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Binomial options pricing model

In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (), and formalized by Cox, Ross and Rubinstein in 1979 and by Rendleman and Bartter in that same year.

Rational pricing

Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.

Rate of return

In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return.

Diversification (finance)

In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets. If asset prices do not change in perfect synchrony, a diversified portfolio will have less variance than the weighted average variance of its constituent assets, and often less volatility than the least volatile of its constituents.

Security market line

Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk. The risk of an individual risky security reflects the volatility of the return from security rather than the return of the market portfolio. The risk in these individual risky securities reflects the systematic risk. The Y-intercept of the SML is equal to the risk-free interest rate.

Internal rate of return

Internal rate of return (IRR) is a method of quantifying the merits of a project or investment opportunity. The calculation is termed internal because it depends only on the cash flows of the investment being analyzed and excludes external factors, such as returns available elsewhere, the risk-free rate, inflation, the cost of capital, or financial risk. The method may be applied either ex-post or ex-ante. Applied ex-ante, the IRR is an estimate of a future annual rate of return.

Risk premium

A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. Where is the risky expected rate of return and is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections.

Return on capital

Return on capital (ROC), or return on invested capital (ROIC), is a ratio used in finance, valuation and accounting, as a measure of the profitability and value-creating potential of companies relative to the amount of capital invested by shareholders and other debtholders. It indicates how effective a company is at turning capital into profits. The ratio is calculated by dividing the after tax operating income (NOPAT) by the average book-value of the invested capital (IC).

Consumption-based capital asset pricing model

The consumption-based capital asset pricing model (CCAPM) is a model of the determination of expected (i.e. required) return on an investment. The foundations of this concept were laid by the research of Robert Lucas (1978) and Douglas Breeden (1979). The model is a generalization of the capital asset pricing model (CAPM). While the CAPM is derived in a static, one-period setting, the CCAPM uses a more realistic, multiple-period setup.

Markowitz model

In finance, the Markowitz model ─ put forward by Harry Markowitz in 1952 ─ is a portfolio optimization model; it assists in the selection of the most efficient portfolio by analyzing various possible portfolios of the given securities. Here, by choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk. The HM model is also called mean-variance model due to the fact that it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios.