Improving the option pricing performance of GARCH models in inefficient market
-
DOIhttp://dx.doi.org/10.21511/imfi.17(2).2020.02
-
Article InfoVolume 17 2020, Issue #2, pp. 14-25
- 904 Views
-
150 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
Understanding the relation between option pricing and market efficiency is important. Indeed, emphasizing this relation generates new insights that are appropriate in practice. These insights give a better understanding of the current limitations of the option pricing and hedging methods. This article thus aims to improve the performance of the option pricing approach. To start, the relation between the option pricing methodology and the informational market efficiency was discussed. It is, therefore, useful, before proceeding to apply the standard risk-neutral approach, to check the efficiency assumption. New modified GARCH processes were used to model the dynamics of the asset returns in the option pricing framework. The new considered approaches allow describing the dynamic of returns when the market is inefficient. Using real data on CAC 40 index, the performance of different models as a function of maturity and moneyness was studied. The in-sample analysis, interested in the stability of the pricing models across time, showed that the new approach, developed under the affine GARCH process, is the most accurate. The study of the out-of-sample performance, which aims to evaluate the forecasting ability of different approaches, confirmed the results of the in-sample analysis. For the optional portfolio hedging, always the best hedging approach is that obtained under the affine GARCH model. After a regression study, it was found that the difference between theoretical and observed option values can be explained by factors, which are not taken into account in the proposed pricing formulae.
- Keywords
-
JEL Classification (Paper profile tab)C12, C13, G14
-
References24
-
Tables4
-
Figures5
-
- Figure 1. Autocorrelation functions of the CAC 40 index price, log-price and log-return (12/31/1987 – 12/31/2018)
- Figure 2. Statistical t-test of the parameter θ
- Figure 3. In-sample average absolute errors as a function of maturity
- Figure 4. In-sample average absolute errors as a function of moneyness
- Figure 5. Hedging absolute errors as a function of moneyness
-
- Table 1. Estimations and properties (daily returns of CAC 40 from January 1988 to December 2012)
- Table 2. Goodness-of-fit of the TFS-GARCH models
- Table 3. Out-of-sample forecast errors as a function of the maturity
- Table 4. Out-of-sample forecast errors as a function of moneyness
-
- Amin, K., & Engle, V. (1993). ARCH processes and option valuation (Working paper, University of Michigan, Ann Arbor, MI).
- Arshanapalli, B., & Nelson, W. (2016). Testing for stock price bubbles: a review of econometric tools. International Journal of Business and Finance Research, 10(4), 29-42.
- Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654.
- Bollerslev, T. (1986). Generalized auto regressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
- Camerer, C. (1989). Bubbles and fads in asset prices. Journal of Economic Surveys, 3(1), 3-41.
- Christoffersen, P., Dorion, C., Jacobs, K., & Wang, K. (2010). Volatility components: affine restrictions and non-normal innovations. Journal of Business and Economic Statistics, 28, 483-502.
- Christoffersen, P., & Jacobs, K. (2004). Which GARCH model for option valuation? Management Science, 1204.
- Corsi, F., & Sornette, D. (2014). Follow the money: The monetary roots of bubbles and crashes. International Review of Financial Analysis, 32, 47-59.
- Cox, A. M. G., & Hobson, D. G. (2005). Local martingales, bubbles and option prices. Finance and Stochastics, 9(4), 477-492.
- Duan, J. C. (1995). The GARCH option pricing models. Mathematical Finance, 5, 13-32.
- Duan, J. C, Ritchken, P. H., & Sun, Z. (2007). Jump Starting GARCH: Pricing and Hedging Options with Jumps in Returns and Volatilities (Working Paper 0619). Federal Reserve Bank of Cleveland.
- Engle, R., & Rosenberg, J. V. (2000). Testing volatility term structure using option hedging criteria. Journal of Derivatives, 8, 10-28.
- Fama, E. F. (1970). Efficient capital markets: a review of theory and empirical work. Journal of Finance, 384-417.
- Ghoudi, K., & Rémillard, B. (2014). Comparison of specification tests for GARCH models. Computational Statistics and Data Analysis, 76, 291-300.
- Härdle, W., & Hafner, C. M. (2000). Discrete time option pricing with flexible volatility estimation. Finance and Stochastics, 189-207.
- Heston, S. L., Loewenstein, M., & Willard, G. A. (2007). Options and bubbles. Review of Financial Study, 20(2), 359-390.
- Heston, S. L., & Nandi, S. (2000). A closed-form GARCH option pricing model. Review of Financial Studies, 13(3), 585-625.
- Hull, J., & White, A. (2017). Optimal delta hedging for options. Journal of Banking and Finance, 82, 180-190.
- Jarrow, R. (2013). Option Pricing and Market Efficiency. Journal of Portfolio Management, 88-94.
- Jarrow, R. (2016). Testing for asset price bubbles: three new approaches. Quantitative Finance Letters, 4-9.
- Jarrow, R., & Larsson, M. (2012). The meaning of Market efficiency. Mathematical Finance, 1-30.
- Jarrow, R., Protter, P., & Shimbo, K. (2007). Asset price bubbles in a complete market. Advances in Mathematical Finance, 97-121.
- Jarrow, R. A., Protter, P., & Shimbo, K. (2010). Asset price bubbles in incomplete markets. Mathematical Finance, 20(2), 145-185.
- Wöckl, I. (2019). Bubble Detection in Financial Markets: A Survey of Theoretical Bubble Models and Empirical Bubble Detection Tests (Working Paper, Institute of Finance, University of Graz, Universit¨atsstraße 15, 8010 Graz, Austria).