AsianOptions: Valuation of Asian Options

In fExoticOptions: Rmetrics - Pricing and Evaluating Exotic Option

Description

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.

Usage

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)

Arguments

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*] - is the time to the beginning of the average period.
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 "c" for a call option or a "p" for a put option.
X	the exercise price, a numeric value.

Details

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]

Value

The option price, a numeric value.

Note

The functions implement the algorithms to valuate plain vanilla options as described in Chapter 2.12 of Haug's Book (1997).

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

References

Haug E.G. (1997); The complete Guide to Option Pricing Formulas, Chapter 2.12, McGraw-Hill, New York.

Examples

## 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)
     

Example output

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: [e-mail]
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: [e-mail]

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 

fExoticOptions documentation built on May 2, 2019, 7:31 a.m.