Description Usage Arguments Details Value Note Author(s) References Examples
This is a collection of functions to valuate asian
options. Asian options are path-dependent options,
with payoffs that depend on the average price of the
underlying asset or the average exercise price.
There are two categories or types of Asian options:
average rate options (also known as average price
options) and average strike options. The payoffs
depend on the average price of the underlying asset
over a predetermined time period. An average is less
volatile than the underlying asset, therefore making
Asian options less expensive than standard European
options. Asian options are commonly used in currency
and commodity markets. Asian options are of interest
in markets with thinly traded assets. Due to the
little effect it will have on the option's value,
options based on an average, such as Asian options,
have a reduced incentive to manipulate the underlying
price at expiration.
The functions are:
GeometricAverageRateOption | Geometric Average Rate Option, |
TurnbullWakemanAsianApproxOption | Turnbull and Wakeman's Approximation, |
LevyAsianApproxOption | Levy's Approximation. |
1 2 3 4 5 6 | GeometricAverageRateOption(TypeFlag, S, X, Time, r, b, sigma,
title = NULL, description = NULL)
TurnbullWakemanAsianApproxOption(TypeFlag, S, SA, X, Time, time,
tau, r, b, sigma, title = NULL, description = NULL)
LevyAsianApproxOption(TypeFlag, S, SA, X, Time, time, r, b,
sigma, title = NULL, description = NULL)
|
b |
the annualized cost-of-carry rate, a numeric value; e.g. 0.1 means 10% pa. |
description |
a character string which allows for a brief description. |
r |
a numeric value, the annualized rate of interest; e.g. 0.25 means 25% pa. |
S, SA |
the asset price, a numeric value. |
sigma |
a numeric value, the annualized volatility of the underlying security; e.g. 0.3 means 30% volatility pa. |
tau |
[TurnWakeAsianApprox*] - |
time, Time |
a numeric value, the time to maturity measured in years; e.g. 0.5 means 6 months. |
title |
a character string which allows for a project title. |
TypeFlag |
a character string either |
X |
the exercise price, a numeric value. |
The Geometric average is the nth root of the product of the n sample
points. The Arithmetic average is the sum of the stock values divided
by the number of sampling points. Although Geometric Asian options are
not commonly used in practice, they are often used as a good initial
guess for the price of arithmetic Asian options. This technique is
used to improve the convergence rate of the Monte Carlo model when
pricing arithmetic Asian options.
Two cases are considered, the geometric and the arithmetic average-rate
option. For the latter one can choose between three different kinds of
approximations: Turnbull and Wakeman's approximations, Levy's approximation
and Curran's approximation.
[Haug's Book, Chapter 2.12]
The option price, a numeric value.
The functions implement the algorithms to valuate plain vanilla options as described in Chapter 2.12 of Haug's Book (1997).
Diethelm Wuertz for the Rmetrics R-port.
Haug E.G. (1997); The complete Guide to Option Pricing Formulas, Chapter 2.12, McGraw-Hill, New York.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ## Examples from Chapter 2.12 in E.G. Haug's Option Guide (1997)
## Geometric Average Rate Option:
GeometricAverageRateOption(TypeFlag = "p", S = 80, X = 85,
Time = 0.25, r = 0.05, b = 0.08, sigma = 0.20)
## Turnbull Wakeman Approximation:
TurnbullWakemanAsianApproxOption(TypeFlag = "p", S = 90, SA = 88,
X = 95, Time = 0.50, time = 0.25, tau = 0.0, r = 0.07,
b = 0.02, sigma = 0.25)
## Levy Asian Approximation:
LevyAsianApproxOption(TypeFlag = "c", S = 100, SA = 100, X = 105,
Time = 0.75, time = 0.50, r = 0.10, b = 0.05, sigma = 0.15)
|
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics
Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Loading required package: fOptions
Rmetrics Package fOptions
Pricing and Evaluating Basic Options
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Title:
Geometric Average Rate Option
Call:
GeometricAverageRateOption(TypeFlag = "p", S = 80, X = 85, Time = 0.25,
r = 0.05, b = 0.08, sigma = 0.2)
Parameters:
Value:
TypeFlag p
S 80
X 85
Time 0.25
r 0.05
b 0.08
sigma 0.2
Option Price:
4.69222
Description:
Fri Aug 11 09:31:43 2017
Title:
Turnbull Wakeman Asian Approximated Option
Call:
TurnbullWakemanAsianApproxOption(TypeFlag = "p", S = 90, SA = 88,
X = 95, Time = 0.5, time = 0.25, tau = 0, r = 0.07, b = 0.02,
sigma = 0.25)
Parameters:
Value:
TypeFlag p
S 90
SA 88
X 102
Time 0.5
time 0.25
tau 0
r 0.07
b 0.02
sigma 0.25
Option Price:
5.848187
Description:
Fri Aug 11 09:31:43 2017
Title:
Levy Asian Approximated Option
Call:
LevyAsianApproxOption(TypeFlag = "c", S = 100, SA = 100, X = 105,
Time = 0.75, time = 0.5, r = 0.1, b = 0.05, sigma = 0.15)
Parameters:
Value:
TypeFlag c
S 100
SA 100
X 105
Time 0.75
time 0.5
r 0.1
b 0.05
sigma 0.15
Option Price:
0.3564905
Description:
Fri Aug 11 09:31:43 2017
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