# price.bsm.option: Price BSM Option In RND: Risk Neutral Density Extraction Package

## Description

`bsm.option.price` computes the BSM European option prices.

## Usage

 `1` ```price.bsm.option(s0, k, r, te, sigma, y) ```

## Arguments

 `s0` current asset value `k` strike `r` risk free rate `te` time to expiration `sigma` volatility `y` dividend yield

## Details

This function implements the classic Black-Scholes-Merton option pricing model.

## Value

 `d1 ` value of `(log(s0/k) + (r - y + (sigma^2)/2) * te)/(sigma * sqrt(te))` `d2 ` value of `d1 - sigma * sqrt(te)` `call ` call price `put ` put price

Kam Hamidieh

## References

E. Jondeau and S. Poon and M. Rockinger (2007): Financial Modeling Under Non-Gaussian Distributions Springer-Verlag, London

J. Hull (2011) Options, Futures, and Other Derivatives and DerivaGem Package Prentice Hall, Englewood Cliffs, New Jersey, 8th Edition

R. L. McDonald (2013) Derivatives Markets Pearson, Upper Saddle River, New Jersey, 3rd Edition

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# # call should be 4.76, put should be 0.81, from Hull 8th, page 315, 316 # r = 0.10 te = 0.50 s0 = 42 k = 40 sigma = 0.20 y = 0 bsm.option = price.bsm.option(r =r, te = te, s0 = s0, k = k, sigma = sigma, y = y) bsm.option # # Make sure put-call parity holds, Hull 8th, page 351 # (bsm.option\$call - bsm.option\$put) - (s0 * exp(-y*te) - k * exp(-r*te)) ```

RND documentation built on May 1, 2019, 10:52 p.m.