# BS_Simple: Black-Scholes formula In QFRM: Pricing of Vanilla and Exotic Option Contracts

## Description

Black-Scholes (aka Black-Scholes-Merton, BS, BSM) formula for simple parameters

## Usage

 `1` ```BS_Simple(S0 = 42, K = 40, r = 0.1, q = 0, ttm = 0.5, vol = 0.2) ```

## Arguments

 `S0` The spot price of the underlying security `K` The srike price of the underlying (same currency as S0) `r` The annualized risk free interest rate, as annual percent / 100 (i.e. fractional form. 0.1 is 10 percent per annum) `q` The annualized dividiend yield, same units as `r` `ttm,` The time to maturity, fraction of a year (annualized) `vol` The volatility, in units of standard deviation.

## Details

Uses BS formula to calculate call/put option values and elements of BS model

## Value

a list of BS formula elements and BS price, such as `d1` for d_1, `d2` for d_2, `Nd1` for N(d_1), `Nd2` for N(d_2), N`CallPxBS` for BSM call price, `PutPxBS` for BSM put price

## Author(s)

Robert Abramov, Department of Statistics, Rice University, Spring 2015

## References

Hull, J.C., Options, Futures and Other Derivatives, 9ed, 2014. Prentice Hall. ISBN 978-0-13-345631-8, http://www-2.rotman.utoronto.ca/~hull/ofod. http://amzn.com/0133456315 http://www.theresearchkitchen.com/archives/106

## Examples

 ```1 2 3 4 5 6 7 8``` ```#See Hull p.339, Ex.15.6. (o <- BS_Simple(S0=42,K=40,r=.1,q=0,ttm=.5,vol=.2))\$Px\$Call #returns 4.759422 o\$Px\$Put # returns 0.8085994 as the price of the put BS_Simple(100,90,0.05,0,2,0.30) BS_Simple(50,60,0.1,.2,3,0.25) BS_Simple(90,90,0.15,0,.5,0.20) BS_Simple(15,15,.01,0.0,0.5,.5) ```

### Example output

```[1] 4.759422
[1] 0.8085994
\$d1
[1] 0.6961714

\$d2
[1] 0.2719073

\$Nd1
[1] 0.7568393

\$Nd2
[1] 0.6071534

\$Px
\$Px\$Call
[1] 26.24017

\$Px\$Put
[1] 7.675535

\$d1
[1] -0.8973676

\$d2
[1] -1.33038

\$Nd1
[1] 0.1847614

\$Nd2
[1] 0.09169651

\$Px
\$Px\$Call
[1] 0.9941339

\$Px\$Put
[1] 18.00265

\$d1
[1] 0.6010408

\$d2
[1] 0.4596194

\$Nd1
[1] 0.7260936

\$Nd2
[1] 0.6771053

\$Px
\$Px\$Call
[1] 8.812221

\$Px\$Put
[1] 2.309134

\$d1
[1] 0.1909188

\$d2
[1] -0.1626346

\$Nd1
[1] 0.5757054

\$Nd2
[1] 0.4354031

\$Px
\$Px\$Call
[1] 2.137109

\$Px\$Put
[1] 2.062296
```

QFRM documentation built on May 2, 2019, 8:26 a.m.