Exploiting market-implied information for option pricing, calibration, and portfolio management

• Applicant: Professorin Dr. Eva-Maria Lütkebohmert-Holtz
• Subject Area: Accounting and Finance ; Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 558724124

Since the work of Black and Scholes (1973), financial models have grown increasingly complex to better reflect market phenomena. However, exact price replication is impractical and undesirable due to potential model misspecifications and inherent uncertainties. Moreover, in advanced option pricing models, certain parameters are notoriously challenging to estimate, which can have significant consequences for the pricing and hedging of derivatives as well as for option portfolio management. This raises key questions: (a) How can we efficiently exploit market information to quantify parameter uncertainty? (b) Can we optimize portfolios using only market-implied data in a model-free, forward-looking way? (c) Can market information reveal risk premia dynamics? (d) Which market information is relevant in forecasting derivative prices? The suggested project addresses these questions from various perspectives. (a) Managing model uncertainty in affine option pricing models: Starting from an affine option pricing model, we address the important topic of parameter uncertainty from a Bayesian perspective. In particular, we calculate sensitivities of option prices w.r.t. all model parameters and evaluate measures of the uncertainty associated with the model parameters given their full posterior distribution. (b) Portfolio management based on model-free real-world scenario simulation: We develop a fast, model-free, and forward-looking method to efficiently simulate future scenarios of an asset’s return as well as returns on options written on this asset under the physical probability measure. With this we target two important applications: forward-looking, model-free option portfolio optimization as well as equity portfolio management. (c) Joint P − Q estimation of affine option pricing models: We suggest a new methodology for the joint estimation of affine option pricing models under both the physical and the risk-neutral probability measure. This allows us to identify the risk premium, a challenging task in financial econometrics. Ultimately, we target the formulation of a novel affine option pricing model that allows for time-varying risk premia and we explicitly derive the dynamics of the pricing kernel. (d) Deep Asian option pricing using moments: Our aim is to price continuously monitored Asian options with a deep learning approach taking risk-neutral cumulants as additional highly informative input features which will improve the training process and the accuracy of the pricing function. The project thus provides both methodological contributions and relevant implications for practical applications in the field of financial derivatives valuation, the calibration of option pricing models and risk and portfolio management.

• DFG Programme: Research Grants
• International Connection: Italy
• Cooperation Partner: Dr. Riccardo Brignone