Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
권호 표지
DOI QR코드

DOI QR Code

KOSPI200 옵션의 내재변동성 추정

An estimation of implied volatility for KOSPI200 option

  • 최지은 (단국대학교 응용통계학과) ;
  • 이장택 (단국대학교 응용통계학과)
  • 투고 : 2014.02.09
  • 심사 : 2014.04.01
  • 발행 : 2014.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

옵션가격의 결정에 있어서 실제 변동성은 사후에 알 수 있는 정보이므로 대용값으로 내재변동성을 가장 많이 사용하는데 본 연구에서는 동일한 기초자산을 가진 옵션의 잔존만기와 행사가격을 이용하여 내재변동성을 추정하고자 한다. KOSPI200 옵션 데이터와 서포트벡터회귀, 나무모형 및 회귀모형을 통해 모형의 설명력을 평균제곱근오차 (RMSE)와 평균절대오차 (MAE)를 사용하여 살펴보았다. 그 결과 서포트벡터회귀와 MART의 성능이 최소제곱회귀보다 우수한 것으로 나타났으며, 서포트벡터회귀와 MART의 성능은 거의 비슷하였다.

Using the assumption that the price of a stock follows a geometric Brownian motion with constant volatility, Black and Scholes (BS) derived a formula that gives the price of a European call option on the stock as a function of the stock price, the strike price, the time to maturity, the risk-free interest rate, the dividend rate paid by the stock, and the volatility of the stock's return. However, implied volatilities of BS method tend to depend on the stock prices and the time to maturity in practice. To address this shortcoming, we estimate the implied volatility function as a function of the strike priceand the time to maturity for data consisting of the daily prices for KOSPI200 call options from January 2007 to May 2009 using support vector regression (SVR), the multiple additive regression trees (MART) algorithm, and ordinary least squaress (OLS) regression. In conclusion, use of MART or SVR in the BS pricing model reduced both RMSE and MAE, compared to the OLS-based BS pricing model.

키워드

참고문헌

  1. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-659. https://doi.org/10.1086/260062
  2. Duan, J. (1995). The GARCH option pricing model. Mathematical Finance, 5, 13-32. https://doi.org/10.1111/j.1467-9965.1995.tb00099.x
  3. Friedman, J. H. (1999). Stochastic gradient boosting, http://www-stat.stanford.edu/-jhf/ftp/stobst.ps.
  4. Friedman J. H. (2001). Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29, 1189-1232.
  5. Friedman, J. H. (2002). Tutorial: Getting started with MART in R, http://statweb.stanford.edu/-jhf/r-mart/tutorial/tutorial.pdf.
  6. Heston, S. (1993). A closed form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6, 327-343. https://doi.org/10.1093/rfs/6.2.327
  7. Hwang, C. and Shim, J. (2010). Semiparametric support vector machine for accelerated failure time model. Journal of the Korean Data & Information Society, 21, 467-477.
  8. Hwang, C. and Shim, J. (2011). Cox proportional hazard model with L1 penalty. Journal of the Korean Data & Information Society, 22, 613-618.
  9. Jo, D. H., Shim, J. and Seok, K. (2010). Doubly penalized kernel method for heteroscedastic autoregressive data. Journal of the Korean Data & Information Society, 21, 155-162.
  10. Kim, M., Park, H., Hwang, C. and Shim, J. (2008). Claims reserving via kernel machine. Journal of the Korean Data & Information Society, 19, 1419-1427.
  11. Kuhn, H. W. and Tucker, A. W. (1951). Nonlinear programming. In Proceedings of 2nd Berkeley Symposium, Berkeley, University of California Press, 481-491.
  12. Kwon, S. and Lee, J. (2008). The function of intraday implied volatility in the KOSPI200 options. Asia-Pacific Journal of Financial Studies, 37, 913-948.
  13. Rubenstein, M. (1994). Implied binomial trees. Journal of Finance, 49, 771-818. https://doi.org/10.1111/j.1540-6261.1994.tb00079.x
  14. Tay, F. E. H. and Cao, L. J. (2001). Application of support vector machines in financial time series forecasting. Omega, 29, 309-317. https://doi.org/10.1016/S0305-0483(01)00026-3
  15. Vapnik, V. N. (1995). The nature of statistical learning theory, Springer, New York.
  16. Vapnik, V. N. (1998). Statistical learning theory, Springer, New York.