Margrabe: Margrabe formula for option pricing

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Margrabe formula for option pricing

Description

the function uses the Margrabe formula to compute option prices

Usage

Margrabe(s1, s2, v1, v2, t, rho, q1, q2) 

Arguments

s1	price of the first risky asset
s2	price of the second risky asset
v1	volatility first asset
v2	volatility second asset
t	maturity
rho	correlation coefficient between asset 1 and asset 2
q1	expected dividend rates of the prices s1 under the appropriate risK -neutral measure
q2	expected dividend rates of the prices s2 under the appropriate risK -neutral measure

Details

Margrabe formula is an option pricing formula applicable to an option to exchange one risky asset for another risy asset at maturity

Value

Price of an option computed using Mrgrabe Formula given the price of the first risky asset s1, price of the second risky asset s2, volatility of the first asset v1, volatility of the second asset v2, maturity of the option t, correlation coefficient between asset 1 and asset 2 rho, expected dividend rates of the prices s1 under the appropriate risK -neutral measure q1, expected dividend rates of the prices s2 under the appropriate risK -neutral measure q2

Author(s)

Colzani Luca, Magni Marta, Mancassola Gaia, Kakkanattu Jenson

References

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

Examples

Margrabe(125,100,0.45,0.47,1,0,0.04,0.02)

## The function is currently defined as
function (s1, s2, v1, v2, t, rho, q1, q2) 
{
    v <- sqrt(v1^2 + v2^2 - 2 * v1 * v2 * rho)
    d1 <- (log(s1/s2) + (q2 - q1 + v^2/2) * t)/(v * sqrt(t))
    d2 <- (log(s1/s2) + (q2 - q1 - v^2/2) * t)/(v * sqrt(t))
    Magrabe <- s1 * exp(-q1 * t) * pnorm(d1) - s2 * exp(-q2 * 
        t) * pnorm(d2)
    return(round(Magrabe, 2))
  }

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