BarrierMC {QFRM}

Barrier option valuation via Monte Carlo (MC) simulation.

Description

Calculates the price of a Barrier Option using 10000 Monte Carlo simulations. The helper function BarrierCal() aims to calculate expected payout for each stock prices.

Important Assumptions: The option follows a General Brownian Motion (GBM) ds = mu * S * dt + sqrt(vol) * S * dW where dW ~ N(0,1). The value of mu (the expected percent price increase) is assumed to be o$r-o$q.

Usage

BarrierMC(o = OptPx(o = Opt(Style = "Barrier")), knock = c("In", "Out"),
  B = 60, NPaths = 5)

Arguments

o

The OptPx Barrier option to price.

knock

Defines the Barrier option to be "In" or "Out"

B

The Barrier price level

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 and the Barrier option properties set by the users themselves

Author(s)

Huang Jiayao, Risk Management and Business Intelligence at Hong Kong University of Science and Technology, Exchange student at Rice University, Spring 2015

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. Also, http://stackoverflow.com/questions/25946852/r-monte-carlo-simulation-price-path-converging-volatility-issue

Examples

(o = BarrierMC())$PxMC #Price =~ $11

 o = OptPx(o=Opt(Style='Barrier'),NSteps = 10)
 (o = BarrierMC(o))$PxMC #Price =~ $14.1

 (o = BarrierMC(NPaths = 5))$PxMC # Price =~ $11

 (o = BarrierMC(B=65))$PxMC # Price =~ $10

 (o = BarrierMC(knock="Out"))$PxMC #Price =~ $1