method on data observed at discrete time points, we need to know the transition density of the diffusion. In order to approximate the transition densities of diffusion models, we suggests the method to approximate the path integral of the random process with normal random variables, and compare the numerical properties of the method with other approximation methods.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.165-175
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• 2002

We consider the problem of estimating the change-point in mean change model with the one change-point. Lombard (1987) suggested change-point estimation based on score functions. Gombay and Huskova (1998) derived a class of change-point estimators with the score function of rank. Various change-point estimators with the log score functions of ranks are suggested and compared via simulation.