• deep learning
• martingales
• neural networks
• options
• sde
• time series
• universal approximation

In the field of financial modeling, Stochastic Differential Equations (SDEs) are commonly
used to analyze and predict market behavior. This thesis proposes a novel approach to
calibrating SDE-based models using real market data. Traditional calibration methods can
be computationally expensive and inflexible, limiting their effectiveness. To address these
challenges, we introduce the Neural Martingales approach, which leverages deep learning
approximation techniques to adjust Geometric Brownian Motion (GBM) models. Our
method involves training a Neural Network to produce martingales that serve as correc-
tion terms, which are subsequently applied to the existing GBM model. This correction
process ensures that the model aligns more accurately with observed market data, effec-
tively capturing the complex dynamics and nonlinearities inherent in financial time series.
By employing Neural Networks, the approach benefits from their universal approximation
capabilities, enabling the model to adapt to a wide range of market scenarios without the
need for extensive manual adjustments. The calibrated model can then be used to predict
future asset values and option pricing more accurately. By combining the flexibility of deep
learning with real market data, this approach aims to enhance the accuracy and reliability
of financial models, ultimately benefiting risk management and investment strategies in
the financial industry.