NUMA OPTION CALCULATOR

Input/Output Data Definitions

See also the examples
Recommended books on option pricing

  1. Brief description of the calculator
  2. Input definitions
  3. Output definitions

CALCULATOR DESCRIPTION

The calculator uses an adjusted Black-Scholes model to value European options. (European options are those that can only be exercised at expiry). The model is adjusted to take into account dividends paid on the underlying security. The calculator can in fact be used for: In all references here, the term share price can be used interchangeably with index level, currency rate or futures price. The calculator features:

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INPUT DEFINITIONS

INPUT DATA
Share Price: [data] Strike Price: [data] Maturity(yrs): [data]
Dividend Yld: [data] Interest Rate: [data] Volatility: [data]

Share Price; Strike Price
These can be input in any units (e.g. dollars or cents) but the input must be consistent for the share price, strike price (and, if calculating implied volatility, for the option price as well).

Note: as an aid for input, there is the facility to input the share/strike/option prices all as "eighth's". For this, select the button (to the right of the input strike price). With /8 selected, a price of 67 3/8 can be input as 67.3; the program will then automatically convert "67.3" to the decimal 67.375 for use in the calculations. All outputs from the calculator will always be expressed in decimal.

Dividend Yield
The standard Black-Scholes model has been "adjusted" to account for dividends payable. (If this is not required then simply input 0 in the dividend yield field). To input a dividend yield of 3.4%, enter "3.4".

Note: if valuing currency options, then the foreign interest rate should be input to this field.

Interest Rate
The simple risk-free interest rate for the period should be input. For example, if valuing a 6 month option, then the 6-month risk-free rate should be used. To input a rate of 6.7%, input "6.7".

Note: strictly, the Black-Scholes valuation model requires the interest rate to be a continuously compounded rate. So the calculator converts the simple rate input, to a continuously compounded rate. However, some option calculators and examples in books do not make this adjustment, so there is the facility to "switch off" this conversion, by de-selecting the button called cc-int. This might then enable calibration with other option calculators.

Maturity
Maturity can be input as days, months or years; simply select the appropriate button to the right of the input field.

Volatility
If calculating the theoretical option value, then a forecast of future share price volatility must be input. To input a volatility of 25.5%, input "25.5". (If calculating implied volatility, any figure in the volatility input field will be ignored). For more detail on volatility see Option Volatility - a discussion of historic/implied/forecast volatilites.

Option Price
If calculating the implied volatility, then the actual market price of the option is input. This should be input in the same units as those used for the share price and strike price. If the /8 button has been selected then, the option price must be input expressed as a fractional eighth.

Option Type
Select whether the option is a call or put.

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OUTPUT DEFINITIONS

THEORETICAL VALUE CALCULATIONS
Option Value: [data] Delta: [data] Theta: [data] Rho1: [data]
% of share: [data] Gamma: [data] Vega: [data] (Rho2): [data]

Option Value
The theoretical (or fair) value of the option as determined by the input parameters. The value will be expressed in the same units as those used for the input of share and exercise prices.

% of share
The option value (above) expressed as a percentage of the share price. It is sometimes useful to express the option value as such, when comparing options on different underlying securities.

Delta
Measures the sensitivity of the calculated option value to small changes in the share price.

Gamma
Measures the sensitivity of the calculated delta to small changes in the share price.

Theta
Measures the sensitivity of the calculated option value to small changes in time as expiration approaches.

Vega
Measures the sensitivity of the calculated option value to small changes in the volatility.

Rho1
Measures the sensitivity of the calculated option value to small changes in the interest rate.

(Rho2)
If using the calculator to value a currency option, then Rho2 indicates the sensitivity of the calculated option value to small changes in the foreign interest rate.

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