Description Usage Arguments Value Author(s) References Examples
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$r
, the risk free rate of return (RoR).
The averaging period is the life of the option.
1 |
o |
The |
NPaths |
The number of simulation paths to use in calculating the price, |
The option o
with the price in the field PxMC
based on MC simulations.
Jake Kornblau, Department of Statistics and Department of Computer Science, Rice University, 2016
Hull, John C., Options, Futures and Other Derivatives, 9ed, 2014.
Prentice Hall. ISBN 978-0-13-345631-8,
http://www-2.rotman.utoronto.ca/~hull/ofod/index.html
http://www.math.umn.edu/~spirn/5076/Lecture16.pdf
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | (o = AsianMC())$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
|
[1] 7.524863
[1] 8.871735
[1] 6.199711
[1] 4.412071
[1] 5.616792
[1] 2.684731
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