Pricing VXX option with default risk and positive volatility skew

In this paper, we study the VXX Exchange Traded Note (ETN), that has been actively traded in recent years, but has lost 99.84% of its value. Using Zhang's formula for VIX futures prices, we develop the first theoretical model for the VXX that links the SPX, VIX, and VXX. We show that the roll yield of VIX futures drives the difference between the VXX and VIX returns. The roll yield is a mostly negative process. We then provide a simple yet robust estimation of the market price of variance risk using VXX and VIX futures prices. The model can be used to price VXX options.

Section: Conclusion and Discussionmentioning

confidence: 99%

Modeling VXX

Gehricke

Zhang

2018

“…They calibrate their model using a similar calibration method to that in our study. Bao, Li, and Gong (2012) price VXX options by assuming an affine structure for the VXX and its volatility. This approach ignores the relationship between the SPX, VIX term structure, VIX futures, and the VXX.…”

Section: Introductionmentioning

confidence: 99%

Modeling VXX under jump diffusion with stochastic long‐term mean

Gehricke

Zhang

2020

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.

“…Although there is an extensive literature on the pricing of VIX futures and options (see, e.g., Detemple & Kitapbayev, 2018; Dotsis et al, 2007; Goard & Mazur, 2013; Grünbichler & Longstaff, 1996; Jing et al, 2020; Kaeck & Alexander, 2013; Lin et al, 2019; Marabel Romo, 2017; Mencía & Sentana, 2013; Park, 2016; Psychoyios et al, 2010; Tan et al, 2018), only three basic models have been put forward in VXX options modeling in the existing research. The first model is the jump‐to‐default framework that Bao et al (2012) have proposed to model VXX dynamics as a standalone stochastic process, with a concentration on the issue of VXX options pricing. Factors such as mean‐reversion, jumps, default risk, and positive volatility skew are taken into consideration, and this paper indicates that the jump‐to‐default extended logarithmic mean‐reverting single‐factor plus upward jumps serves as the competitive model.…”

Section: Introductionmentioning

confidence: 99%

The term structure of the VXX option smirk: Pricing VXX option with a two‐factor model and asymmetry jumps

Tan

Wang

Lin

et al. 2020

Self Cite

This paper proposes a comprehensive jump‐to‐default extended two‐factor stochastic volatility plus asymmetry jumps model for the valuation of VXX derivatives. The model provides a more flexible modeling of the time variation in VXX options smirk and VXX options volatility term structure compared with previous model alternatives. Empirical results indicate that our model outperforms Bao et al.'s model by 28.19% in‐sample and 23.38% out‐of‐sample. Moreover, our model improves the probability that the estimated prices fall inside the quoted option bid‐ask spread and has a better fitting capacity for the term structure of VXX implied volatility, especially for out‐of‐the‐money options.