title: Deep learning calibration framework for detecting asset price bubbles from option prices
Creators: name: Arora, Manish Rajkumar
Publisher: name: University of Glasgow
Year: 2025

description: Asset price bubbles are associated with exuberant trading and unsustainable price increases, eventually culminating in abrupt collapses, causing widespread socioeconomic and financial devastation. Such phenomena have become increasingly frequent across various asset classes in recent times, and given the interconnectedness of global markets, the potential damage from bubbles bursts has significantly amplified. This is evidenced by the enduring repercussions of the Global Financial Crisis from nearly two decades ago.

This research is motivated to enhancing efficiency of bubble detection from option prices by employing neural networks, such that exuberance in the underlying asset is examined more comprehensively. Following an exhaustive overview of historical occurrences and detection methods, a three-step approach under the framework of the local martingale theory of bubbles was preferred. It captures forward looking expectations of market participants, and overcomes joint-hypothesis related issues, as opposed to traditional methods. The three-step approach relies on calibrating a sophisticated stochastic volatility jump diffusion model to market put observations, prior to testing for exuberance in call option prices. However, computational inefficiencies during calibration, limit its ability in extracting crucial information from option prices.

To overcome this roadblock, a deep calibration framework is constructed such that an optimally trained neural network is employed as a numerical solver for the desired stochastic process. This framework boosts computational efficiency by orders of magnitude, without sacrificing accuracy. It enables the extraction of crucial information regarding the formation of bubbles from the entire surface of option prices, without any compromises. Such calibrations further allow for exploration of bubbles within different maturity groups, and even across the lifetime of call options. At first, the deep calibration framework is applied to observe bubbles in the S&amp;P 500 index, and then for a more recent case study on selected technology stocks. Finally, factors influencing the formation exuberance are examined, which also doubles down as a robustness test for the methodology.

Construction of the deep calibration framework, improves tractability of the three-step 
approach, making it more attractive for practitioners. Typically, despite possessing greater sophistication, inefficient stochastic processes are overlooked due to their computationally cumbersome nature, creating a trade-off between accuracy and efficiency. This trade-off is overcome with the application of neural networks, allowing for a deeper exploration and subsequently, greater comprehension of call option and underlying price bubbles. The significant boost in efficiency ensures that practitioners are able to extract real-time information regarding bubble formations, repeatedly, at superior speeds. The contributions of this research are important for policymakers and institutions seeking to properly manage risk and adjust positions in abidance with the ever-fluctuating essence of financial markets.