AsianMC {QFRM}

Asian option valuation with Monte Carlo (MC) simulation.

Description

Calculates the price of an Asian option using Monte Carlo simulations to determine expected payout.
Assumptions:
The option follows a General Brownian Motion (BM),
ds = mu * S * dt + sqrt(vol) * S * dW where dW ~ N(0,1).
The value of mu (the expected price increase) is o$r, the risk free rate of return (RoR).
The averaging period is the life of the option.

Usage

AsianMC(o = OptPx(o = Opt(Style = "Asian"), NSteps = 5), NPaths = 5)

Arguments

o

The OptPx Asian option to price.

NPaths

The number of simulation paths to use in calculating the price,

Value

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

Author(s)

Jake Kornblau, Department of Statistics and Department of Computer Science, Rice University, 2016

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

Examples

(o = AsianMC())$PxMC #Price = ~5.00,  using default values

  o = OptPx(Opt(Style='Asian'), NSteps = 5)
  (o = AsianMC(o, NPaths=5))$PxMC #Price = ~$5

  (o = AsianMC(NPaths = 5))$PxMC # Price = ~$5

  o = Opt(Style='Asian', Right='Put',S0=10, K=15)
  o = OptPx(o, r=.05, vol=.1, NSteps = 5)
  (o = AsianMC(o, NPaths = 5))$PxMC # Price = ~$4

  #See J.C.Hull, OFOD'2014, 9-ed, ex.26.3, pp.610.
 o = Opt(Style='Asian',S0=50,K=50,ttm=1)
 o = OptPx(o,r=0.1,q=0,vol=0.4,NSteps=5)
 (o = AsianBS(o))$PxBS   #Price is 5.62.
 (o = AsianMC(o))$PxMC