This paper provides an econometric explanation for the pricing kernel puzzle, an empirical finding that estimated pricing kernels often display shapes and properties inconsistent with standard asset-pricing theory. I demonstrate that this puzzle can arise from an informational mismatch between investors, who condition on a rich macrofinancial information set, and econometricians, who typically rely only on returns observed up to the option’s inception. To address this informational disparity, I develop a parsimonious macro-financial volatility framework in which return dynamics under both the physical and risk-neutral measures are allowed to vary with low-frequency macroeconomic conditions. Using S&P 500 returns, real-time (vintage) macroeconomic data, and cross-sections of out-of-the-money S&P 500 European options, I find that the macro-augmented model delivers substantial improvements in volatility forecasts and option pricing relative to benchmark  specifications in the literature. I also validate the volatility dynamics of the model against the VIX index, showing that the implied volatilities are consistent with market expectations. The estimated pricing kernels are smooth and monotonically decreasing, and satisfy the Euler equation restrictions. Taken together, the evidence indicates that the pricing kernel puzzle is mainly due to informational incompleteness in conventional econometric implementations, rather than a failure of the underlying asset-pricing theory.

We propose a general framework, which accommodates both joint dynamics between the market and a stock and non-normality and can be used straightforwardly to test the (relative) importance of these features. We use the model to price 1, 702, 753 American options written on 25 individual stocks from the U.S. stock market. Our results confirm that allowing for non-normality or jointly modelling dynamics improves on pricing, that it is more important to consider the risk related to the market than allowing for nonnormality, but that jointly modelling the market and the stock dynamics in a model with non-normality always leads to the smallest pricing error across all the stocks. The results are robust across option moneyness and maturity, but the relative performance of our proposed model is improved in crisis periods.

This paper develops a mixture-of-normals multivariate GARCH model in which the mixing probabilities are explicitly linked to macroeconomic conditions and studies its implications for equity option pricing. The conditional return distribution is modeled as a two-component normal mixture with a BEKK-type volatility structure, allowing for time-varying correlations and rich higher-moment dynamics. Unlike standard mixture-GARCH models with fixed regime probabilities, the proposed specification lets the weights on the calm and turbulent regimes respond to observable macroeconomic indicators, capturing state-dependent shifts in tail risk and volatility clustering. Preliminary results highlight the importance of allowing macroeconomic conditions to shape the probability of volatility regimes when modelling multivariate return dynamics and pricing equity options. 

This comparative study compares the forecasting ability of Bayesian high dimensional VAR models, dynamic factor models, and sophisticated machine learning models like the LSTM neural network. The study uses the U.S. macroeconomic and financial variables to estimate the models. In line with the current literature, the Bayesian method is used to estimate dynamic factor and high-dimensional VAR models, with all implementations carried out in MATLAB programming language. Conversely, Python is used to estimate the machine learning models. The performance of the models is assessed based on their forecasting accuracy for variables of interest, using root mean squared forecasting error as a metric. The findings show that high-dimensional VAR models with time-varying parameters and stochastic volatility offer good forecasting ability for macroeconomic variables, while the LSTM models are competitively good for financial market variables. The findings underscore the complementary roles of Bayesian estimation methods and machine learning frameworks in modern forecasting.