# ShoutMC: Shout option valuation via Monte Carlo (MC) simulations. In QFRM: Pricing of Vanilla and Exotic Option Contracts

## Description

Calculates the price of a shout option using Monte Carlo simulations to determine expected payout. Assumes that the option follows a General Brownian Motion (GBM) process, ds = mu * S * dt + sqrt(vol) * S * dW where dW ~ N(0,1). Note that the value of mu (the expected price increase) is assumped to be `o\$r`, the risk free rate of return.

## Usage

 `1` ```ShoutMC(o = OptPx(o = Opt(Style = "Shout")), NPaths = 10) ```

## Arguments

 `o` The `OptPx` Shout option to price. `NPaths` The number of simulation paths to use in calculating the price; must be >= 10

## Value

The option object `o` with the price in the field `PxMC` based on the MC simulations.

## Author(s)

Jake Kornblau, Department of Statistics, Rice University, 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/index.html.
Also: http://www.math.umn.edu/~spirn/5076/Lecture16.pdf

## Examples

 ```1 2 3 4 5 6 7 8``` ```(o = ShoutMC())\$PxMC # Approximately valued at \$11 o = Opt(Style='Shout') (o = ShoutMC(OptPx(o, NSteps = 5)))\$PxMC # Approximately valued at \$18.6 o = Opt(Style='Shout',S0=110,K=100,ttm=.5) o = OptPx(o, r=.05, vol=.2, q=0, NSteps = 10) (o = ShoutMC(o, NPaths = 10))\$PxMC ```

### Example output

``` 14.13774
 14.4556
 16.33076
```

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