• Title/Summary/Keyword: Stochastic interest rates

Search Result 14, Processing Time 0.026 seconds

OPTIMAL PORTFOLIO SELECTION UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES

  • KIM, MI-HYUN;KIM, JEONG-HOON;YOON, JI-HUN
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.19 no.4
    • /
    • pp.417-428
    • /
    • 2015
  • Although, in general, the random fluctuation of interest rates gives a limited impact on portfolio optimization, their stochastic nature may exert a significant influence on the process of selecting the proportions of various assets to be held in a given portfolio when the stochastic volatility of risky assets is considered. The stochastic volatility covers a variety of known models to fit in with diverse economic environments. In this paper, an optimal strategy for portfolio selection as well as the smoothness properties of the relevant value function are studied with the dynamic programming method under a market model of both stochastic volatility and stochastic interest rates.

LOCAL VOLATILITY FOR QUANTO OPTION PRICES WITH STOCHASTIC INTEREST RATES

  • Lee, Youngrok;Lee, Jaesung
    • Korean Journal of Mathematics
    • /
    • v.23 no.1
    • /
    • pp.81-91
    • /
    • 2015
  • This paper is about the local volatility for the price of a European quanto call option. We derive the explicit formula of the local volatility with constant foreign and domestic interest rates by adapting the methods of Dupire and Derman & Kani. Furthermore, we obtain the Dupire equation for the local volatility with stochastic interest rates.

Stochastic analysis for Real Rate Interest of Building Life Cycle Cost(LCC) with Monte-Carlo Simulation (몬테카를로 시뮬레이션을 이용한 건축물 생애주기비용(LCC)의 실질할인율에 대한 확률론적 분석)

  • Kim, Bum-Sic;Jung, Young-Han
    • Proceedings of the Korean Institute of Building Construction Conference
    • /
    • 2012.05a
    • /
    • pp.161-163
    • /
    • 2012
  • Recently on Value Engineering(VE) and Life Cycle Cost(LCC) social interests is increasing. The government Turn Key, BTL projects and public works projects, such as VE and LCC Analysis on the value and economic analysis is mandatory. And accordingly the VE and LCC analysis is underway for the various studies. However, there is a problem existing in the LCC analysis. Worth the cost varies according to the flow of time. However, the real interest rate during the LCC analysis of buildings in calculation time for interest rates and inflation are not considering the value of the flow. In other words, a few years using the average value of the deterministic analysis method has been adopted. These costs for the definitive analysis of the cost of an uncertain future, unforeseen changes resulting hazardous value. In this study of the last 15 years interest rates and inflation targeting by using Monte-Carlo Simulation is to perform probabilistic analysis. This potential to overcome uncertainties of the cost of building a more scientific and LCC Estimation of the probability value of the real interest rate is presented.

  • PDF

A Study on the Long-Run Consumption Risk in Foreign Currency Risk Premia (장기소비 위험을 이용한 통화포트폴리오 수익률에 관한 연구)

  • Liu, Won-Suk;Son, Sam-Ho
    • Journal of Distribution Science
    • /
    • v.11 no.10
    • /
    • pp.55-62
    • /
    • 2013
  • Purpose - The purpose of this study is to suggest a risk factor that significantly explains foreign currency risk premia. In recent years, some studies have found that the performance of the simultaneous consumption risk model improves considerably when tested on foreign currency portfolios, which are constructed based on the international interest rates differentials. However, this paper focuses on the long-run consumption risk factor. In our empirical research, we found that the real excess returns of high interest rate currency portfolios depreciate on average, when the future American long-run consumption growth rate appears low. This makes the high interest rate currency portfolios have relatively high risk premia. Meanwhile, the real excess returns of low interest rate currency portfolios appreciate on average, under the same conditions, which results in relatively low risk premia for these portfolios. Therefore, this long-run consumption risk factor might explain why low interest rate currencies do not appreciate as much as the interest rate differential, and why high interest rate currencies do not depreciate as much as the interest rate differential. Research design, data, methodology - In our explanation, we provide new evidence on the success of long-run consumption risks in currency risk premia by focusing on the long-run consumption risks borne by American representative investors. To uncover the hidden link between exchange rates and long-run consumption growth, we set the eight currency portfolios as our basic assets, which have been built based on the foreign interest rates of eighty countries. As these eight currency portfolios are rebalanced every year, the first group always contains the lowest interest rate currencies, and the last group contains the highest interest rate currencies. Against these basic eight currency portfolios, we estimate the long-run consumption risk model. We use recursive utility framework and the stochastic discount factor that depends on the present value of expected future consumption growth rates. We find that our model is optimized in the two-year period of constructing the durable consumption expectation factor. Our main results surprisingly surpass the performance of the existing benchmark simultaneous consumption model in terms of R2, relatively risk aversion coefficient γ, and p-value of J-test. Results - The performance of our model is superior. R2, relatively risk aversion coefficient γ, and p-value of J-test of our long-run durable consumption model are 90%, 93%, and 65.5%, respectively, while those of EZ-DCAPM are 87%, 113%, and 62.8%, respectively. Thus, we can speculate that the risk premia in foreign currency markets have been determined by the long-run consumption risk. Conclusions - The aggregate long-run consumption growth risk explains a large part of the average change in the real excess returns of foreign currency portfolios. The real excess returns of high interest rate currency portfolios depreciate on average when American long-run consumption growth rate is low, and the real excess returns of low interest rate currency portfolios appreciate under the same conditions. Thus, the low interest rate currency portfolios allow investors to hedge against aggregate long-run consumption growth risk.

DISCOUNT BARRIER OPTION PRICING WITH A STOCHASTIC INTEREST RATE: MELLIN TRANSFORM TECHNIQUES AND METHOD OF IMAGES

  • Jeon, Junkee;Yoon, Ji-Hun
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.1
    • /
    • pp.345-360
    • /
    • 2018
  • In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.

Some Dependence Structures of Multivariate Processes

  • Jong Il Baek
    • Communications for Statistical Applications and Methods
    • /
    • v.2 no.1
    • /
    • pp.201-208
    • /
    • 1995
  • In the last years there has been growing interest in concepts of positive dependence for families of random variables such that concepts are considerable us in deriving inequalities in probability and statistics. Lehman introdued various concepts of positive dependence for bivariate random variables. A much stronger notions of positive dependence were later considered by Esary, Proschan, and Walkup. Ahmed et al and Ebrahimi and Ghosh also obtained multivariate versions of various bivariate positive dependence as descrived by Lehman. See also Block al. Glaz and Johnson an Barlow and Proschan and the references there. Multivariate processes arise when instead of observing a single process we observe several processes, say $X_19t), \cdots, X_n(t)$ simultaneously. For example, in an engineering context we may want to study the simultaneous variation of current and voltage, or temperature, pressure and volume over time. In economics we may be interested in studying inflation rates and money supply, unemployment and interest rates. We could of course, study each quantity on its own and treat each as a separate univariate process. Although this would give us some information about each quantity it could never give information about the interrelationship between various quantities. This leads us to introduce some concepts of positive and for multivariate stochastic processes. The concepts of positive dependence have subsequently been extended to stochastic processes in different directions by many authors.

  • PDF

Evaluation of interest rate-linked DLSs

  • Kim, Manduk;Song, Seongjoo
    • Communications for Statistical Applications and Methods
    • /
    • v.29 no.1
    • /
    • pp.85-101
    • /
    • 2022
  • Derivative-linked securities (DLS) is a type of derivatives that offer an agreed return when the underlying asset price moves within a specified range by the maturity date. The underlying assets of DLS are diverse such as interest rates, exchange rates, crude oil, or gold. A German 10-year bond rate-linked DLS and a USD-GBP CMS rate-linked DLS have recently become a social issue in Korea due to a huge loss to investors. In this regard, this paper accounts for the payoff structure of these products and evaluates their prices and fair coupon rates as well as risk measures such as Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). We would like to examine how risky these products were and whether or not their coupon rates were appropriate. We use Hull-White Model as the stochastic model for the underlying assets and Monte Carlo (MC) methods to obtain numerical results. The no-arbitrage prices of the German 10-year bond rate-linked DLS and the USD-GBP CMS rate-linked DLS at the center of the social issue turned out to be 0.9662% and 0.9355% of the original investment, respectively. Considering that Korea government bond rate for 2018 is about 2%, these values are quite low. The fair coupon rates that make the prices of DLS equal to the original investment are computed as 4.76% for the German 10-year bond rate-linked DLS and 7% for the USD-GBP CMS rate-linked DLS. Their actual coupon rates were 1.4% and 3.5%. The 95% VaR and TVaR of the loss for German 10-year bond rate-linked DLS are 37.30% and 64.45%, and those of the loss for USD-GBP CMS rate-linked DLS are 73.98% and 87.43% of the initial investment. Summing up the numerical results obtained, we could see that the DLS products of our interest were indeed quite unfavorable to individual investors.

Profit analysis of life insurance products with interest rate options (이자율 보증옵션이 내재된 생명보험의 이차익 분석)

  • Lee, Hangsuck
    • Journal of the Korean Data and Information Science Society
    • /
    • v.24 no.4
    • /
    • pp.737-753
    • /
    • 2013
  • Interest rate options embedded in life insurance products provide policyholders with minimum guaranteed rates credited to the corresponding surrender values. This paper discusses current low-interest environment and several types of interest rate options embedded in life insurance products. In addition, this paper shows profit structures of the life insurance products and calculates values of the interest rate options under stochastic interest model and the corresponding VaR (value at risk). Finally, some implications are discussed.

Condition-Based Model for Preventive Maintenance of Armor Units of Rubble-Mound Breakwaters using Stochastic Process (추계학적 확률과정을 이용한 경사제 피복재의 예방적 유지관리를 위한 조건기반모형)

  • Lee, Cheol-Eung
    • Journal of Korean Society of Coastal and Ocean Engineers
    • /
    • v.28 no.4
    • /
    • pp.191-201
    • /
    • 2016
  • A stochastic process has been used to develop a condition-based model for preventive maintenance of armor units of rubble-mound breakwaters that can make a decision the optimal interval at which some repair actions should be performed under the perfect maintenance. The proposed cost model in this paper based on renewal reward process can take account of the interest rate, also consider the unplanned maintenance cost which has been treated like a constant in the previous studies to be a time-dependent random variable. A function for the unplanned maintenance cost has been mathematically proposed so that the cumulative damage, serviceability limit and importance of structure can be taken into account, by which a age-based maintenance can be extended to a condition-based maintenance straightforwardly. The coefficients involved in the function can also be properly estimated using a method expressed in this paper. Two stochastic processes, Wiener process and gamma process have been applied to armor stones of rubble-mound breakwaters. By evaluating the expected total cost rate as a function of time for various serviceability limits, interest rates and importances of structure, the optimal period of preventive maintenance can easily determined through the minimization of the expected total cost rate. For a fixed serviceability limit, it shows that the optimal period has been delayed while the interest rate increases, so that the expected total cost rate has become lower. In addition, the gamma process tends to estimate the optimal period more conservatively than the Wiener process. Finally, it is found that the more crucial the level of importance of structure becomes, the more often preventive maintenances should be carried out.