AoN: Price of an Asset or Nothing Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of an Asset or Nothing Option

Description

The function computes the price of an Asset or Nothing Option

Usage

AoN(s, K, r, b, v, t, type)

Arguments

s	price of the underlying
K	strike price
r	risk free interest rate
b	cost of carrying rate
v	volatility
t	maturity
type	call "C" or put "P"

Details

Asset-or-Nothing Options is a type of digital option whose payout is fixed after the underlying asset exceeds the predetermined threshold or striK e price. The payout depends only on whether or not the underlying asset closes above the striK e price-in the money (ITM)-at the expiration date. It does not matter how deep ITM as the payout is fixed. We price the Asset-or-Nothing Options with the Cox and Rubinstein (1985) formula.

Value

Price of an Asset or Nothing Option given s, K, r, b, v, t and type.

Author(s)

Colzani Luca, Magni Marta, Mancassola Gaia, Kakkanattu Jenson

References

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

Examples

 AoN(70,65,0.07,0.02,0.27,0.5,"P")

## The function is currently defined as
function (s, K, r, b, v, t, type) 
{
    d <- (log(s/K) + (b + v^(2)/2) * t)/(v * sqrt(t))
    if (type == "C") {
        price <- s * exp((b - r) * t) * pnorm(d)
    }
    if (type == "P") {
        price <- s * exp((b - r) * t) * pnorm(-d)
    }
    return(round(price, 2))
  }

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