QFRM (version 1.0.1)

AverageStrikeMC: Average Strike option valuation via Monte Carlo (MC) simulation

Description

Calculates the price of an Average Strike option using Monte Carlo simulations by determining the determine expected payout. Assumes that the input option follows a General Brownian Motion $ds = mu * S * dt + sqrt(vol) * S * dz$ where $dz ~ N(0,1)$ Note that the value of $mu$ (the expected price increase) is assumped to be o$r, the risk free rate of return. Additionally, the averaging period is assumed to be the life of the option.

Usage

AverageStrikeMC(o = OptPx(o = Opt(Style = "AverageStrike")), NPaths = 5)

Arguments

o

The AverageStrike OptPx option to price.

NPaths

the number of simulations to use in calculating the price,

Value

The original option object o with the price in the field PxMC based on the MC simulations.

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://www.math.umn.edu/~spirn/5076/Lecture16.pdf

Examples

(o = AverageStrikeMC())$PxMC   #Price =~ $3.6

  o = OptPx(o = Opt(Style='AverageStrike'), NSteps = 5)
  (o = AverageStrikeMC(o))$PxMC # Price =~ $6

  (o = AverageStrikeMC(NPaths = 20))$PxMC  #Price =~ $3.4

  o = OptPx(o = Opt(Style='AverageStrike'), NSteps = 5)
  (o = AverageStrikeMC(o, NPaths = 20))$PxMC  #Price =~ $5.6