QFRM (version 1.0.1)

ShoutMC: Shout option valuation via Monte Carlo (MC) simulations.

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

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.

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

(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