This Element provides a comprehensive guide to deep learning in quantitative trading, merging foundational theory with hands-on applications. It is organized into two parts. The first part introduces the fundamentals of financial time-series and supervised learning, exploring various network architectures, from feedforward to state-of-the-art. To ensure robustness and mitigate overfitting on complex real-world data, a complete workflow is presented, from initial data analysis to cross-validation techniques tailored to financial data. Building on this, the second part applies deep learning methods to a range of financial tasks. The authors demonstrate how deep learning models can enhance both time-series and cross-sectional momentum trading strategies, generate predictive signals, and be formulated as an end-to-end framework for portfolio optimization. Applications include a mixture of data from daily data to high-frequency microstructure data for a variety of asset classes. Throughout, they include illustrative code examples and provide a dedicated GitHub repository with detailed implementations.

An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in random fields described by the Kolmogorov and Klein-Kramers equations, the Ornstein-Uhlenbeck and Feller processes, and their generalizations. They are reduced to affine differential and pseudo-differential equations and solved in a unified way by using Kelvin waves and developing a comprehensive math framework for calculating transition probabilities and expectations. Kelvin waves are instrumental for studying the well-known Black-Scholes, Heston, and Stein-Stein models and more complex path-dependent volatility models, as well as the pricing of Asian options, volatility and variance swaps, bonds, and bond options. Kelvin waves help to solve several cutting-edge problems, including hedging the impermanent loss of Automated Market Makers for cryptocurrency trading. This title is also available as Open Access on Cambridge Core.

The main goal of this Element is to provide a psychological explanation for why actual global climate policy is so greatly at odds with the prescriptions of most neoclassical economists. To be sure, the behavioral approach does focus on why neoclassical models are often psychologically unrealistic. However, in this Element the author argues that the unrealistic elements are minor compared to the psychological pitfalls driving politically determined climate policy. Why this is the case is what the author describes as the 'big behavioral question.' More precisely, the big behavioral question asks about unsettling behaviors, why there is a huge gap between actual policy and even the weakest of the prescriptions in the range of plausible recommendations coming from neoclassical economists' integrated assessment models. This title is also available as Open Access on Cambridge Core.

Virtually all journal articles in the factor investing literature make associational claims, in denial of the causal content of factor models. Authors do not identify the causal graph consistent with the observed phenomenon, they justify their chosen model specification in terms of correlations, and they do not propose experiments for falsifying causal mechanisms. Absent a causal theory, their findings are likely false, due to rampant backtest overfitting and incorrect specification choices. This Element differentiates between type-A and type-B spurious claims, and explains how both types prevent factor investing from advancing beyond its current phenomenological stage. It analyzes the current state of causal confusion in the factor investing literature, and proposes solutions with the potential to transform factor investing into a truly scientific discipline. This title is also available as Open Access on Cambridge Core.

In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis for building option valuation models. They start with an informal review of Girsanov's theorem, followed by a brief summary of the basic concepts of the arbitrage free pricing, and the technique of change of numeraire. This is followed by a number of applications of the change of numeraire technique including interest rate models, FX quanto adjustments, credit risk modeling, mortgage backed securities, and CMS rates.

This Element is intended for students and practitioners as a gentle and intuitive introduction to the field of discrete-time yield curve modelling. I strive to be as comprehensive as possible, while still adhering to the overall premise of putting a strong focus on practical applications. In addition to a thorough description of the Nelson-Siegel family of model, the Element contains a section on the intuitive relationship between P and Q measures, one on how the structure of a Nelson-Siegel model can be retained in the arbitrage-free framework, and a dedicated section that provides a detailed explanation for the Joslin, Singleton, and Zhu (2011) model.

To supplement replacement income provided by Social Security and employer­sponsored pension plans, individuals need to rely on their own saving and investment choices during accumulation. Once retired, they must also decide at which rate to spend their savings, with the usual dilemma between present and future consumption in mind. This Element explains how financial engineering and risk management techniques can help them in these complex decisions. First, it introduces 'retirement bonds', or retirement bond replicating portfolios, that provide stable and predictable replacement income during the decumulation period. Second, it describes investment strategies that combine the retirement bond with an efficient performance­seeking portfolio so as to reduce uncertainty over the future amount of income while offering upside potential. Finally, strategies using risk insurance techniques are proposed to secure minimum levels of replacement income while giving the possibility of reaching higher levels of income.

Successful investment strategies are specific implementations of general theories. An investment strategy that lacks a theoretical justification is likely to be false. Hence, an asset manager should concentrate her efforts on developing a theory rather than on backtesting potential trading rules. The purpose of this Element is to introduce machine learning (ML) tools that can help asset managers discover economic and financial theories. ML is not a black box, and it does not necessarily overfit. ML tools complement rather than replace the classical statistical methods. Some of ML's strengths include (1) a focus on out-of-sample predictability over variance adjudication; (2) the use of computational methods to avoid relying on (potentially unrealistic) assumptions; (3) the ability to “learn” complex specifications, including nonlinear, hierarchical, and noncontinuous interaction effects in a high-dimensional space; and (4) the ability to disentangle the variable search from the specification search, robust to multicollinearity and other substitution effects.