• 제목/요약/키워드: stochastic interest rate

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THE VALUATION OF VARIANCE SWAPS UNDER STOCHASTIC VOLATILITY, STOCHASTIC INTEREST RATE AND FULL CORRELATION STRUCTURE

  • Cao, Jiling;Roslan, Teh Raihana Nazirah;Zhang, Wenjun
    • 대한수학회지
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    • 제57권5호
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    • pp.1167-1186
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    • 2020
  • This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possesses the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirm that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.

PRICING CONVERTIBLE BONDS WITH KNOWN INTEREST RATE

  • Kim, Jong Heon
    • Korean Journal of Mathematics
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    • 제14권2호
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    • pp.185-202
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    • 2006
  • In this paper, using the Black-Scholes analysis, we will derive the partial differential equation of convertible bonds with both non-stochastic and stochastic interest rate. We also find numerical solutions of convertible bonds equation with known interest rate using the finite element method.

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TWO APPROACHES FOR STOCHASTIC INTEREST RATE OPTION MODEL

  • Hyun, Jung-Soon;Kim, Young-Hee
    • 대한수학회지
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    • 제43권4호
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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.

LOCAL VOLATILITY FOR QUANTO OPTION PRICES WITH STOCHASTIC INTEREST RATES

  • Lee, Youngrok;Lee, Jaesung
    • Korean Journal of Mathematics
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    • 제23권1호
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    • pp.81-91
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    • 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.

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

  • 김범식;정영한
    • 한국건축시공학회:학술대회논문집
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    • 한국건축시공학회 2012년도 춘계 학술논문 발표대회
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    • pp.161-163
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    • 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.

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

  • 유원석;손삼호
    • 유통과학연구
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    • 제11권10호
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    • pp.55-62
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    • 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
    • 대한수학회논문집
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    • 제33권1호
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    • pp.345-360
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    • 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.

The Nexus Between Monetary Policy and Economic Growth: Evidence from Vietnam

  • NGUYEN, Hoang Chung
    • The Journal of Asian Finance, Economics and Business
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    • 제9권1호
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    • pp.153-166
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    • 2022
  • The study estimates the Structured VAR and the Dynamic Stochastic General Equilibrium Model for the Vietnamese economy based on the new Keynesian model for small and open economies, with the output gap, inflation, policy interest rate, the Vietnamese exchange rate, and the inflation and interest rate in the United States. The paper aims to clarify the impulse response of the macro variables through their shocks. It offers to model the SVAR and DSGE processes, as well as describe why and how interest rate policy is important in the impulse response of macro variables like the output gap and inflation process. The study supports the central role of monetary policy by giving empirical evidence for the new Keynesian theory, according to which an interest rate shock causes the output gap to widen and inflation to decrease. Finally, the application of the DSGE model is becoming more and more popular in the State Bank of Viet Nam to improve its policy planning, analyzing, and forecasting policy towards sustainable and stable growth.

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

  • 이항석
    • Journal of the Korean Data and Information Science Society
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    • 제24권4호
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    • pp.737-753
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    • 2013
  • 금리변동형 보험상품은 시장금리에 연동하여 이자율 (공시이율)을 적용하는 보험상품이지만, 시장금리의 하락시에도 해약환급금의 이자율을 보증하기 위해 최저보증이율을 설정하도록 하고 있다. 즉, 공시이율이 계약할 당시 설정한 최저보증이율을 하회할 경우 보험사는 공시이율과 최저보증이율 중에 큰 금액으로 책임준비금을 적립하고 계약자가 보험계약을 해지할 경우 해약환급금을 지급해야 한다. 이러한 이자율 보증옵션은 시장금리가 하락하는 최근의 저금리 기조에서 생명보험회사의 손익을 악화시키는 요인이 되고 있다. 본 논문에서는 현재의 저금리 상황과 이자율 보증옵션 적용방식 현황을 살펴보고, 금리변동형 종신보험과 금리변동형 연금보험의 이차손익 구조 및 이자율 보증옵션의 가치와 리스크를 분석한다. 그리고, 이자율 보증옵션의 분석 결과를 토대로 시장이율과 최저보증이율의 금리차와 이차손익과의 관계에 대한 시사점을 제시한다.