Regress-Later with Interpretable Neural Networks for Pricing, Static hedging and Exposure management of Financial Derivatives

Abstract

In the past two decades, there has been a significant growth in the trading of financial derivatives, witnessed in both Centralised Exchange and Over-The-Counter (OTC) markets. One of the main reasons for this growth is due to the technological advancements in computing/system infrastructure, that has enabled the adoption of complex models capable of handling high-frequency trades and large-scale computations. While keeping pace with these advancements, there is also increased importance in effective risk management of derivatives market to ensure overall stability of the financial system. In parallel, there has been increased focus in the adoption of innovative 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, an area that is of keen interest to the financial institutions as well as regulators. 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 the 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. For Bermudan style derivatives, it is shown 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 path towards harnessing AI/ML models within the regulatory modelling framework of trading book for financial institutions.

Though static hedging of options has garnered a substantial amount of research attention, there are relatively few studies on empirical analysis and testing on the performance of static hedge against a delta hedge. A data-driven framework for semi-static hedging of Exchange-traded options is presented, taking into account real-time trading constraints such as transaction costs, liquidity and availability of options. Using test for superior predictive ability, a comparison is performed between the performance of static and dynamic hedge for exchange traded options in National Stock Exchange (NSE), a prominent exchange in India. Additionally, a detailed Profit and Loss (PnL) attribution analysis is illustrated to discern the factors contributing to the better hedging properties of static hedging.

The focus then shifts to optimally price and manage risks of a specific class of options, i.e., early exercise options. Due to the computational complexity involved in the pricing of early exercise options using Monte Carlo simulation, an emphasis is placed on optimizing the pricing algorithm for Bermudan options (that are known to have early exercise feature at discrete time points) to achieve better convergence. Additionally, efficient mechanisms for generating Counterparty Credit Risk (CCR) exposure distributions and profiles for Bermudan options are also explored under both risk-neutral and real-world measures.

In practice, there is a typical need for a holistic approach to managing risks in derivatives trading book at portfolio level in addition to managing risks at individual trade level. Further, managing risks with substantial portfolio size becomes a challenge. One feasible way to counter this challenge 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. Subsequently, the efforts are directed towards efficiently generating exposures and Greeks at the portfolio level by using compressed portfolio. Finally, it is demonstrated that the portfolio compression technique can be used to compress a large portfolio into a compact portfolio with shorter maturities, which can be re-invested at the end of every short-term to realise the original portfolio characteristics. Through the adoption of these techniques, we observe a significant reduction in Exposure At Default (EAD) and, consequently, the minimum CCR capital requirement for compressed portfolios under the Standardised approach of BASEL norms, established by the Basel Committee on Banking Supervision (BCBS).