# FinancialToolbox

##### This is a Julia package containing some useful Financial functions for Pricing and Risk Management under the Black and Scholes Model.

###### The syntax is the same of the Matlab Financial Toolbox.

It currently contains the following functions:

- blsprice : Black & Scholes Price for European Options.
- blkprice : Black Price for European Options.
- blsdelta : Black & Scholes Delta sensitivity for European Options.
- blsgamma : Black & Scholes Gamma sensitivity for European Options.
- blstheta : Black & Scholes Theta sensitivity for European Options.
- blsvega : Black & Scholes Vega sensitivity for European Options.
- blsrho : Black & Scholes Rho sensitivity for European Options.
- blslambda: Black & Scholes Lambda sensitivity for European Options.
- blspsi : Black & Scholes Psi sensitivity for European Options.
- blsvanna : Black & Scholes Vanna sensitivity for European Options.
- blsimpv : Black & Scholes Implied Volatility for European Options (using Brent Method).
- blkimpv : Black Implied Volatility for European Options (using Brent Method).

Currently supports classical numerical input and other less common like:

- Complex Numbers
- Dual Numbers
- HyperDual Numbers

It also contains some functions that could be useful for the Dates Management:

- yearfrac : fraction of years between two Dates (currently only the first seven convention of Matlab are supported).
- daysact : number of days between two Dates.

The module is standalone.

## How to Install

To install the package simply type on the Julia REPL the following:

`Pkg.add("FinancialToolbox")`

## How to Test

After the installation, to test the package type on the Julia REPL the following:

`Pkg.test("FinancialToolbox")`

## Example of Usage

The following example is the pricing of a European Call Option with underlying varying according to the Black Scholes Model, given the implied volatility. After that it is possible to check the result computing the inverse of the Black Scholes formula.

```
#Import the Package
using FinancialToolbox
#Define input data
spot=10;K=10;r=0.02;T=2.0;σ=0.2;d=0.01;
#Call the function
Price=blsprice(spot,K,r,T,σ,d)
#Price=1.1912013169995816
#Check the Result
Volatility=blsimpv(spot,K,r,T,Price,d)
#Volatility=0.20000000000000002
```

### Contributors

Thanks to Modesto Mas for the implementation of the Brent Method.