Black-Scholes Inputs (Parameters)

6 Inputs of the Black-Scholes Option Pricing Model

There are 6 basic inputs (parameters) to set when pricing an option using the Black-Scholes model. They are the following:

Below you can find more details and notes concerning individual inputs.

Underlying Price Input

Underlying price is the price at which the underlying security is trading on the market at the moment you are doing the option pricing. For example, if you are pricing an option on J.P. Morgan (JPM) stock and the stock is trading at 44.50 at the time you are doing the pricing, you enter 44.50 as underlying price.

Strike Price Input

Strike price, also called exercise price, is the price at which you would buy (or sell) the underlying security if you choose to exercise the call (or put) option. It is one of the fixed specifications of each particular option contract and it does not change during the life of the option.

Time to Expiration Input

Time to expiration is the time between the moment you are doing the pricing and the expiration of the option. Like strike price, expiration date is a fixed characteristic of every individual option. The expiration date does not change during the life of the option, but as the time passes, the time left to expiration (the number that enters the Black-Scholes model as an input) decreases. Time to expiration enter the calculations as percentage of year, but most software (including the sesyixo.ru Black-Scholes Calculator) enables you to enter today’s date and expiration date (and time if you need to be more precise) and converts it to percentage of year automatically. You may also decide if you want to measure time to expiration in calendar days or trading days.

Volatility Input

The volatility input, measured in percent per year, is how much you generally expect the underlying security to move during the life of the option. For people new to option pricing, the volatility concept may be a bit complicated at first, before you fully understand what the number really represents (standard deviation of returns). If you are not much familiar with volatility, hopefully you will find answers to your questions on the main volatility page.

Also note that volatility is probably the one Black-Scholes input that is the hardest to estimate (and at the same time it can have huge effect on the resulting option prices). Two common ways of estimating volatility are:

Risk-Free Interest Rate Input

Like volatility, risk free interest rate is also measured in percent per year. For a particular trader it should be the rate at which you can deposit or borrow cash over the life of the option (the interest rate tenor should match the time to expiration). The interest rate input is not that important when interest rates are low (like now), but it can get very important when they are high (the importance depends on a particular option’s strike price, type, and time to expiration).

Dividend Yield Input

Dividend yield was not among the inputs in the original version of the Black-Scholes model, but was added soon as an expansion.

Here you can see more details about dividend treatment in the Black-Scholes model and to the respective papers by Black, Scholes, and Merton.


Related pages


sharpe ratio formula exampleuup etfhow to calculate the coefficient of skewnessexcel square root formulastrangle option strategy exampleput option profit calculatorformula for finding the sample meanproshares etfscalculating standard deviation calculatorexponential moving average calculatordividend yield calculationhow to short the vixnormal distribution kurtosisblack scholes vega formuladelta adjusted market valueoption payoff graphwarren buffett 13fbutterfly option exampleblack scholes analysiscalculate skewnesscalculating standard deviation exceloption trading greekscitibank reverse splitrsi emaoption greek definitionsmeasures of variation calculatorcalculate geometric mean in excelvix 3x etfc# moving averagepearson coefficient excelcot cftcblack scholes explainedmacd histogram indicatorgeometric mean advantages and disadvantagesadvantages and disadvantages of weighted average methodcall option implied volatilitysample variance examplesvix etn listwhat does a negative kurtosis meanshort payoff definitionblack scholes calculator with dividendshow to calculate var in excelmarket cap weighted indexformula for calculating variance in excelweighted cost of capital calculatorwhen do vix options expiredirectional hedge fundhow to calculate the coefficient of skewnessprofit loss formula excelblack scholes equationapple stock history graphmonospace fonts listshortcut standard deviation formulahow to calculate weighted average cost of debttrend following trading rulesgreek calculatormomentum indicators technical analysisvix ticker symbolvixy ushow to calculate intrinsic value of an optioncalculating annual returncftc govsoros hedge fund holdingsmsft historical stock pricesharpe ratio analysisstoxx indicesema calculation formulafree float market capitalizationwhat is leptokurticoption calculator excelvolatile stocks meaningexponential function in excel 2010arithmetic mean calculation formulaexcel standard deviation calculationstandard deviation calculation in excel