Particle filtering of volatility dynamics for KOSPI200 and its sequential prediction

• Date: 01 November 2018
• Published date: 01 November 2018
• Author: Tae Yeon Kwon
• DOI: http://doi.org/10.1002/for.2546

Received: 30 March 2018 Revised: 11 July 2018 Accepted: 3 August 2018

DOI: 10.1002/for.2546

RESEARCH ARTICLE

Particle filtering of volatility dynamics for KOSPI200 and its

sequential prediction

Tae Yeo n Kwo n

Department of International Finance,

Hankuk University of Foreign Studies,

Gyeonggi-do, Korea

Correspondence

Tae YeonKwon, Department of

International Finance, Hankuk University

of Foreign Studies, 81 Mohyeon-myeon,

Oedae-ro, Cheoin-gu, Yongin-si,

Gyeonggi-do, Republic of Korea.

Email: tykwon@hufs.ac.kr

Funding information

The National Research Foundation of

Korea(NRF) grant funded by the Korea

government(MSIT), Grant/Award

Number: NRF-2018R1C1B5043739;

Hankuk University of Foreign Studies

Research Fund

Abstract

This paper examines a method of filtering the volatility dynamics of the

KOSPI200 index under a stochastic volatility model. This study applies a par-

ticle filter algorithm for sequential estimation of volatility dynamics. In order

to improve our estimation, the cross-asset class approach is adopted by adding

option price information to the model. The entire estimation procedure includ-

ing the derivation of theoretical option price is based on Bayesian Markov chain

Monte Carlo methods, so the method presented in this paper can be applied

to diversified volatility models. Through the simulation study, we confirm that

this method can estimate unknown volatility dynamics correctly, and the use

of additional option prices improves both the accuracy and efficiency of volatil-

ity filtering. The sequential one-step-ahead prediction of the distribution of the

KOSPI 200 index and index option prices shows that the additional option price

information also enhances the prediction performance.

KEYWORDS

particle filter, posterior predictive distribution, stochastic volatility, sequential prediction

1INTRODUCTION

Although the method proposed by Black and Scholes

(1973) is widely used as an option pricing model that

reflects volatility in the stock market, limitations still exist,

such as the volatility smile due to the constant volatility

assumption. Johannes, Polson, and Stroud (2009) applied

a filtering scheme utilizing volatility dynamics instead of

constant volatility. In this paper, we filter the volatility

dynamics of the KOSPI 200 under the stochastic volatil-

ity (SV) model of Heston (1993). In this study of fil-

tering method of volatility dynamics, we focus on two

aspects: (1) the role of cross-asset class information, espe-

cially option price; and (2) applying a sequential Bayesian

Markov chain Monte Carlo (MCMC) method that makes

sequential online price prediction possible and which is

applicable to all types of stochastic volatility models.

First, this paper approaches estimation problems in

terms of cross-asset class research. Option price is addi-

tionally used in order to improve the estimation per-

formance. Ni, Pan, and Poteshman (2007) illustrate that

option prices tend to be more informative than stock prices

in the estimation of stochastic volatility models. Johannes

et al. (2009) used US stock and option market data to esti-

mate stock market volatility. In this paper, the volatility

of the KOSPI 200 index market is filtered by using both

the KOSPI 200 index and its call option prices. More-

over, through a simulation study, we show how much the

additional option market information improves the esti-

mation performance in terms of estimation accuracy and

efficiency.

Second, since the financial market prices utilized for fil-

tering volatility are observed sequentially, a method for

online estimation and prediction of volatility is needed.

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