Corporate finance research requires close consideration of the assumptions underlying the econometric models applied to test hypotheses. This is partly because, as the field has evolved, more complex relationships have been examined, some of which pose problems of endogeneity. Endogeneity is one problem that violates the assumptions of the CLRM. It is so central that this book devotes a whole chapter to discussing it. The chapter covers the sources of endogeneity bias and the most commonly used methods that can be applied to cross-sectional data to deal with the endogeneity problem in corporate finance. These methods cover two-stage least squares (so-called IV approach), treatment effects, matching techniques, and regression discontinuity design (RDD). An application is provided for an IV approach and an RDD approach. The chapter ends with an application of the most common methods to real data, lab work, and a mini case study.

We introduce the concepts of a map, a sigma-field generated by a map and the measurability of a map. This leads to the notion of random variable on a probability space, which is just a map being measurable with respect to the considered sigma-field. This guarantees that the distribution of a random variable is well-defined on a given probability space. Next, we review the main families of random variables, discrete (uniform, Bernoulli, binomial) and continuous (uniform, exponential, normal, log-normal), and recall their mass and density functions, as well as their cumulative distribution functions. In particular, we highlight that any random variable can be built by transforming a continuous uniform random variable in an appropriate manner, following the probability integral transform. Finally, we introduce random vectors (vector of random variables), joint and marginal distributions, and the independence property. We illustrate those concepts on toy examples as well as on our stock price model, computing the distribution of prices at various points in time. We explain how correlation can significantly impact the risk of a portfolio of stocks in simple discrete models.

This chapter extends the results found in the Cox–Ross–Rubinstein model (where the stock price is modeled as the exponential of a scaled random walk) to the Black–Scholes–Merton model (where the stock price is modeled as the exponential of a Brownian motion). We argue that, because the risk-neutral approach works when considering any time-step for the scaled random walk, it should also work in the limit where the time-step tends to zero; that is, when the stock price follows a geometric Brownian motion. Therefore, we apply the result of Chapter 9 and compute the price of the product as the risk-neutral expectation of the discounted payoff. The distribution of the stock price under the risk-neutral measure is recovered from the martingale property of the discounted stock price combined with Girsanov’s theorem. This yields a first expression for the fair price of derivative products in continuous time, without having to rely on stochastic calculus.

This chapter studies when the price found using the risk-neutral expectation approach coincides with the no-arbitrage price of the derivative, interpreted as the cost of launching a strategy replicating the product’s payoff. To this end, we define rigorously the concepts of payoff, arbitrage, self-financing strategy, and market model featuring multiple risky assets. A market model is arbitrage-free if it is impossible to find an arbitrage opportunity by trading in the primary assets at the prevailing prices. It is complete if every payoff can be replicated. In general, sophisticated models need to be arbitrage-free but are incomplete. How can we avoid arbitrage if we are unable to replicate the payoff by trading in the primary assets? And how can we determine whether a model is arbitrage-free or complete, given that one cannot reasonably review all the possible strategies to check whether they generate an arbitrage opportunity or not? The answer is provided by the fundamental theorems of asset pricing based on whether the model admits no, one, or multiple risk-neutral measures. This amazing result emphasizes how powerful mathematical modeling can be in finance.

Data management concerns collecting, processing, analyzing, organizing, storing, and maintaining the data you collect for a research design. The focus in this chapter is on learning how to use Stata and apply data-management techniques to a provided dataset. No previous knowledge is required for the applications. The chapter goes through the basic operations for data management, including missing-value analysis and outlier analysis. It then covers descriptive statistics (univariate analysis) and bivariate analysis. Finally, it ends by discussing how to merge and append datasets. This chapter is important to proceed with the applications, lab work, and mini case studies in the following chapters, since it is a means to become familiar with the software. Stata codes are provided in the main text. For those who are interested in using Python or R instead, the corresponding code is provided on the online resources page (www.cambridge.org/mavruk).

Good nursing practice is based on evidence, and undertaking a community health needs assessment is a means of providing evidence to guide community nursing practice. A community health needs assessment is a process that examines the health status and social needs of a particular population. It may be conducted at a whole-of-community level, a sub-community level or even a subsystem level. Nursing practice frequently involves gathering data and assessing individuals or families to determine appropriate nursing interventions. This concept is transferable to an identified community when the community itself is viewed as the client.

A masters-level overview of the mathematical concepts needed to master the art of derivatives pricing, this textbook is a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, the book allows students with limited technical background to build a solid knowledge base of the most important notions. It offers a unique compromise between intuition and mathematics, even when discussing abstract notions such as change of measure. Mathematical concepts are initially introduced using “toy” examples, before moving on to examples of finance cases, in both discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students’ understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code, and an interactive app.

Sex and gender have a significant relationship to health and health outcomes for women, men, and sexually and gender-diverse people. Sex relates to biological attributes, whether born female or male, while gender identity relates to how someone feels and experiences their gender, which may or may not be different to their physiology or sex at birth. Biological characteristics expose women and men to different health risks and health conditions. Gender also exposes people to different health risks, and gender inequity impacts on their potential to achieve health and well-being.

This chapter provides an introduction to the book. The book aims to deepen the reader’s (Bachelor and higher) understanding of empirical research in corporate finance studies and improve their ability to apply econometric methods in their own studies. It may not be general enough for an econometrics course for all finance students, including those interested in asset-pricing studies. However, some of the examples in the book cover studies of the behavior of individual/institutional investors and how this relates to the cost of capital of firms. This link is important to understand in empirical corporate finance studies. The chapter provides a short discussion on this link and then provides a detailed outline of the book. The book is a practical method book, covering essential basic econometric models to illustrate how to apply them in research, closely following some of the well-written and pedagogical books in econometrics.

Chronic conditions, or non-communicable diseases, are the leading cause of death worldwide. Chronic conditions are responsible for 41 million deaths and 17 million premature deaths across the world each year. Most of these deaths are due to four major conditions: cardiovascular disease, cancer, chronic respiratory disease and diabetes. However, other chronic conditions, including injuries that result in persistent disability and mental health disorders, also contribute to increased morbidity and mortality. The significant increase in preventable chronic conditions and the need to manage these are major healthcare concerns of the industrialised world.

Chapter 14 highlights that the solution to a stochastic differential equation cannot be found by treating the sample paths of stochastic processes as smooth functions of time. This is because of the nonzero quadratic variation of a Brownian motion. The purpose of Ito’s lemma is to account for this phenomenon and provides the expression of the differential of a function of a Brownian motion. This is explained using a Taylor expansion and is generalized along various dimensions. The martingale representation theorem highlights that, in some circumstances, any non-negative martingale takes the form of an exponential martingale. Therefore, in such a framework, Girsanov’s theorem does not only work for `special’ measure changes (where the Radon–Nikodym derivative process (RNDP) would coincide with an exponential martingale), but actually encompasses every equivalent measure. We establish a formal link between driftless differential equations and the martingale property of its solution. The RNDP process leading to the risk-neutral measure seen in Chapter 11 is the exponential martingale whose coefficient is such that the drift of the stock price becomes equal to the risk-free rate.

Primary health care (PHC) is a philosophy or approach to health care where health is acknowledged as a fundamental right, as well as an individual and collective responsibility. A PHC approach to health and health care engages multisectoral policy and action which aims to address the broader determinants of health; the empowerment of individuals, families and communities in health decision making; and meeting people’s essential health needs throughout their life course. A key goal of PHC is universal health coverage, which means that all people have access to the full range of quality health services that they need, when and where they need them, without financial hardship.

A masters-level overview of the mathematical concepts needed to master the art of derivatives pricing, this textbook is a must-have for anyone considering a career in quantitative finance in industry or academia. Starting from the foundations of probability, the book allows students with limited technical background to build a solid knowledge base of the most important notions. It offers a unique compromise between intuition and mathematics, even when discussing abstract notions such as change of measure. Mathematical concepts are initially introduced using “toy” examples, before moving on to examples of finance cases, in both discrete and continuous time. Throughout, numerical applications and simulations illuminate the analytical results. The end-of-chapter exercises test students’ understanding, with solved exercises at the end of each part to aid self-study. Additional resources are available online, including slides, code, and an interactive app.