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

Abstract

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.

Specification analysis of VXX option pricing models under Lévy processes

“…For example, compared with Bao et al (2012), we examine longer‐period VXX index and VXX option data using the out‐of‐sample performance test. More importantly, in contrast to Bao et al (2012) and Tan et al (2021), we clarify that the discounted price of VXX, as a tradable asset, under the risk‐neutral measure, should remain a martingale unconditionally (e.g., Shreve, 2004; Carr & Wu, 2010). This paper corrects the VXX option pricing theory in the literature.…”

“…Because the VIX is a nontradable volatility index, so the VIX process does not need to satisfy the martingale condition described in Lemma 1. For modelling the VXX, however, the literature also often uses the same mean‐reverting process motivated by the VIX studies, for example, Bao et al (2012) and Tan et al (2021). This mean‐reverting setting makes the VXX fail to satisfy the martingale condition described in Lemma 1.…”

Option‐Implied Ambiguity and Equity Return Predictability

“…The SSE 50 ETF has been created to track the SSE 50 Index, comprised of the 50 most representative stocks with large scale and good liquidity as sample stocks, and is considered representative of the Shanghai Stock Market. The SSE 50 ETF options are the earliest exchange-traded equity options in China, with high information content for efficiency, violation and intraday behavior (Wang et al 2018;Ahn, Bi, and Sohn 2019;Chi, Hao, and Zhang 2022;Luo, Cai, and Ryu 2022;Wu et al 2022;Luo et al 2024;Jiang and Zhou 2024;Wang et al 2024).…”

Pricing VXX options by modeling VIX directly

“…The paper suggests that a jump‐to‐default extended logarithmic model with jumps (LRJ) and positive correlated stochastic volatility serves as the best model in all the required aspects. Tan et al (2021) propose a comprehensive jump‐to‐default extended two‐factor stochastic volatility plus asymmetry jumps model for the valuation of VXX derivatives. Cao et al (2021) conduct a comprehensive study on the specifications of VXX option pricing models under Lévy processes.…”