# blsprice

Black-Scholes put and call option pricing

## Syntax

```[Call, Put] = blsprice(Price, Strike, Rate, Time, Volatility, Yield)
```

## Arguments

 `Price` Current price of the underlying asset. `Strike` Exercise price of the option. `Rate` Annualized, continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number. `Time` Time to expiration of the option, expressed in years. `Volatility` Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), expressed as a positive decimal number. `Yield` (Optional) Annualized, continuously compounded yield of the underlying asset over the life of the option, expressed as a decimal number. (Default = 0.) For example, for options written on stock indices, `Yield` could represent the dividend yield. For currency options, `Yield` could be the foreign risk-free interest rate.

## Description

```[Call, Put] = blsprice(Price, Strike, Rate, Time, Volatility, Yield)``` computes European put and call option prices using a Black-Scholes model.

Any input argument may be a scalar, vector, or matrix. When a value is a scalar, that value is used to price all the options. If more than one input is a vector or matrix, the dimensions of all non-scalar inputs must be identical.

`Rate`, `Time`, `Volatility`, and `Yield` must be expressed in consistent units of time.

 Note:   `blsprice` can handle other types of underlies like Futures and Currencies. When pricing Futures (Black model), enter the input argument `Yield` as:`Yield = Rate` When pricing currencies (Garman-Kohlhagen model), enter the input argument `Yield` as:`Yield = ForeignRate`where `ForeignRate` is the continuously compounded, annualized risk free interest rate in the foreign country.

## Examples

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### Compute European Put and Call Option Prices Using a Black-Scholes Model

This example shows how to price European stock options that expire in three months with an exercise price of \$95. Assume that the underlying stock pays no dividend, trades at \$100, and has a volatility of 50% per annum. The risk-free rate is 10% per annum.

```[Call, Put] = blsprice(100, 95, 0.1, 0.25, 0.5) ```
```Call = 13.6953 Put = 6.3497 ```

## References

Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003.

Luenberger, David G., Investment Science, Oxford University Press, 1998.