Simple Heuristics for Pricing VIX Options (original) (raw)
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The performance of VIX option pricing models: Empirical evidence beyond simulation
Journal of Futures Markets, 2011
We examine the pricing performance of VIX option models. Such models possess a wide-range of underlying characteristics regarding the behavior of both the S&P500 index and the underlying VIX. Our contention that "simpler is better" is supported by the empirical evidence using actual VIX option market data. Our tests employ three representative models for VIX options: Whaley (1993), , and Carr and Lee . We also compare our results to Lin and Chang , who test four stochastic volatility models, as well as to previous simulation results of VIX option models. We find that no model has small pricing errors over the entire range of strike prices and times to expiration. In particular, out-of-the-money VIX options are difficult to price, with Grunbichler and Longstaff's mean-reverting model producing the smallest dollar errors in this category. In general, Whaley's Black-like option model produces the best overall results, supporting the "simpler is better" contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is opposite the behavior of stock index option pricing models.
Volatility Model Specification: Evidence from the Pricing of VIX Derivatives
2013
This study examines whether a jump component or an additional factor better supports volatility modeling by investigating the pricing of VIX derivatives. To reduce the computational burdens for the empirical estimation significantly, we propose an efficient and easily implemented numerical approximation for the pricing of VIX derivatives. In terms of the term structure of VIX futures, we show that the additional volatility factor can replicate the common empirical patterns and explain the changes in the term structure, but the jump component cannot. In terms of the pricing of VIX options, we find that the two-factor volatility models significantly outperform the jump volatility models and that adding jumps in volatility only provides a minor improvement. Therefore, our general findings support the merit of the two-factor volatility specification.
A Corridor Fix for VIX: Developing a Coherent Model-Free Option-Implied Volatility Measure
2010
The VIX index is computed as a weighted average of SPX option prices over a range of strikes according to specific rules regarding market liquidity. Using tick-by-tick observations on the underlying options, we document that this strike range varies substantially in how much coverage it provides of the distribution of future S&P 500 index prices, producing significant biases, or distortions, in the time series of VIX measures. We propose a novel high-frequency Corridor Implied Volatility index (CX) computed from a strike range covering an "economically invariant" proportion of the future S&P 500 index values and using only reliable option quotes. Comparing the time series properties of these alternative volatility indices from June 2008 through June 2010, we find that our CX measure is superior in terms of filtering out noise and avoiding large artificial jumps. Consequently, the properties of the two series at both the daily and the intraday level are dramatically different in important dimensions of relevance for asset pricing, risk management and real-time trading strategies.
VIX derivatives: Valuation models and empirical evidence
Pacific-Basin Finance Journal, 2019
This study proposes an efficient approach for the pricing of VIX derivatives under the affine framework and investigates the respective value of two variance components and variance jumps in the pricing of VIX derivatives. Our numerical results show that our approach significantly reduce the computational burden. Our empirical findings provide support for the use of two-variance component models as the means of capturing the fickle term structure of VIX derivatives, and the use of variance jumps is vital when included in the long-run variance component.
Coherent Model-Free Implied Volatility: A Corridor Fix for High-Frequency VIX
SSRN Electronic Journal, 2011
The VIX index is computed as a weighted average of SPX option prices over a range of strikes according to specific rules regarding market liquidity. It is explicitly designed to provide a model-free option-implied volatility measure. Using tick-by-tick observations on the underlying options, we document a substantial time variation in the coverage which the stipulated strike range affords for the distribution of future S&P 500 index prices. This produces idiosyncratic biases in the measure, distorting the time series properties of VIX. We introduce a novel "Corridor Implied Volatility" index (CX) computed from a strike range covering an "economically invariant" proportion of the future S&P 500 index values. We find the CX measure superior in filtering out noise and eliminating artificial jumps, thus providing a markedly different characterization of the high-frequency volatility dynamics. Moreover, the VIX measure is particularly unreliable during periods of market stress, exactly when a "fear gauge" is most valuable.
We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semianalytical formula for option prices as in Heston and Nandi [2000]. Secondly, we try to reproduce some features of the Vix Index. We derive a simple formula for the Vix index and use it for option pricing purposes.
Modeling VIX Futures and Pricing VIX Options in the Jump Di usion Modeling
2014
In this thesis, a closed-form solution for the price of options on VIX futures is derived by developing a term-structure model for VIX futures. We analyze the VIX futures by the Merton Jump Diffusion model and allow for stochastic interest rates in the model. The performance of the model is investigated based on the daily VIX futures prices from the Chicago Board Option Exchange (CBOE) data. Also, the model parameters are estimated and option prices are calculated based on the estimated values. The results imply that this model is appropriate for the analysis of VIX futures and is able to capture the empirical features of the VIX futures returns such as positive skewness, excess kurtosis and decreasing volatility for long-term expiration. ∗Postal address: Mathematical Statistics, Stockholm University, SE-106 91, Sweden. E-mail: fatemeharamian@yahoo.com. Supervisor: Mia Hinnerich.
SSRN Electronic Journal, 2013
A double gamma model is proposed for the VIX. The VIX is modeled as gamma distributed with a mean and variance that respond to a gamma-distributed realized variance over the preceeding month. Conditional on VIX and the realized variance, the logarithm of the stock is variance gamma distributed with affine conditional drift and quadratic variation. The joint density for the triple realized variance, VIX, and the SPX is in closed form. Maximum likelihood estimation on time series data addresses model adequacy. A joint calibration of the model to SPX and VIX options is employed to illustrate a risk management application hedging realized volatility options.
Constructing a Class of Stochastic Volatility Models: Empirical Investigation with Vix Data
SSRN Electronic Journal, 2000
We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semianalytical formula for option prices as in Heston and Nandi [2000]. Secondly, we try to reproduce some features of the Vix Index. We derive a simple formula for the Vix index and use it for option pricing purposes.
An analytical formula for VIX futures and its applications
Journal of Futures Markets, 2011
In this paper we present a closed-form, exact solution for the pricing of VIX futures in a stochastic volatility model with simultaneous jumps in both the asset price and volatility processes. The newly-derived formula is then used to show that the well-known convexity correction approximations can sometimes lead to large errors. Utilizing the newly-derived formula, we also conduct an empirical study, the results of which demonstrate that the Heston stochastic volatility model is a good candidate for the pricing of VIX futures. While incorporating jumps into the underlying price can further improve the pricing of VIX futures, adding jumps to the volatility process appears to contribute little improvement for pricing VIX futures.