• Industrial Engineering and Management Systems
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• v.10 no.1
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• pp.84-94
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• 2011

In this paper, we propose a method to provide the distribution of option price under local volatility model when market-provided implied volatility data are given. The local volatility model is one of the most widely used smile-consistent models. In local volatility model, the volatility is a deterministic function of the random stock price. Before estimating local volatility surface (LVS), we need to estimate implied volatility surfaces (IVS) from market data. To do this we use local polynomial smoothing method. Then we apply the Dupire formula to estimate the resulting LVS. However, the result is dependent on the bandwidth of kernel function employed in local polynomial smoothing method and to solve this problem, the proposed method in this paper makes use of model averaging approach by means of bandwidth priors, and then produces a robust local volatility surface estimation with a confidence interval. After constructing LVS, we price barrier option with the LVS estimation through Monte Carlo simulation. To show the merits of our proposed method, we have conducted experiments on simulated and market data which are relevant to KOSPI200 call equity linked warrants (ELWs.) We could show by these experiments that the results of the proposed method are quite reasonable and acceptable when compared to the previous works.

• 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.

• Industrial Engineering and Management Systems
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• v.8 no.2
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• pp.93-100
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• 2009

In this paper, we review widely used methods to extract local volatility surfaces (LVSs) from implied volatility surfaces (IVSs) and suggest a model averaging method for constructing implied and local volatility surfaces weighted by trading volumes. It makes use of model averaging method by means of bandwidth priors, and then produces a robust LVS estimation. The method is shown to provide the information about the confidence interval of estimators as well as a rather less variable weighted mean value for the IVS and LVS. To show the merits of our proposed method, we conduct simulations on equity-linked warrants (ELWs) with reasonable and acceptable results.

• Asia-Pacific Journal of Business
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• v.13 no.2
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• pp.23-37
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• 2022

Purpose - The purpose of this paper is to analyze the dynamic factors of the daily FX implied volatility based on the fractional integration methods focusing on long memory feature and structural changes. Design/methodology/approach - This paper uses the daily FX implied volatility data of the EUR-USD and the JPY-USD exchange rates. For the fractional integration analysis, this paper first applies the basic ARFIMA-FIGARCH model and the Local Whittle method to explore the long memory feature in the implied volatility series. Then, this paper employs the Adaptive-ARFIMA-Adaptive-FIGARCH model with a flexible Fourier form to allow for the structural changes with the long memory feature in the implied volatility series. Findings - This paper finds statistical evidence of the long memory feature in the first two moments of the implied volatility series. And, this paper shows that the structural changes appear to be an important factor and that neglecting the structural changes may lead to an upward bias in the long memory feature of the implied volatility series. Research implications or Originality - The implied volatility has widely been believed to be the market's best forecast regarding the future volatility in FX markets, and modeling the evolution of the implied volatility is quite important as it has clear implications for the behavior of the exchange rates in FX markets. The Adaptive-ARFIMA-Adaptive-FIGARCH model could be an excellent description for the FX implied volatility series

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.43-50
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• 2020

We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo simulation. Next, we define the inner and outer domains to find the effective volatility region. To confirm the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational experiments confirm that there is an effective region which dominates the option pricing.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.507-528
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• 2022

We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.

• East Asian Economic Review
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• v.18 no.1
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• pp.3-27
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• 2014

This paper examines the effects of financial crises on the long memory volatility dependency of daily exchange returns focusing on the Asian crisis in 97-98 and the Global crisis in 08-09. By using the daily KRW-USD and JPY-USD exchange rates which have different trading regions and volumes, this paper first applies both the parametric FIGARCH model and the semi-parametric Local Whittle method to estimate the long memory volatility dependency of the daily returns and the temporally aggregated returns of the two exchange rates. Then it compares the effects of the two financial crises on the long memory volatility dependency of the daily returns. The estimation results reflect that the long memory volatility dependency of the KRW-USD is generally greater than that of the JPY-USD returns and the long memory dependency of the two returns appears to be invariant to temporal aggregation. And, the two financial crises appear to affect the volatility dynamics of all the returns by inducing greater long memory dependency in the volatility process of the exchange returns, but the degree of the effects of the two crises seems to be different on the exchange rates.

• Korean Business Review
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• v.20 no.2
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• pp.15-27
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• 2007

This paper analyzed the relationship between Housing Purchase Price volatility of Seoul and Housing Purchase Price volatility of local large city. Other studies investigates the effect on the observed volatility Observed volatility consists of fundamental volatility and transitory volatility. Fundamental volatility is caused by information arrival and transitory volatility is caused by noise trading. Fundamental volatility is trend component and is modelled as a random walk with drift. Transitory volatility is cyclical component and is modelled as a stationary process. In contrast to other studies, this study investigates the effect on the fundamental volatility and transitory volatility individually. Observed volatility is estimated by GJR GARCH(1,1) model. We find that GJH GARCH model is superior to GARCH model and good news is more remarkable effect on volatility than bad news. This study decomposes the observed volatility into fundamental volatility and transitory volatility using Kalman filtering method. The findings in this paper is as follows. The correlation between Seoul housing price volatility and Busan housing price volatility is high. But, the correlation between Seoul and Daejeon is low. And the correlation between Daejeon and Busan is low. As a distinguishing feature, the correlation between fundamental volatilities is high in the case of all pairs. But, the correlation between transitory volatilities turns out low. The reason is as follows. When economic information arrives, Seoul, Daejeon, and Busan housing markets, all together, are affected by this information.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.467-477
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• 2017

This paper is about the derivations of local volatilities for European quanto call option prices according to various types of payoffs. We derive the explicit formulas of local volatilities with constant foreign and domestic interest rates by adapting the method of Derman-Kani.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.295-304
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• 2019

This article deals with threshold-asymmetric volatility models for over-dispersed and zero-inflated time series of count data. We introduce various threshold integer-valued autoregressive conditional heteroscedasticity (ARCH) models as incorporating over-dispersion and zero-inflation via conditional Poisson and negative binomial distributions. EM-algorithm is used to estimate parameters. The cholera data from Kolkata in India from 2006 to 2011 is analyzed as a real application. In order to construct the threshold-variable, both local constant mean which is time-varying and grand mean are adopted. It is noted via a data application that threshold model as an asymmetric version is useful in modelling count time series volatility.