fOptions (version 251.70)

AsianOptions: Valuation of Asian Options

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:

ll{ 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.

Value

• The option 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]

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)