SPO: Price of a Standard Power Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Standard Power Option

Description

The function computes the price of a standard Power Option

Usage

SPO(s, K, r, b, v, t, p, type)

Arguments

s	underlying value
K	strike price
r	risk free rate
b	cost of carry
v	volatility
t	maturity
p	power > 0
type	call "C" or put "P"

Details

Standard Power Options (aka asymmetric power options) have nonlinear payoff at maturity. They apply the power to the underlying asset price at maturity.

Value

price of a standard powered option given the underlying price s, the strike price K, the risk free ratem the cost of carrying ratem the volatility v, the power p, the time to maturity of the option t and the type of option call "C" or put "P"

Author(s)

Colzani Luca, Magni Marta, Mancassola Gaia, Kakkanattu Jenson

References

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

Examples

 SPO(10,100,0.08,0.02,0.3,0.5,2,"C")

## The function is currently defined as
function (s, K, r, b, v, t, p, type) 
{
    d1 <- (log(s/K^(1/p)) + (b + (p - 0.5) * v^2) * t)/v * sqrt(t)
    d2 <- d1 - p * v * sqrt(t)
    if (type == "C") {
        price <- (s^p) * exp(((p - 1) * (r + p * (v^2/2)) - p * 
            (r - b)) * t) * pnorm(d1) - K * exp(-r * t) * pnorm(d2)
    }
    if (type == "P") {
        price <- K * exp(-r * t) * pnorm(-d2) - (s^p) * exp((p - 
            1) * (r + p * (v^2/2) - p * (r - b)) * t) * pnorm(-d1)
    }
    return(round(price, 2))
  }

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