Ph.D Thesis Defense of
Mr. Vikranth Lokeshwar D

Research Supervisor: Prof. Shashi Jain
Co-Supervisor: Dr Amrutha A

Title: Regress-later with Interpretable Neural Networks for Pricing, Static hedging and Exposure management of derivatives

Venue: Online Microsoft Teams Meeting
Date and Time: May 24, 2024 (Friday) at 16:00

Teams link:

Over the last two decades, derivatives have profoundly transformed financial markets, witnessing remarkable expansion in Exchange and Over-The-Counter (OTC) markets. One major reason for this transformation is significant advancements in system infrastructure, which have enabled the adoption of complex and computationally intensive models capable of handling high-frequency and large-scale computations. This emphasises the increased importance of effective risk management in ensuring the financial system’s stability. There has also been increased focus on innovative new pricing and risk management techniques by leveraging the benefits of Artificial Intelligence (AI) and Machine Learning (ML) algorithms. However, the key challenge of AI applications is explainability or the interpretation of the model (especially under regulatory frameworks), a keen area that interests financial institutions. Developing interpretable pricing and risk management models under AI/ML frameworks has been one of the key motivations of this thesis.

A novel method called Regress-Later with Neural Networks (RLNN) using the Monte-Carlo approach for pricing high-dimensional discretely monitored (including early-exercise features) contingent claims is presented along with a proof of convergence for the price. The choice of specific architecture of the neural networks used in the proposed algorithm provides for the interpretability of the model, a feature that is often desirable in the financial context. The interpretation demonstrates that any discretely monitored contingent claim, possibly high dimensional and path-dependent, under Markovian and no-arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. The proposed design of neural network architecture, dissolving the black-box nature of neural networks, provides a clear path to harness AI models within the regulatory modelling framework of trading books for financial institutions.

We also show, for Bermudan style derivatives, how the RLNN method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound is found by exploiting the dual formulation. Unlike other duality-based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate the simplicity and efficiency of the method for pricing and semi-static hedging of path-dependent options through numerical examples.

Though static hedging has garnered substantial research attention, there are relatively few studies to study empirically the performance of a static hedge against a delta hedge. We present a data-driven framework for semi-static hedging of Exchange-traded options, considering real-time trading constraints such as transaction costs, liquidity and availability of options. Using a test for superior predictive ability, we conduct a thorough empirical comparison between the performance of static and dynamic hedges for exchange-traded options traded in the National Stock Exchange (NSE), a prominent exchange in India. We also perform a detailed Profit and Loss (PnL) attribution analysis to discern the factors contributing to the better hedging properties of static hedging.

The focus then shifts to a specific class of options, i.e., early exercise options. Due to their computational complexity when priced using Monte-Carlo simulation, an emphasis is placed on optimising the pricing algorithm for Bermudan options to achieve better convergence. Additionally, efficient mechanisms for generating Counterparty Credit Risk (CCR) exposure distributions and profiles for Bermudan options are explored under risk-neutral and real-world measures. The exposures are benchmarked with the industry-standard Longstaff Schwartz method using the novel pricing model named COS method (based on Fourier-cosine series expansions) as a reference model for accuracy.

In reality, individually handling risks for each option is impractical and a holistic approach to managing risks at the portfolio level is required. Maintaining bookings and effectively managing associated risks, particularly with substantial portfolios, becomes challenging. One feasible way is to achieve a shorter portfolio that can replicate a huge target portfolio for managing risks, leading to the concept of portfolio compression, which is one of the key areas covered in this thesis. Further, recognising that risks are managed at the portfolio level in practice, efforts are directed towards efficiently generating exposures and Greeks at the portfolio level. The exposure profiles for a huge target portfolio of European options are generated by the compressed portfolio generated by the proposed algorithm. Additionally, the algorithm is leveraged to reduce standardised regulatory CCR capital under BASEL norms, the set of standards formulated by the Basel Committee of Banking and Supervision (BCBS).