Nonlinear Kalman Filtering in Affine Term Structure Models

Christoffersen, Peter; Dorion, Christian; Jacobs, Kris; Karoui, Lotfi

doi:10.1287/mnsc.2013.1870

Cited by 81 publications

(29 citation statements)

References 52 publications

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“…The application of UKF to model estimation has been employed in the derivatives literature in recent years. Christoffersen, Dorion, Jacobs, and Karoui () provide a detailed examination of the nonlinear Kalman filtering, with a focus on UKF applications to affine term structure models of interest rates. Carr and Wu () have applied the UKF methodology to currency options and Carr and Wu () to equity options and credit default swaps.…”

Section: Methodsmentioning

confidence: 99%

A dimension‐invariant cascade model for VIX futures

Dupoyet

2019

Journal of Futures Markets

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We propose a new stochastic volatility model by allowing for a cascading structure of volatility components. The model, under a minor assumption, allows us to add as many components as desired with no additional parameters, effectively defeating the curse of dimensionality often encountered in traditional models. We derive a semi‐closed‐form solution to the VIX futures price, and find that our six‐factor model with only six parameters can closely fit spot VIX and VIX futures prices from 2004 to 2015 and produce out‐of‐sample pricing errors of magnitudes similar to those of in‐sample errors.

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Section: Methodsmentioning

confidence: 99%

A dimension‐invariant cascade model for VIX futures

Dupoyet

2019

Journal of Futures Markets

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“…This method is accurate up to the third order for a Gaussian state vector and the second order for a non-Gaussian state vector, and has been widely used in the option pricing literature (see Carr and Wu, 2007;Trolle and Schwartz, 2009a,b;and Mencía and Sentana, 2012). In particular, Christoffersen, Dorion, Jacobs, and Karoui (2014) show that unscented Kalman filtering is superior to extended Kalman filtering in the application of interest rate derivatives. Refer to Appendix C for further details on unscented Kalman filtering and Appendix D for the data used in the estimation.…”

Section: Estimation Methodsmentioning

confidence: 99%

Variance Disparity and Market Frictions

Park

2019

FEDS

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This paper introduces a new model-free approach to measuring the expectation of market variance using VIX derivatives. This approach shows that VIX derivatives carry different information about future variance than S&P 500 (SPX) options, especially during the 2008 financial crisis. I find that the segmentation is associated with frictions such as funding illiquidity, market illiquidity, and asymmetric information. When they are segmented, VIX derivatives contribute more to the variance discovery process than SPX options. These findings imply that VIX derivatives would offer a better estimate of expected variance than SPX options, and that a measure of segmentation may be useful for policymakers as it signals the severity of frictions. JEL Classification: G01; G13; G14

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“…Finally, in line with Christoffersen et al (2014)) and Du and Luo (2019)), we construct the daily log-likelihood function of VIX derivatives at time t as…”

Section: Estimation Proceduresmentioning

confidence: 99%

“…Christoffersen, Dorion, Jacobs, and Karoui (2014) find that the UKF is a good method to estimate affine factor models. In this paper, we apply a combined estimation approach of the unscented Kalman filter (UKF) and the maximum log-likelihood estimation method (MLE) to our model.…”

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confidence: 91%

“…In this paper, we apply a combined estimation approach of the unscented Kalman filter (UKF) and the maximum log-likelihood estimation method (MLE) to our model. Christoffersen, Dorion, Jacobs, and Karoui (2014) find that the UKF is a good method to estimate affine factor models. Following the literature, we use the root mean squared errors (RMSEs) as our major performance measurement criterion (Mencía & Sentana, 2013;Park, 2015;Yang & Kanniainen, 2017, etc.…”

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Pricing VIX derivatives with infinite‐activity jumps

Cao

Ruan

et al. 2019

Journal of Futures Markets

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In this paper, we investigate a two-factor VIX model with infinite-activity jumps, which is a more realistic way to reduce errors in pricing VIX derivatives, compared with Mencía and Sentana (2013), J Financ Econ, 108, 367-391. Our two-factor model features central tendency, stochastic volatility and infiniteactivity pure jump Lévy processes which include the variance gamma (VG) and the normal inverse Gaussian (NIG) processes as special cases. We find empirical evidence that the model with infinite-activity jumps is superior to the models with finite-activity jumps, particularly in pricing VIX options. As a result, infinite-activity jumps should not be ignored in pricing VIX derivatives. K E Y W O R D S infinite-activity jumps, maximum log-likelihood estimation, unscented Kalman filter, VIX derivatives J E L C L A S S I F I C A T I O N G12, G13 | INTRODUCTIONTime-varying volatility is a key risk factor in financial markets; thus, understanding the dynamics of volatility variation is crucial for market practitioners and academic researchers. The Chicago Board Options Exchange (CBOE) Volatility Index, known by its ticker symbol VIX, is a risk-neutral gauge of the future implied volatility in the U.S. stock market. It is calculated by the S&P 500 index options market over the next 30-day period and indicates overall stock market fear. 1 VIX can be traded through the VIX derivatives. Because of a negative correlation between the return of VIX and the return of the S&P 500 index, market participants treat the VIX derivatives as an important trading vehicle for reducing exposure to risk. Reported by CBOE, the VIX derivatives include VIX futures and VIX options. In 2004, CBOE introduced VIX futures. According to the CBOE website, the average daily volume of VIX futures rose more than 135fold from 2004 to 2017, with a significant growth after 2010. 2 After the successful launch of VIX futures, CBOE introduced VIX options in 2006, which can provide an alternative way for hedging the market risk with relatively low costs. Since then, the VIX options have become popular financial tools in risk management. Not surprisingly, the average daily volume of VIX options expanded over 28 times between 2006 and 2017. 3 Therefore, it is important to find an accurate valuation model of the VIX derivatives.The methodologies for pricing VIX derivatives can be classified into two directions. In the first direction, the VIX derivatives pricing formulae are derived from the instantaneous volatilities of the S&P 500 index, which can provide a clear picture of the relationship among the S&P 500 index, VIX, and VIX derivatives. Researchers in this direction 1 See https://www.cboe.com/micro/vix/vixwhite.pdf. 2 See http://www.cboe.com/blogs/options-hub/2017/03/01/eight-charts-highlighting-growth-in-options-and-vix-futures. 3 See http://www.cboe.com/blogs/options-hub/2017/08/25/record-days-for-vix-futures-and-options-volume-and-open-interest-this-month.Note: The VG and NIG processes are summarized. The "Parameters" row shows the parameters in t...

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Nonlinear Kalman Filtering in Affine Term Structure Models

Cited by 81 publications

References 52 publications

A dimension‐invariant cascade model for VIX futures

A dimension‐invariant cascade model for VIX futures

Variance Disparity and Market Frictions

Pricing VIX derivatives with infinite‐activity jumps

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