Ph.D. Thesis Colloquium of
Mr. Vikranth Lokeshwar D

Thesis Supervisor: Prof. Shashi Jain
Date: 6th March 2024 [Wednesday]
Time: 04:30 PM
Venue: Seminar Hall [Management Studies]

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

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Over the last two decades, derivatives have profoundly transformed financial markets, witnessing remarkable expansion in both 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 emphasizes the increased importance of effective risk management in ensuring the stability of the financial system. There has been also 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 models for pricing and risk management 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 in 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. 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 efficiently. 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 book for financial institutions. Though static hedging has garnered a substantial amount of research attention,

there are relatively few studies to study empirically the performance of static hedge against a delta hedge. We present a data-driven framework for semi-static hedging of Exchange-traded options, taking into account real-time trading constraints such as transaction costs, liquidity and availability of options. Using test for superior predictive ability, we conduct a thorough empirical comparison between the performance of static and dynamic hedge for exchange traded options in National Stock Exchange (NSE), a prominent exchange in India. Additionally, 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 optimizing the pricing algorithm for Bermudan options to achieve better convergence. Additionally, efficient mechanisms for generating Counterparty Credit Rsk (CCR) exposure distributions and profiles for Bermudan options are also explored under both risk-neutral and real-world measure. In reality, individually handling risks for each option is impractical and a holistic approach to managing risks at the portfolio level is required. Managing risks with substantial portfolios becomes a challenge. 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, the efforts are directed towards efficiently generating exposures and Greeks at the portfolio level by using compressed portfolio. Finally, it is demonstrated that the compressed portfolio generated by the proposed algorithm reduces the standardized regulatory CCR capital under BASEL norms, the set of standards formulated by Basel Commiittee of Banking and Supervision (BCBS).