# AsianMC: Asian option valuation with Monte Carlo (MC) simulation. In QFRM: Pricing of Vanilla and Exotic Option Contracts

## Description

Calculates the price of an Asian option using Monte Carlo simulations to determine expected payout.
Assumptions:
The option follows a General Brownian Motion (BM),
ds = mu * S * dt + sqrt(vol) * S * dW where dW ~ N(0,1).
The value of mu (the expected price increase) is `o\$r`, the risk free rate of return (RoR).
The averaging period is the life of the option.

## Usage

 `1` ```AsianMC(o = OptPx(o = Opt(Style = "Asian"), NSteps = 5), NPaths = 5) ```

## Arguments

 `o` The `OptPx` Asian option to price. `NPaths` The number of simulation paths to use in calculating the price,

## Value

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

## Author(s)

Jake Kornblau, Department of Statistics and Department of Computer Science, Rice University, 2016

## References

Hull, John 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
http://www.math.umn.edu/~spirn/5076/Lecture16.pdf

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```(o = AsianMC())\$PxMC #Price = ~5.00, using default values o = OptPx(Opt(Style='Asian'), NSteps = 5) (o = AsianMC(o, NPaths=5))\$PxMC #Price = ~\$5 (o = AsianMC(NPaths = 5))\$PxMC # Price = ~\$5 o = Opt(Style='Asian', Right='Put',S0=10, K=15) o = OptPx(o, r=.05, vol=.1, NSteps = 5) (o = AsianMC(o, NPaths = 5))\$PxMC # Price = ~\$4 #See J.C.Hull, OFOD'2014, 9-ed, ex.26.3, pp.610. o = Opt(Style='Asian',S0=50,K=50,ttm=1) o = OptPx(o,r=0.1,q=0,vol=0.4,NSteps=5) (o = AsianBS(o))\$PxBS #Price is 5.62. (o = AsianMC(o))\$PxMC ```

### Example output

```[1] 7.524863
[1] 8.871735
[1] 6.199711
[1] 4.412071
[1] 5.616792
[1] 2.684731
```

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