BarrierMC function

Barrier option valuation via Monte Carlo (MC) simulation.

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.

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

Returns

The option o with the price in the field PxMC based on MC simulations and the Barrier option properties set by the users themselves

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

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