Classic Econometric Models. Part 4: Options, Microstructure & Event Studies

How Transactional Data, Event Analysis, and Options Pricing Fit In

So far in the series, we have covered tools for modeling returns, volatility, and risk. In this last part, we will focus on the remaining categories that we haven’t covered yet—though, while a bit lengthy, this will by no means be a complete list.

It should be mentioned that there are far more econometric models in use, such as various option pricing models (Black-Scholes, binomial, Heston) or models widely applied across all the mentioned categories, like those based on the Monte Carlo method. The write-up should also include models used for high-frequency data, transactional data, and market microstructure (e.g., Ordered Probit Model, Decomposition Model, rounding and barrier models), as well as approaches like event study analysis. We could also note that these models are often categorized into linear and non-linear models. Option pricing models could also be mentioned here.

The above categorization is not set in stone. Models used for volatility forecasting can also be applied to returns forecasting, and so on.

Event Study

Event Study Analysis (Fama et al., 1969) is used to evaluate the impact of specific events on the value of a financial asset. This approach measures abnormal returns by comparing observed returns during an event window with expected returns based on historical data. It is still widely applied in finance to understand the effects of events such as corporate announcements, mergers, policy changes, or macroeconomic shocks like interest rate hikes on asset prices.

Older models in this category include the Market Model (Sharpe, 1963), which assumes a linear relationship between a stock's returns and market returns. Another early approach is the Constant Mean Return Model (Brown & Warner, 1980), which assumes returns are consistent over time. More recent models include advancements like the GARCH model to account for time-varying volatility or apply machine learning techniques to identify abnormal returns with higher accuracy. See Campbell et al. (1997) for more.

Photo by Dawson Lovell on Unsplash

High-Frequency, Transactional Data, and Market Microstructure Models

The study of high-frequency trading (HFT), transactional data, and market microstructure focuses on the mechanisms used in the execution of trades and the formation of prices at very short time intervals. These models aim to describe the behavior of market participants, the evolution of order books, liquidity provision, and the dynamics of price discovery in environments where trades are executed within milliseconds or even microseconds.

A fundamental class of models in this area includes the Ordered Probit Model (Hausman et al., 1992), which probabilistically models the direction of price changes based on observable order flow variables. The Decomposition Model (Hasbrouck, 1991) offers a framework to decompose price changes into components such as trade direction, trade size, and inter-arrival times between transactions. In addition to these we have rounding models and barrier models (Harris, 1991), which address microstructural effects such as price clustering and the presence of support and resistance levels created by the strategic placement of limit orders.

Modern applications increasingly use self-exciting point processes, such as Hawkes processes (Hawkes, 1971), to capture the temporal clustering of events — where the occurrence of trades or order submissions increases the probability of subsequent events within short time frames. Furthermore, the integration of machine learning techniques has allowed the modeling of complex, nonlinear dependencies within high-dimensional transactional datasets, resulting in improved predictions of price movements and liquidity shifts.

Options Pricing Models

Options pricing models provide a quantitative framework to estimate the value of derivative contracts based on underlying market variables and assumptions about future price behavior. While derivative pricing is a field of its own, deeply integrated with financial mathematics, econometric models play a key role in empirical estimation, calibration, and validation of theoretical pricing models.

The foundational model in this domain is the Black-Scholes-Merton model (Black & Scholes, 1973; Merton, 1973), which assumes continuous trading, constant volatility, and lognormally distributed returns. Despite its simplifying assumptions, it remains a widely used benchmark for pricing European-style options. Extensions of this framework, such as the Heston model (Heston, 1993), use stochastic volatility to better capture the empirical features observed in option prices, including volatility smiles and skews.

The binomial option pricing model (Cox et al., 1979) offers a discrete-time alternative, constructing a recombining tree of potential future price paths. This model is particularly useful for valuing American options, where early exercise features must be considered. Additionally, jump-diffusion models, such as the Merton jump-diffusion model (Merton, 1976), integrate the possibility of sudden, discontinuous price changes, reflecting the reality of market shocks and extreme events.

Econometric techniques are frequently employed to estimate parameters for these models, such as volatility, jump intensity, and mean reversion speeds, using historical price data. Furthermore, nonparametric approaches and machine learning methods are increasingly utilized to enhance the flexibility and empirical accuracy of option pricing models.

It is important to note that this overview covers only the most basic description of options pricing. A more comprehensive exploration of derivatives modeling, including advanced strategies and risk management applications, will be described in future parts of this series.

Monte Carlo Methods

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to estimate numerical results (Metropolis & Ulam, 1949). In financial econometrics, they are particularly valuable for solving problems that are analytically intractable, such as pricing complex derivatives (Boyle, 1977), simulating portfolio risk, and estimating the distribution of future asset prices under uncertainty.

The primary application in econometrics involves simulating stochastic processes that model the behavior of financial variables over time. For example, asset price paths can be generated using geometric Brownian motion (modeled by SDEs; Øksendal, 2003) or more advanced dynamics like stochastic volatility models (Heston, 1993). By simulating a large number of such paths, practitioners can estimate expected payoffs, value-at-risk (VaR), or other risk measures.

Monte Carlo techniques are also integral to option pricing, especially for path-dependent options such as Asian options or barrier options, where the payoff depends on the entire path of the underlying asset rather than its final price. They are also frequently employed in the calibration of complex models, where the likelihood function cannot be derived explicitly but can be approximated through simulation.

Improvements to standard Monte Carlo methods include variance reduction techniques (such as antithetic variates and control variates), which improve the efficiency and accuracy of simulations, and Quasi-Monte Carlo methods, which use low-discrepancy sequences to achieve faster convergence.

Monte Carlo simulations are flexible and can be combined with other econometric frameworks, such as Bayesian estimation or GARCH models, to include parameter uncertainty and dynamic features of financial time series.

Multivariate and Continuous-Time Models

Multivariate models are essential in financial econometrics for capturing the dynamic relationships between multiple time series variables. These models allow researchers and practitioners to analyze how variables such as returns, interest rates, volatility, and macroeconomic indicators evolve together over time, accounting for their interdependencies.

A foundational example is the Vector Autoregression (VAR) model (Sims, 1980), which treats all variables in the system as endogenous and models each as a linear function of past values of itself and all other variables. VAR models are widely used for forecasting and for understanding the transmission of shocks across markets and asset classes.

Extensions of VAR include Vector Error Correction Models (VECM; Engle & Granger, 1987) , which are applied when variables show long-run equilibrium relationships (cointegration). VECM allows the short-term dynamics to adjust toward these long-run equilibria, making it particularly useful in studying relationships like interest rate parity or term structure models.

Continuous-time models, on the other hand, represent the evolution of financial variables as continuous stochastic processes. They are important for modern asset pricing theory and derivative pricing. Models such as the Black-Scholes-Merton framework, Vasicek, Cox-Ingersoll-Ross (CIR), and Heston stochastic volatility model are all continuous-time formulations. See Vasicek (Vasicek, 1977), and CIR (Cox et al., 1985) for more.

These models describe asset prices, interest rates, and volatility dynamics using stochastic differential equations (SDEs), allowing for the use of complex features such as mean reversion, stochastic volatility, and jumps. Continuous-time frameworks are also widely used in the term structure of interest rates, credit risk modeling, and the pricing of exotic derivatives.

The works of Campbell et al. (1997) and Ruey Tsay (2010), offer extensive information on these models, including empirical application and theoretical explanation.

Nonlinear Models

Nonlinear models extend beyond the linear assumptions to capture asymmetries, regime changes, and other complexities in financial time series data. Financial markets often exhibit behaviors — such as volatility clustering, leverage effects, and abrupt structural breaks — that linear models cannot adequately explain.

A common class of nonlinear models is Threshold Autoregressive (TAR) models (Tong, 1978), which allow different dynamics depending on whether the variable of interest crosses certain thresholds. For example, market returns may follow distinct patterns during high-volatility versus low-volatility periods.

Similarly, Smooth Transition Autoregressive (STAR) models (Teräsvirta, 1994) generalize this concept by allowing smooth transitions between regimes, rather than sudden shifts. These models are useful in capturing gradual changes in market conditions or investor behavior.

Another important family is Markov Switching Models (Hamilton, 1989), where the economy or market is assumed to switch between a finite number of states, each governed by its own set of parameters. This class is particularly valuable for modeling bull and bear markets, credit cycles, or sudden shifts in volatility regimes.

Nonlinear models also include nonlinear GARCH extensions, such as the Exponential GARCH (EGARCH) or Threshold GARCH (TGARCH) models, which explicitly model asymmetric effects of positive and negative shocks on volatility. See Teräsvirta (2009) for more information on these models.

In addition, models based on machine learning techniques, such as neural networks or nonparametric methods, have gained traction for capturing complex nonlinear dependencies without requiring explicit functional form assumptions.

By including features like asymmetry, regime dependence, and non-constant variance, nonlinear models provide a more flexible framework for analyzing financial data that departs from the simplifying assumptions of linearity.

Summary

In this part of the series, we went beyond the basics of returns, volatility, and risk to look at some of the broader econometric models used in finance. Still, this is still just a starting point. There’s a whole world of quantitative methods ahead. In the next editions, I’ll move into machine learning–based approaches that are increasingly shaping modern financial analysis and trading strategies.

References

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654.

Boyle, P. P. (1977). Options: A Monte Carlo approach. Journal of Financial Economics, 4(3), 323-338.

Brown, S. J., & Warner, J. B. (1980). Measuring security price performance. Journal of Financial Economics, 8(3), 205-258.

Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.

Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385-407.

Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229-263.

Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251-276.

Fama, E. F., Fisher, L., Jensen, M. C., & Roll, R. (1969). The adjustment of stock prices to new information. International Economic Review, 10(1), 1-21.

Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series. Econometrica, 57(2), 357-384.

Harris, L. (1991). Stock price clustering and discreteness. Review of Financial Studies, 4(3), 389-415.

Hasbrouck, J. (1991). Measuring the information content of stock trades. Journal of Finance, 46(1), 179-207.

Hausman, J. A., Lo, A. W., & MacKinlay, A. C. (1992). An ordered probit analysis of transaction stock prices. Journal of Financial Economics, 31(3), 319-379.

Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1), 83-90.

Heston, S. L. (1993). A closed-form solution for options with stochastic volatility. Review of Financial Studies, 6(2), 327-343.

Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics, 4(1), 141-183.

Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125-144.

Metropolis, N., & Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association, 44(247), 335-341.

Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347-370.

Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications. Springer.

Sims, C. A. (1980). Macroeconomics and reality. Econometrica, 48(1), 1-48.

Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management Science, 9(2), 277-293.

Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89(425), 208-218.

Teräsvirta, T. (2009). An Introduction to Univariate GARCH Models. In T. Mikosch, J.-P. Kreiß, R. A. Davis, & T. G. Andersen (Eds.), Handbook of Financial Time Series (pp. 17–42). Springer.

Tsay, R. S. (2010). Analysis of Financial Time Series. John Wiley & Sons.

Tong, H. (1978). On a threshold model. In C.H. Chen (Ed.), Pattern Recognition and Signal Processing. Sijthoff & Noordhoff.

Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177-188.