FSO: Price of a Forward Start Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Forward Start Option

Description

The function computes the price of a Forward Start Option

Usage

FSO(s, r, b, v, t, tau, alpha, type)  

Arguments

s	underlying value
r	risk free rate
b	cost of carry
v	volatility
t	maturity
tau	arbitrary time interval
alpha	positive constant
type	call "C" or put "P"

Details

A forward start option with time to maturity T starts at-the-money or proportionally in- or out-of-the-money after a known elapsed time t in the future. The strike is set equal to a positive constant a times the asset price S after the known time t. If a is less than unity, the call (put) will start 1 - a percent in-the-money (out-of-the- money); if a is unity, the option will start at-the-money; and if a is larger than unity, the call (put) will start a - 1 percentage out-of-the- money (in-the-money).

Value

Price of the Forward Start Option given the underlying price s, the time to maturity t, he risk free rate r, the cost of carrying rate b,the volatility v, an arbitrary time interval tau, a positive constant alpha 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

FSO(60,1,0.08,0.04,0.3,0.25,1.1,"C")
## The function is currently defined as
function (s, r, b, v, t, tau, alpha, type) 
{
    d1 <- (log(1/alpha) + (b + v^(2)/2) * (t - tau))/(v * sqrt(t - 
        tau))
    d2 <- d1 - v * sqrt(t - tau)
    if (type == "C") {
        price <- s * exp((b - r) * t) * (exp((b - r) * (t - tau)) * 
            pnorm(d1) - alpha * exp(-r * (t - tau)) * pnorm(d2))
    }
    if (type == "P") {
        price <- (s * exp(b - r) * t) * (alpha * exp^(-r(t - 
            tau)) * pnorm(-d2) - exp((b - r) * (t - tau)) * pnorm(-d1))
    }
    return(round(price, 4))
  }

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