Elements in Quantitative Finance – serie

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The authors introduce a novel bootstrap approach to resampling asset price data that can be used for both finite-maturity assets and equities. The key insight is that they bootstrap primitive objects with more appealing statistical properties to avoid resampling series with strong time-series and cross-sectional dependence. They then recover the original dependence structure in an internally consistent manner via definitional identities. Their bootstrap is nonparametric in nature and so avoids the common practice of committing to a tightly parameterized pricing model with explicit assumptions on the form of cross-sectional and time-series dependence. They demonstrate the appealing finite-sample properties of their bootstrap approach in a series of simulation experiments and empirical applications.

The authors introduce a novel bootstrap approach to resampling asset price data that can be used for both finite-maturity assets and equities. The key insight is that they bootstrap primitive objects with more appealing statistical properties to avoid resampling series with strong time-series and cross-sectional dependence. They then recover the original dependence structure in an internally consistent manner via definitional identities. Their bootstrap is nonparametric in nature and so avoids the common practice of committing to a tightly parameterized pricing model with explicit assumptions on the form of cross-sectional and time-series dependence. They demonstrate the appealing finite-sample properties of their bootstrap approach in a series of simulation experiments and empirical applications.

This Element explains the architecture of current climate scenarios and discusses whether it is well-suited to the needs of financial analysts and investment professionals. The author argues that prevailing models underrepresent the uncertainty surrounding climate outcomes. He shows that current scenarios architecture mechanically produces a negative climate risk premium, but that this result only obtains under very special circumstances. He quantifies the economic impact of a misspecification of the sign of the climate risk premium, finding that it is large. The current scenario architecture also unwarrantedly emphasizes transition risk over the potentially more severe physical risks, leading to a skewed picture of climate related financial exposure. The lack of probabilistic weighting in scenario design undermines their usefulness for asset valuation and risk assessment. The Element suggests how a new generation of climate scenarios for investors should be structured, emphasizing transparency, sensitivity analysis, and a more balanced representation of possible outcomes.

This Element explains the architecture of current climate scenarios and discusses whether it is well-suited to the needs of financial analysts and investment professionals. The author argues that prevailing models underrepresent the uncertainty surrounding climate outcomes. He shows that current scenarios architecture mechanically produces a negative climate risk premium, but that this result only obtains under very special circumstances. He quantifies the economic impact of a misspecification of the sign of the climate risk premium, finding that it is large. The current scenario architecture also unwarrantedly emphasizes transition risk over the potentially more severe physical risks, leading to a skewed picture of climate related financial exposure. The lack of probabilistic weighting in scenario design undermines their usefulness for asset valuation and risk assessment. The Element suggests how a new generation of climate scenarios for investors should be structured, emphasizing transparency, sensitivity analysis, and a more balanced representation of possible outcomes.

Does the macro-level relationship between temperature and output comprehensively reflect the patterns observed sub-nationally? This Element quantifies heterogeneous productivity-growth responses to plausibly exogenous temperature and precipitation fluctuations using unbalanced panels over 1970-2018 (166 countries from Penn World Tables 10.01; >1,500 sub-national regions from MCC-PIK). It projects climate change-driven permanent damages to the level of GDP per capita by compounding physical risk-induced productivity-growth deviations over time. These transitory shocks are calculated by combining econometrically estimated response functions with an ensemble of NEX-GDDP CMIP6 simulations from 29 global climate models, which are extrapolated to 3,672 provinces covering 95% of global economic production. First, this study provides a basis for producing spatially disaggregated projections of climate-induced economic damages that consistently encompass most productive regions. Second, it shows that accounting for spatially granular climatic exposure and intra-country economic heterogeneity yields aggregated losses that alter the conclusions of previous global GDP models.

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.

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.