Financial term of the day, Tuesday 3rd of March 2015:

Black-Scholes model

The Black-Scholes model is the most commonly used formula when evaluating European call and put options. The equation was first published by economists Myron Scholes and the late Fisher Black in 1973. Later, Scholes and Robert Merton earned the Nobel Prize in Economics (1997) for the work done on the model and for its general contribution to the understanding of valuation of financial assets.

The formula makes some key assumptions that must be fulfilled in order to give the right answers:
  • Works for European options only
  • The price of the underlying instrument is a geometric Brownian motion (future prices have the same lognormal property as underlying stocks)
  • It is possible to short sell the underlying stock
  • There are no riskless arbitrage opportunities
  • Trading in the stock is continous
  • There are no transaction costs
  • All securities are perfect divisible (possible to buy a fraction of a share
  • The risk-free interest rate is constant and the same for all maturities





where S is the underlying stock price, X the strike price, r the risk-free rate of interest, v is the volatility of the share (standard deviation) and T is the time to maturity. N(d1) and N(d2) are the cumulative normal distribution functions for d1 and d2.

In order to understand the model itself, it is feasible to divide it into two parts. The first part, SN(d1), derives the expected benefit from acquiring a stock outright. This is found by multiplying stock price [S] by the change in the call premium with respect to a change in the underlying stock price [N(d1)]. The second part of the model, Ke(-rt)N(d2), gives the present value of paying the exercise price on the expiration day. The fair market value of the call option is then calculated by taking the difference between these two parts.

Similar financial terms

Black-Scholes model
The Black-Scholes model is the most commonly used formula when evaluating European call and put options. The equation was first published by economists Myron Scholes and the late Fisher Black in 1973. Later, Scholes and Robert Merton earned the Nobel Prize in Economics (1997) for the work done on the model and for its general contribution to the understanding of valuation of financial assets.

The formula makes some key assumptions that must be fulfilled in order to give the right answer ...

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Models that can incorporate different volatility assumptions along the yield curve, such as the Black-Derman-Toy model. Also called arbitrage-free option-pricing models.

Two-state option pricing model
An option pricing model in which the underlying asset can take on only two possible (discrete) values in the next time period for each value it can take on in the preceding time period. Also called the binomial option pricing model.

Two-factor model
Black's zero-beta version of the capital asset pricing model.

Stochastic models
Liability-matching models that assume that the liability payments and the asset cash flows are uncertain.

Simple linear trend model
An extrapolative statistical model that asserts that earnings have a base level and grow at a constant amount each period.

Single index model
A model of stock returns that decomposes influences on returns into a systematic factor, as measured by the return on the broad market index, and firm specific factors.

Single factor model
A model of security returns that acknowledges only one common factor.

Pie model of capital structure
A model of the debt/equity ratio of the firms, graphically depicted in slices of a pie that represent the value of the firm in the capital markets.

Modeling
The process of creating a depiction of reality, such as a graph, picture, or mathematical representation.

Market model
This relationship is sometimes called the single-index model. The market model says that the return on a security depends on the return on the market portfolio and the extent of the security's responsiveness as measured, by beta. In addition, the return will also depend on conditions that are unique to the firm. Graphically, the market model can be depicted as a line fitted to a plot of asset returns against returns on the market portfolio.

Binomial option pricing model
An option pricing model in which the underlying asset can take on only two possible, discrete values in the next time period for each value that it can take on in the preceding time period.

Constant-growth model
Also called the Gordon-Shapiro model, an application of the dividend discount model which assumes (a) a fixed growth rate for future dividends and (b) a single discount rate.

Extrapolative statistical models
Statistical models that apply a formula to historical data and project results for a future period. Such models include the simple linear trend model, the simple exponential model, and the simple autoregressive model.

Harrod-Domar growth model
An economic model which maintains that the growth rate of GDP depends upon the level of savings and the capital output ratio.

Ho-Lee Option Model
An arbitrage free model which uses an estimated spot curve to evaluate embedded options in credit or fixed income securities.

Jensen Model
Jensen's model proposes another risk adjusted performance measure. This measure was developed by Michael C. Jensen and is sometimes referred to as the Differential Return Method. This measure involves evaluation of the returns that the fund has generated vs. the returns actually expected out of the fund given the level of its systematic risk. The surplus between the two returns is called Alpha, which measures the performance of a fund compared with the actual returns over the period. Required re ...

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Marketability

A negotiable security is said to have good marketability if there is an active secondary market in which it can easily be resold.


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