Financial theory is studied and developed within the disciplines of
management,
(financial) economics,
accountancy and
applied mathematics. In the abstract, Academics working in this area are typically based in
business school finance departments, in
accounting, or in
management science. The tools addressed and developed relate in the main to
managerial accounting and
corporate finance: the former allow management to better understand, and hence act on, financial information relating to
profitability and performance; the latter, as above, are about optimizing the overall financial structure, including its impact on working capital. Key aspects of managerial finance thus include: •
Capital budgeting •
Capital structure •
Working capital management •
Risk management • Financial analysis and reporting The discussion, however, also extends to the broader field of
business strategy, emphasizing the need for alignment with the overall strategic objectives of the company. It likewise incorporates
managerial perspectives related to planning, directing, and controlling.
Financial economics ", was first formulated by
Harry Markowitz in 1952 as a prototypical concept in
modern portfolio theory. In the
Markowitz model, an "efficient" portfolio has the best possible expected return for its level of risk (represented by the standard deviation of return). , a foundational element of finance theory, introduced in 1958; it forms the basis for modern thinking on
capital structure. Even if
leverage (
D/E) increases, the
weighted average cost of capital (k0) stays constant. Financial economics is the branch of
economics that studies the interrelation of financial
variables, such as
prices,
interest rates and shares, as opposed to
real economic variables, i.e.
goods and services. It thus centers on pricing, decision making, and risk management in the
financial markets,
asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively: • Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes the
portfolio- and
investment theory applied in asset management. The analysis essentially explores how
rational investors would apply
risk and return to the problem of
investment under uncertainty, producing the key "
Fundamental theorem of asset pricing". Here, the twin assumptions of
rationality and
market efficiency lead to
modern portfolio theory (the
CAPM), and to the
Black–Scholes theory for
option valuation. At more advanced levels—and often in response to
financial crises—the study
then extends these
"neoclassical" models to incorporate phenomena where their assumptions do not hold, or to more general settings. • Much of
corporate finance theory, by contrast, considers investment under "
certainty" (
Fisher separation theorem,
"theory of investment value", and
Modigliani–Miller theorem). Here, theory and methods are developed for the decisions about funding, dividends, and capital structure discussed above. A recent development is
to incorporate uncertainty and
contingency—and thus various elements of asset pricing—into these decisions, employing for example
real options analysis.
Financial mathematics are widely applied in mathematical finance; here used in calculating an
OAS. Other common pricing-methods are
simulation and
PDEs. These are used for settings beyond
those envisaged by Black-Scholes.
Post crisis, even in those settings, banks use
local and
stochastic volatility models to incorporate the
volatility surface, while the
xVA adjustments accommodate
counterparty and capital considerations. Financial mathematics is the field of
applied mathematics concerned with
financial markets;
Louis Bachelier's doctoral thesis, defended in 1900, is considered to be the first scholarly work in this area. The field is largely focused on the
modeling of derivatives—with much emphasis on
interest rate- and
credit risk modeling—while other important areas include
insurance mathematics and
quantitative portfolio management. Relatedly, the techniques developed
are applied to pricing and hedging a wide range of
asset-backed,
government, and
corporate-securities. As
above, in terms of practice, the field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed. The
main mathematical tools and techniques are, correspondingly: • for derivatives,
Itô's stochastic calculus,
simulation, and
partial differential equations; see aside boxed discussion re the prototypical
Black-Scholes model and
the various numeric techniques now applied • for risk management,
value at risk,
stress testing and
"sensitivities" analysis (applying the "greeks"); the underlying mathematics comprises
mixture models,
PCA,
volatility clustering and
copulas. • in both of these areas, and particularly for portfolio problems, quants employ
sophisticated optimization techniques Mathematically, these separate into
two analytic branches: derivatives pricing uses
risk-neutral probability (or
arbitrage-pricing probability), denoted by "Q"; while risk and portfolio management generally use physical (or actual or actuarial) probability, denoted by "P". These are interrelated through the above "
Fundamental theorem of asset pricing". The subject is closely related to financial economics, which, as outlined, focuses on much of the underlying theory involved in financial mathematics: generally, financial mathematics will derive and extend the
mathematical models suggested.
Computational finance is the branch of (applied)
computer science that deals with problems of practical interest in finance, and especially aims to establish different market settings and environments to experimentally observe and provide a lens through which science can analyze agents' behavior and the resulting characteristics of trading flows, information diffusion, and aggregation, price setting mechanisms, and returns processes. Researchers in experimental finance study how well existing financial economics theories make accurate predictions and seek to validate them. They also aim to discover new principles to extend these theories for future financial decisions. This research often involves conducting trading simulations or observing human behavior in artificial, competitive, market-like environments.
Behavioral finance Behavioral finance studies how the
psychology of investors or managers affects financial decisions and markets and is relevant when making a decision that can impact either negatively or positively on one of their areas. With more in-depth research into behavioral finance, it is possible to bridge what actually happens in financial markets with analysis based on financial theory. Behavioral finance has grown over the last few decades to become an integral aspect of finance. Nowadays there is a need for more theory and testing of the effects of feelings on financial decisions. Especially, because now the time has come to move beyond behavioral finance to social finance, which studies the structure of social interactions, how financial ideas spread, and how social processes affect financial decisions and outcomes. Behavioral finance includes such topics as: • Empirical studies that demonstrate significant deviations from classical theories; • Models of how psychology affects and impacts trading and prices; • Forecasting based on these methods; • Studies of experimental asset markets and the use of models to forecast experiments. A strand of behavioral finance has been dubbed
quantitative behavioral finance, which uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation.
Quantum finance Quantum finance involves applying quantum mechanical approaches to financial theory, providing novel methods and perspectives in the field.
Quantum finance is an interdisciplinary field, in which theories and methods developed by
quantum physicists and economists are applied to solve financial problems. It represents a branch known as econophysics. Although
quantum computational methods have been around for quite some time and use the basic principles of physics to better understand the ways to implement and manage cash flows, it is mathematics that is actually important in this new scenario. Finance theory is heavily based on
financial instrument pricing such as
stock option pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as
computational finance. Many computational finance problems have a high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. As a result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. Most commonly used quantum financial models are quantum continuous model, quantum binomial model, multi-step quantum binomial model etc. == History of finance ==