Gap: Price of a Gap Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Gap Option

Description

The function computes the price of a Gap Option

Usage

Gap(s, K1, K2, r, b, v, t, type)

Arguments

s	underlying value
K1	strike price
K2	trigger price
r	interest free rate
b	cost of carryig rate
v	volatility
t	maturity
type	call "C" or put "P"

Details

Gap option is binary option whose stated strike price is different from its payoff strike. That is, there is a gap between the price at which the option can be exercised and the price at which it would produce a payoff to the holder. We price the option using the Reinerand Rubinstein (1991b) formula

Value

Price of a Gap Option given the price of the underlying s, the strike price K1, the trigger price K2, the risk free rate r, the cost of carrying rate b, the volatility v, the time to maturity of the option t, 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

Gap(50,50,57,0.09,0.09,0.2,0.5,"C")

## The function is currently defined as
function (s, K1, K2, r, b, v, t, type) 
{
    d1 <- (log(s/K1) + (b + v^(2)/2) * t)/(v * sqrt(t))
    d2 <- d1 - v * sqrt(t)
    if (type == "C") {
        price <- s * exp((b - r) * t) * pnorm(d1) - K2 * exp(-r * 
            t) * pnorm(d2)
    }
    if (type == "P") {
        price <- K2 * exp(-r * t) * pnorm(-d2) - s * exp((b - 
            r) * t) * pnorm(-d1)
    }
    return(round(price, 4))
  }

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