Estimating and Using GARCH Models with VIX Data for Option Valuation

Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach

“…10 The analytical approximation (7) ensures that the Vega-adjusted option pricing error is free from sampling error and therefore a well defined objective function. , and we note that its square root, e is identical to a term labeled RMSE in Kanniainen et al (2014).…”

“…Second, we re-estimate * 1 and * 2 with stationary constraints. 13 As parameters 1 , 2 , * 1 , and * 2 driven to their limits (almost to the boundary defined by the constraints), the volatility risk premium is very small and the e is a little larger than the Realized GARCH 11 Kanniainen et al (2014) use NGARCH and GJR-GARCH with NLS estimation where price is calculated using a Monte Carlo simulation. This method is slow and can generate different prices for the same option even with the same set of parameters (due to sampling error) without holding the seed of the random variable generator constant.Therefore, we use approximation method instead.…”

“…4 Usually, in terms of the difference in implied volatility or other equivalent measures such as the Vega weighted pricing error. 5 Or fitting error for other Q-measure series such as the volatility index (see Kanniainen et al (2014) etc. ).…”

“…This transformation makes the model more stable, especially during periods with high volatility of volatility.A quasi closed-form option pricing formula is very hard to obtain for a non-affine model, using the standard method based on the moment-generating function and the inverse Fourier transformation. When a closed-form expression is unavailable one can resort to Monte Carlo methods, see, for example, Corsi et al (2013) and Kanniainen, Lin, and Yang (2014). While this method is straight forward to apply, it can be very time consuming to achieve a desirable accuracy.…”

The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation

“…Before comparing the theoretical and actual VIX values, it is important to note that the G-VIX is defined on a trading day count convention while the CBOE VIX index is defined on a calendar day count convention. Hence, as in Kanniainen et al (2014), in order to perform coherent comparisons, we convert the observed VIX index values from The top two lines of results presented in Table 3 show some basic statistics about the daily observed VIX values with the calendar day and trading day count conventions. As expected, the use of the trading day count convention has a modest but noticeable effect on the basic statistics.…”