• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.393-406
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• 2015

We examine how to model mortality risk using the adaptation of the mean-reverting processes for the two factor model proposed by Cairns et al. (2006b). Mortality improvements have been recently observed in some countries such as United Kingdom; therefore, we assume long-run mortality converges towards a trend at some unknown time and the mean-reverting processes could therefore be an appropriate stochastic model. We estimate the parameters of the two-factor model incorporated with mean-reverting processes by a Metropolis-Hastings algorithm to fit United Kingdom mortality data from 1991 to 2015. We forecast the evolution of the mortality from 2014 to 2040 based on the estimation results in order to evaluate the issue price of a longevity bond of 25 years maturity. As an application, we propose a method to quantify the speed of mortality improvement by the average mean reverting times of the processes.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.10
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• pp.239-247
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• 2021

Central Bank authorities should carefully manage inflation rate uncertainties to achieve economic growth and development not only in the short-run but also in the long-run. Since inflation is a key macroeconomic variable, an increased understanding about its behavior is undoubtedly important. Thus, paper employs unit root with breakpoints to examine the mean reverting behavior of inflation rate in the Philippines using monthly data from 2002 to 2020. Empirically, the unit root breakpoint innovational and additive outlier tests favor the stationarity or mean reverting behavior of inflation in the Philippines. Also, results of standard unit root tests, ADF, PP, GLS-Dickey-Fuller, KPSS and NP, provide strong evidence of mean reverting processes. The mean reverting behavior of inflation rate reveals that the monetary policy using inflation targeting framework has succeeded in reducing chronic inflation persistence in the Philippines. Thus, this research supports inflation targeting policy that aims to maintain general price level stability for the Philippine economy's long-term growth and development prospects. The findings of this research remain important for the central bankers for not only providing them better understanding about the behavior of inflation rate, but also helping them formulate and implement policy reforms related to money, credit and banking.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.129-139
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• 2011

We consider an optimal trading rule in this paper. We assume that the underlying asset follows a mean-reverting process and the transaction consists of one buying and one selling. To maximize the profit, we find price levels to buy low and to sell high. Associated HJB equations are used to formulate the value function. A verification theorem is provided for sufficient conditions. We conclude the paper with a numerical example.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Environmental and Resource Economics Review
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• v.27 no.4
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• pp.613-637
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• 2018

Fuel cell power plant which has advantages as a distributed generation is influenced by high cost of investment and uncertainty of electricity price. This study suggests the model of real options which considers the irreversibility of investment in the fuel cell plant and the uncertainty of electricity price. Most models of real options assume the geometric Brownian motion for convenience, but this study develops the model for the feasibility analysis considering the mean reverting process of electricity price, with the closed form solution on the value of investment option. The result of the empirical analysis considering the data related to the fuel cell generation with the scale of 20MW and the domestic RPS circumstance represents that the investment is feasible without the uncertainty, and is not feasible with the uncertainty. This result implies that the political support as well as the improvement of profit system including revenue and cost are necessary for the activation of the fuel cell power plant.

• The Korean Journal of Financial Management
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• v.10 no.2
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• pp.239-262
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• 1993

본 연구에서는 한국 주식시장에서의 주가결정과정에 비합리적인 요소가 내포되어 있는지의 여부를 정가하기 위하여 Fama-French(1988)의 검증방법론을 이용하여 한국종합주가지수, 자본금규모별 주가지수, 산업 별 주가지수, 그리고 한경다우지수 등을 대상으로 실증분석을 실시하였다. 주가의 평균회귀과정(mean-reverting process)이 주식수익률들간의 음의 자기상관관계를 유발한다는 관찰에서 출발한 본 연구는 미국에서의 실증분석 결과와는 판이하게 주식수익률들이 2년까지의 수익률계산기간(return horizon)에서 지속적인 양의 자기 상관을 갖고 있음을 발견하였다. 본 연구에서 발견된 실증분식결과는 대상주가지수에 관계없이 일관성있는 패턴을 유지하고 있는데, 이는 Fama-French(1988)의 결과에 정면으로 배치된다. 따라서 본 연구에서의 실증분석 결과는 우리나라 주식시장의 경우 주가에 비합리적인 평균회귀요소(mean-reverting components)가 포함되어 있다는 가설을 지지하지 않는 것으로 해석 될 수 있을 것이다. 물론, 이것이 반드시 우리 주식 시장에서의 주가결정이 합리적으로 이루어진다는 것을 의미하지는 않으며, 단지 본 연구에서 주장되고 있는 것은 우리 주식시장에서의 주가결정과정을 랜덤웍과 평균회귀과정의 합성 혹은 평균회귀과정 그 자체로 모형화하려는 시도는 실증적 증거에 뿌리를 두고 있지 않다는

• East Asian mathematical journal
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• v.37 no.1
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• pp.79-85
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• 2021

In this paper, we investigate the valuation of vulnerable exchange option that has credit risk of option issuer. The reduced-form model is used to model credit risk. We assume that credit event is determined by the jump of the counting process with stochastic intensity, which follows the mean reverting process. We propose a simple approach to derive the closed-form pricing formula of vulnerable exchange option under the reduced-form model and provide the pricing formula as the standard normal cumulative function.

• The Korean Journal of Applied Statistics
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• v.28 no.4
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• pp.703-719
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• 2015

We propose an extension of the Lee and Jho (2015) mean reverting the two factor mortality model by incorporating a period-specific cohort effect. We found that the consideration of cohort effect improves the mortality fit of Korea male data above age 65. Parameters are estimated by the weighted least squares method and Metropolis algorithm. We also emphasize that the cohort effect is necessary to choose the base survival index to calculate longevity bond issue price. A key contribution of the article is the proposal and development of a method to calculate the longevity bond price to hedge the longevity risk exposed to Korea National Pension Services.

• Environmental and Resource Economics Review
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• v.26 no.4
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• pp.499-517
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• 2017

The purpose of this article is to show profit margin hedging can be an optimal strategy in crude oil purchasing. This study theoretically analyzes profit margin hedging strategy is optimal in crude oil purchasing using expected target utility function and conducts simulations to show if the profit margin hedging is profitable. In addition, this study tests existence of mean reversion of crude oil futures prices to confirm the theory that profit margin hedging is more profitable than other strategies, such as always hedging or buying at expiration with spot price, if futures prices are mean reverting. The simulation results show that the expected utility of profit margin hedging higher than other strategies. Although we cannot find any evidence that crude oil futures prices follow mean reverting process, we can conclude that profit margin hedging can be optimal strategy in crude oil purchasing based on theoretical proof and simulation results.

• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.3
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• pp.13-24
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• 2017

This paper aims to implement "structural changes detection procedure" in pairs trading algorithm and to show that the proposed approach outperforms the extant pair trading algorithm. Structural changes in pairs trading are defined in terms of changes in cointegrating factors and broken cointegration relationship. These changes are designed to test extant structural changes and unit root test methodologies. The simulation finds that expanding the changes in structure, increasing the mean reverting process of spread, and extending the consecutive days of broken cointegration will increase the performances of the proposed algorithm. Empirical study results are also consistent those of the simulation studies. The proposed algorithm outperforms the extant algorithm relative to risk and return given that the cumulative profit/loss has a significant upward-slope with minimal variance.