Option Pricing Based on REGARCH Model with High-Frequency Information
DOI:
https://doi.org/10.54097/ntdq8k78Keywords:
Option pricing, High-frequency information, Realized volatility, REGARCH model, S&P 500 index optionsAbstract
As a prevalent tool for hedging risk, the trading volume of options has been growing increasingly in the derivatives market. Precision in the estimation of volatility leads to accurate option pricing. Since volatility is time-varying and has a clustering effect, GARCH class of volatility models is effective in modeling volatility precisely. This paper utilizes the realized EGARCH (REGARCH) model combined with Monte Carlo simulation to investigate the role of high-frequency information in option pricing. The parameter estimates of the REGARCH model are obtained via joint maximum likelihood estimation using observations on returns and realized measure. Applying the model to S&P options market, the empirical results show that the REGARCH model that using high-frequency data is more efficient than the model that only use daily closing prices, including the EGARCH, NGARCH and GJR-GARCH models. This paper demonstrates that incorporating realized measures into volatility models can improve the accuracy of option pricing. The REGARCH model contained more intraday trading information from high-frequency data, can measure the additional risk premiums and specific volatility shocks.
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[1] J.-P. Chavas, J. Li, and L. Wang, “Option pricing revisited: The role of price volatility and dynamics,” Journal of Commodity Markets, 2024.
[2] D. H. Oh and Y.-H. Park, “GARCH option pricing with volatility derivatives,” 2023.
[3] M. Escobar-Anel, J. Rastegari, and L. Stentoft, “Option pricing with conditional GARCH models,” European Journal of Operational Research, 2021.
[4] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, vol. 81, no. 3, pp. 637–654, May 1973.
[5] S. L. Heston, “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” Rev. Financ. Stud., vol. 6, no. 2, pp. 327–343, Apr. 1993.
[6] J. Hull and A. White, “The Pricing of Options on Assets with Stochastic Volatilities,” The Journal of Finance, vol. 42, no. 2, pp. 281–300, Jun. 1987.
[7] R. Kiesel and F. Rahe, “Option pricing under time-varying risk-aversion with applications to risk forecasting,” Journal of Banking & Finance, vol. 76, pp. 120–138, Mar. 2017.
[8] J. Duan, “THE GARCH OPTION PRICING MODEL,” Mathematical Finance, vol. 5, no. 1, pp. 13–32, Jan. 1995.
[9] D. B. Nelson, “Conditional Heteroskedasticity in Asset Returns: A New Approach,” Econometrica, vol. 59, no. 2, p. 347, Mar. 1991.
[10] R. F. Engle and V. K. Ng, “Measuring and Testing the Impact of News on Volatility,” The Journal of Finance, vol. 48, no. 5, pp. 1749–1778, Dec. 1993.
[11] L. R. Glosten, R. Jagannathan, and D. E. Runkle, “On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,” The Journal of Finance, vol. 48, no. 5, pp. 1779–1801, Dec. 1993.
[12] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Nov. 2013.
[13] P. Christoffersen, V. Errunza, K. Jacobs, and X. Jin, “Correlation dynamics and international diversification benefits,” International Journal of Forecasting, vol. 30, no. 3, pp. 807–824, Jul. 2014.
[14] P. R. Hansen and Z. Huang, “Exponential GARCH Modeling With Realized Measures of Volatility,” Journal of Business & Economic Statistics, vol. 34, no. 2, pp. 269–287, Apr. 2016.
[15] P. R. Hansen, Z. Huang, C. Tong, and T. Wang, “Realized GARCH, CBOE VIX, and the Volatility Risk Premium,” Journal of Financial Econometrics, vol. 22, no. 1, pp. 187–223, Jan. 2024.
[16] P. Christoffersen, R. Elkamhi, B. Feunou, and K. Jacobs, “Option Valuation with Conditional Heteroskedasticity and Nonnormality,” Rev. Financ. Stud., vol. 23, no. 5, pp. 2139–2183, May 2010.
[17] Z. Huang, T. Wang, and P. R. Hansen, “Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach,” Journal of Futures Markets, vol. 37, no. 4, pp. 328–358, Apr. 2017.
[18] J.-C. Duan and J.-G. Simonato, “Empirical Martingale Simulation for Asset Prices,” Management Science, vol. 44, no. 9, pp. 1218–1233, Sep. 1998.
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