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1.
In this paper, we examine and compare the performance of a variety of continuous‐time volatility models in their ability to capture the behavior of the VIX. The “3/2‐ model” with a diffusion structure which allows the volatility of volatility changes to be highly sensitive to the actual level of volatility is found to outperform all other popular models tested. Analytic solutions for option prices on the VIX under the 3/2‐model are developed and then used to calibrate at‐the‐money market option prices. 相似文献
2.
This study uses multiple maturity-independent variables to examine whether the volatility information implied in the term structure of volatility index can improve the prediction of realized volatility. The empirical results for the S&P 500 index show that, in terms of both the in-sample estimation and out-of-sample forecasting, the term structure variables provide substantial incremental contribution to the models with only level variables. Our empirical results are robust to various forms of volatility, alternative ways to develop the term structure variable, the impact of macroeconomic variables, and alternative underlying assets. 相似文献
3.
In this paper we propose semiclosed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte–Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options. 相似文献
4.
We develop a model for the VXX, the most actively traded VIX futures exchange-traded note, using Duffie, Pan, and Singleton's affine jump diffusion framework, where the volatility process has jumps and a stochastic long-term mean. We calibrate the model parameters using the VIX term structure data and show that our model provides the theoretical link between the VIX, VIX futures, and the VXX. Our model can be used for pricing VIX futures, the VXX and other short-term VIX futures exchange-traded products (ETPs). Our model could be extended to price options on the VXX and other short-term VIX futures ETPs. 相似文献
5.
This paper presents an analytical approach for pricing variance swaps with discrete sampling times when the underlying asset follows a Hawkes jump-diffusion process characterized with both stochastic volatility and clustered jumps. A significantly simplified method, with which there is no need to solve partial differential equations, is used to derive a closed-form pricing formula. A distinguished feature is that many recently published formulas can be shown to be special cases of the one presented here. Some numerical examples are provided with results demonstrating that jump clustering indeed has a significant impact on the price of variance swaps. 相似文献
6.
This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures. 相似文献
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We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed‐form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX‐implied volatilities, and their sensitivities, in the joint limit of short time‐to‐maturity and small log‐moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol‐of‐vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications. 相似文献
9.
Using an extended LHARG model proposed by Majewski et al. (2015, J Econ, 187, 521–531), we derive the closed-form pricing formulas for both the Chicago Board Options Exchange VIX term structure and VIX futures with different maturities. Our empirical results suggest that the quarterly and yearly components of lagged realized volatility should be added into the model to capture the long-term volatility dynamics. By using the realized volatility based on high-frequency data, the proposed model provides superior pricing performance compared with the classic Heston–Nandi GARCH model under a variance-dependent pricing kernel, both in-sample and out-of-sample. The improvement is more pronounced during high volatility periods. 相似文献
10.
We develop a new generalized autoregressive conditional heteroskedasticity (GARCH) model that accounts for the information spillover between two markets. This model is used to detect the usefulness of the CBOE volatility index (VIX) for improving the performance of volatility forecasting and option pricing. We find the significant ability of VIX to predict stock volatility both in-sample and out-of-sample. VIX information also helps to greatly reduce the option pricing error. The proposed volatility spillover GARCH model performs better than the related approaches proposed by Kanniainen et al. (2014, J Bank Finance, 43, pp. 200-211) and P. Christoffersen et al. (2014, J Financ Quant Anal, 49, pp. 663–697). 相似文献
11.
We propose a flexible framework for modeling the joint dynamics of an index and a set of forward variance swap rates written on this index. Our model reproduces various empirically observed properties of variance swap dynamics and enables volatility derivatives and options on the underlying index to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index. 相似文献
12.
We study the relationship of the VIX index and the exchange-traded note VXX on various timescales. We find that changes of VIX and VXX are correlated only contemporaneously on timescales of days, but VIX leads VXX on timescales of months. Next, we construct a simple joint model for VXX and VIX which replicates all the key characteristics of these two time series, but in which VIX and VXX are related only via a correlated error term. Therefore, VIX cannot be used as a predictor of VXX and there is no apparent trading profit opportunity. 相似文献
13.
Most of the existing pricing models of variance derivative products assume continuous sampling of the realized variance processes, though actual contractual specifications compute the realized variance based on sampling at discrete times. We present a general analytic approach for pricing discretely sampled generalized variance swaps under the stochastic volatility models with simultaneous jumps in the asset price and variance processes. The resulting pricing formula of the gamma swap is in closed form while those of the corridor variance swaps and conditional variance swaps take the form of one‐dimensional Fourier integrals. We also verify through analytic calculations the convergence of the asymptotic limit of the pricing formulas of the discretely sampled generalized variance swaps under vanishing sampling interval to the analytic pricing formulas of the continuously sampled counterparts. The proposed methodology can be applied to any affine model and other higher moments swaps as well. We examine the exposure to convexity (volatility of variance) and skew (correlation between the equity returns and variance process) of these discretely sampled generalized variance swaps. We explore the impact on the fair strike prices of these exotic variance swaps with respect to different sets of parameter values, like varying sampling frequencies, jump intensity, and width of the monitoring corridor. 相似文献
14.
John Elder 《期货市场杂志》2019,39(12):1549-1564
There has been a surge in interest in the effects of uncertainty on investment decisions, motivated at least in part by the theory of real options. For example, Bloom (2009, Econometrica, 77, 623–685) shows that higher uncertainty causes firms to temporarily pause investment and hiring, generating sharp economic downturns. This paper investigates these effects by examining the response of disaggregated measures of production to volatility in oil prices. We find that increased oil price volatility has strong negative effects on the production of durable goods, such as transportation equipment, and oil exploration, such as the drilling of oil and gas wells. 相似文献
15.
James S. Doran 《期货市场杂志》2020,40(6):841-859
Hedging market downturns without sacrificing upside has long been sought by investors. If VIX was directly investable, adding it as a hedge to the S&P 500 would result in significantly improved performance over the equity only portfolio. However, tradable VIX products do not provide the hedge or returns investors seek over long-term horizons. Alternatively, deconstructing VIX to find the key S&P 500 options which drive VIX movements leads to a synthetic VIX portfolio that provides a more effective hedge. Using these options captures correlations and returns similar to VIX, and combined with the S&P 500, outperforms the buy-and-hold index portfolio. 相似文献
16.
针对标准的差分进化算法只能处理连续空间的优化问题,提出了一种基于取整策略的差分进化算法。该方法只需要对优化变量进行四舍五入取整,就能够把标准差分进化算法用于稀疏阵列天线方向图优化。将取整策略的差分进化算法应用到六边形平面稀疏天线阵的布阵设计。为了计算六边形阵列天线的方向图,提出在口径中添加虚拟单元的计算模型,把六边形阵列转化为可以实现二维快速傅里叶变换的矩形阵列。以改善阵列峰值副瓣电平为目的进行仿真试验,结果表明,优化后的稀疏天线阵峰值旁瓣电平与采用遗传算法相比改善了4.5~5.1 dB,且具有计算速度快、稳定性好的优点。 相似文献
17.
This paper studies a large number of bitcoin (BTC) options traded on the options exchange Deribit. We use the trades to calculate implied volatility (IV) and analyze if volatility forecasts can be improved using such information. IV is less accurate than AutoRegressive–Moving-Average or Heterogeneous Auto-Regressive model forecasts in predicting short-term BTC volatility (1 day ahead), but superior in predicting long-term volatility (7, 10, 15 days ahead). Furthermore, a combination of IV and model-based forecasts provides the highest accuracy for all forecasting horizons revealing that the BTC options market contains unique information. 相似文献
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In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the underlying asset price and the instantaneous value of the volatility By studying the variation m the first argument, we show that the usual hedging methods, through the Black and Scholes model, lead to an underhedged (resp. overhedged) position for in-the-money (resp out-of the-money) options, and a perfect partial hedged position for at the-money options These results are shown to be closely related to the smile effect, which is proved to be a natural consequence of the stochastic volatility feature the deterministic dependence of the implied volatility on the underlying volatility process suggests the use of implied volatility data for the estimation of the parameters of interest A statistical procedure of filtering (of the latent volatility process) and estimation (of its parameters) is shown to be strongly consistent and asymptotically normal. 相似文献
19.
This study investigates the cross-sectional implication of informed options trading across different strikes and maturities. We explore the term structure perspective of the one-way information transmission from options markets to stock markets by adopting well-known option-implied volatility measures to examine stock return predictability. Using equity options data for U.S. listed stocks spanning 2000–2013, we find that the shape of the long-term implied volatility curve exhibits extra predictive power for stock returns of subsequent months even after orthogonalizing the short-term components. Our findings indicate that the inter-market information asymmetry rapidly disappears before the expiration of long-term option contracts. 相似文献
20.
This paper is a compendium of results—theoretical and computational—from a series of recent papers developing a new American option valuation technique based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given, as is the analysis needed to solve the inverse problem of determining local (one‐factor) volatility from market data. The ideas behind a fast accurate revised simplex method, whose performance is linear in time and space discretizations, are described and the practicalities of fitting the volatility smile are discussed. Numerical results are presented which show the LP valuation technique to be extremely fast—lattice speed with PDE accuracy. American options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile. 相似文献