ShoutMC {QFRM}

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.

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

(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