VARIANCE TERM STRUCTURE AND VIX FUTURES PRICING

2007 ◽  
Vol 10 (01) ◽  
pp. 111-127 ◽  
Author(s):  
YINGZI ZHU ◽  
JIN E. ZHANG
Keyword(s):  
Term Structure ◽  
Futures Market ◽  
Options Market ◽  
Pricing Model ◽  
No Arbitrage ◽  
Drift Term ◽  
Model Combining ◽  
Vix Futures ◽  
Volatility Derivatives ◽  
Futures Pricing

Using no arbitrage principle, we derive a relation between the drift term of risk-neutral dynamics for instantaneous variance and the term structure of forward variance. We show that the forward variance curve can be derived from options market. Based on the variance term structure, we derive a no arbitrage pricing model for VIX futures pricing. The model is the first no arbitrage model combining options market and VIX futures market. The model can be easily generalized to price other volatility derivatives.

VIX VERSUS VXX: A JOINT ANALYTICAL FRAMEWORK

2020 ◽  
Vol 23 (05) ◽  
pp. 2050033 ◽  
Author(s):  
MARTINO GRASSELLI ◽  
LAKSHITHE WAGALATH
Keyword(s):  
Term Structure ◽  
Real Data ◽  
Analytical Framework ◽  
Option Prices ◽  
Options Market ◽  
Vix Futures ◽  
Consistent Manner ◽  
Systematic Behavior ◽  
Exchange Traded Notes ◽  
Reference Index

We propose a framework for modeling in a consistent manner the VIX index and the VXX, an exchange-traded note written on the VIX. Our study enables to link the properties of VXX to those of the VIX in a tractable way. In particular, we quantify the systematic loss observed empirically for VXX when the VIX futures term-structure is in contango and we derive option prices, implied volatilities and skews of VXX from those of VIX in infinitesimal developments. We also perform a calibration on real data which highlights the flexibility of our model in fitting the futures and the vanilla options market of VIX and VXX. Our framework can be used to model other exchange-traded notes on the VIX as well as any market where exchange-traded notes have been introduced on a reference index, hence providing tools to better anticipate and quantify systematic behavior of an exchange-traded note with respect to the underlying index.

VIX term structure and VIX futures pricing with realized volatility

2018 ◽  
Vol 39 (1) ◽  
pp. 72-93 ◽  
Author(s):  
Zhuo Huang ◽  
Chen Tong ◽  
Tianyi Wang
Keyword(s):  
Term Structure ◽  
Realized Volatility ◽  
Vix Futures ◽  
Futures Pricing

STATISTICS OF VIX FUTURES AND APPLICATIONS TO TRADING VOLATILITY EXCHANGE-TRADED PRODUCTS

2019 ◽  
Vol 22 (01) ◽  
pp. 1850061
Author(s):  
M. AVELLANEDA ◽  
A. PAPANICOLAOU
Keyword(s):  
Term Structure ◽  
Historical Data ◽  
Factor Model ◽  
Futures Market ◽  
High Variability ◽  
Price Formula ◽  
Vix Futures ◽  
Futures Price ◽  
Sharpe Ratios

We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is contango with VIX [Formula: see text] and a long-term futures price [Formula: see text]. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic. To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of [Formula: see text] or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are observed sporadically in the volatility futures market.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

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