• Journal of the Korean Mathematical Society
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• v.57 no.5
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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.

• Korean Journal of Mathematics
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• v.14 no.2
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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.

• 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.

• Korean Journal of Mathematics
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• v.23 no.1
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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.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2012.05a
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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.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.415-422
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• 2016

We derive a closed-form expression for the price of a European quanto call option when both foreign and domestic interest rates follow the Vasicek's short rate model.

• Journal of Distribution Science
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• v.11 no.10
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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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 Journal of Asian Finance, Economics and Business
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• v.9 no.1
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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.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.737-753
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• 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.