APO: Price of an American Perpetual Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of an American Perpetual Option

Description

The fucntion computes the price of an American Perpetual Option

Usage

APO(s, K, r, b, v, type)

Arguments

s	underlying value
K	strike price
r	risk free rate
b	cost of carry rate
v	volatility
type	call "C" or put "P"

Details

A perpetual option is a non-standard, or exotic, financial option that has no fixed maturity and no exercise limitation. While the life of a standard option can range from a few days to several years, a perpetual option (XPO) can be exercised at any time and without any expiration.

Value

Price of an American Perpetual Option given s, K, r, b, v, type

Author(s)

Colzani Luca, Magni Marta, Mancassola Gaia, Kakkanattu Jenson

References

Espen Gaarder Haug(2007):The Complete Guide to Option Pricing Formulas

Examples

 APO(90,100,0.1,0.02,0.25,"C")

## The function is currently defined as
function (s, K, r, b, v, type) 
{
    y1 <- 0.5 - (b/v^2) + sqrt(((b/v^2) - 0.5)^2 + (2 * r/v^2))
    y2 <- 0.5 - (b/v^2) - sqrt(((b/v^2) - 0.5)^2 + (2 * r/v^2))
    if (type == "C") {
        price <- (K/(y1 - 1)) * (((y1 - 1)/y1) * s/K)^y1
    }
    if (type == "P") {
        price <- (K/(1 - y2)) * (((y2 - 1)/y2) * s/K)^y2
    }
    return(round(price, 2))
  }

Lcolzani98/OptionPricingFunctions documentation built on June 13, 2022, 5:46 a.m.