# Using High-Frequency Options Data to Evaluate Economic Trading Models

## Abstract

This dissertation provides an empirical assesment of economic models based on high-frequency options data. Options data allows for the investigation of heterogeneous eﬀects across moneyness and maturities, and the use of high-frequency data makes it possible to compute various estimates at higher frequencies and analyze the data behaviour around jumps.

The ﬁrst chapter analyzes the implications of a disagreement model in which investors observe public information but agree to disagree about its interpretation. In this framework, the disagreement between investors can be recovered from the relationship between an asset’s trading volume and its volatility. Using high-frequency data for options on the S&P 500 index, I provide new empirical evidence of disagreement between investors in the market of S&P 500 index options. The options market provides two natural variables that are sharply related to disagreement: moneyness and tenor. I argue that these variables relate to disagreement about the distribution of the market index at diﬀerent quantiles and at diﬀerent times.

I extract the relationship between volume and volatility for options with diﬀerent moneyness and expirations. I ﬁnd evidence of little disagreement among investors, based on options that are at-the-money and near expiration. This evidence can be interpreted as investors’ having little disagreement about new information as it relates to the center of the distribution of returns over the short-run. From options that are far-from-the-money and with longer expirations, I ﬁnd evidence of disagreement among investors. This disagreement increases as options get away from the money, indicating that investors have higher disagreement about rare events. There is also evidence that disagreement increases with the time to expiration of options, indicating that investors have higher disagreement about events farther into the future.

The second chapter examines a general 3-factor options pricing model. This model includes the usual factors that account for short-term and long-term volatility, but also a novel factor that drives the distribution of jump returns. The novel factor, known as the tail factor, impacts the probability of future jump returns, inﬂuencing not only the price of the underlying asset, but also the behaviour of its volatility. The second chapter investigates the plausibility of this tail factor.

To investigate the plausibility of the tail factor, I recover moments of the risk-neutral distribution of market returns. The risk-neutral moments are directly related to the implications of the 3-factor pricing model and the impact of the tail factor. The tail factor jumps whenever there are jumps in the underlying asset, but it can also have independent jumps. The model implies that these diﬀerent types of jump will have diﬀerent impacts on the risk-neutral moments. Indeed, the main implication is that price jumps lead to jumps in all risk-neutral moments of order two and higher. However, idiosyncratic jumps in the tail factor lead only to jumps in moments of order three and higher. I test these implications using high-frequency options data, which allow for the computation of the risk-neutral moments of the S&P 500 index in a model-free fashion and also at higher frequency. I ﬁnd evidence of large and frequent moves in all of the computed risk-neutral moments, far in excess to the number of jumps in the market index. These large moves are in part due to jumps in the market index, that lead to co-jumps in all of the risk-neutral moments. However, the majority of large moves occur in the moments of order higher than three, consistent with the idea of jumps in the tail factor. The existence of the tail factor is further supported by co-jump tests, that reveal co-jumps between the higher order moments that are unrelated to jumps in the market index.

The last chapter examines a common assumption of many well known options pricing models: price jumps bear no impact on volatility. To examine the assumption, I analyze high-frequency moves in the market index and in the implied volatility from the options market. Speciﬁcally, I estimate jump regressions of changes in the implied volatility at times when the makret index jumps. To do so, I use high-frequency data on options and on the S&P 500 index, coupled with jump identiﬁcation techniques and a valid inference for jump regressions.

The jump regressions indicate a negative correlation between jumps in the market index and changes in the implied volatility. The estimates indicate that a market crash of 100 basis points would lead to an increase of 450 basis points in the implied volatility of options. The negative correlation is stable for options with diﬀerent moneyness and is stronger for out-of-the-money options. This indicates that the eﬀect of price jumps is diﬀerent for options that are close-to-the-money and for options that are out-of-the-money, inline with the idea of the volatility smirk. The empirical evidence from the jump regressions can be contrasted to the theoretical implications of options pricing models, such as Merton (1976) and, more recently, Andersen et al. (2015c). Merton’s model states that jumps in the underlying have no eﬀect in options’ implied volatility, while the AFT model states that only positive price jumps do not have an impact. Both models are contradicted by the empirical evidence presented in this chapter: both positive and negative jumps in the market index have an impact on the implied volatility.

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## Citation

Ferreira Pelucio Salome, Guilherme (2020). *Using High-Frequency Options Data to Evaluate Economic Trading Models*. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/20906.

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