ShoutMC {QFRM} | R Documentation |
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$r
, the risk free rate of return.
ShoutMC(o = OptPx(o = Opt(Style = "Shout")), NPaths = 10)
o |
The |
NPaths |
The number of simulation paths to use in calculating the price; must be >= 10 |
The option object o
with the price in the field PxMC
based on the MC simulations.
Jake Kornblau, Department of Statistics, Rice University, 2015
Hull, J.C., Options, Futures and Other Derivatives, 9ed, 2014. Prentice Hall.
ISBN 978-0-13-345631-8, http://www-2.rotman.utoronto.ca/~hull/ofod/index.html.
Also: http://www.math.umn.edu/~spirn/5076/Lecture16.pdf
(o = ShoutMC())$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