PO: Price of a Product Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Product Option

Description

compute the price of a product option

Usage

PO(s1, s2, K, r, b1, b2, v1, v2, rho, t, type)

Arguments

s1	value of underlying 1
s2	value of underlying 2
K	strike price
r	risk free rate
b1	cost of carry rate 1
b2	cost of carry rate 2
v1	volatility asset 1
v2	volatility asset 2
rho	correlation
t	time to maturity
type	call "C" or put "P"

Details

Zhang (1998) describes formulas for product options.

Value

price of a product option give the price of the asset 1 s1, the price of asset 2 s2, the strike price K, teh risk free rate r, the cost of carrying rate of the first asset 1, the cost of carrying rate of asset 2, the volatility of asset 1, the volatility of asset 2, the correlation between the two asset rho, the time to maturity 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

PO(100,105,15000,0.07,0.02,0.05,0.3,0.3,-0.5,0.1,"C")
## The function is currently defined as
function (s1, s2, K, r, b1, b2, v1, v2, rho, t, type) 
{
    f <- s1 * s2 * exp((b1 + b2 + rho * v1 * v2) * t)
    v <- sqrt(v1^2 + v2^2 + 2 * rho * v1 * v2)
    d1 <- (log(f/K) + t * ((v^2)/2))/(v * sqrt(t))
    d2 <- d1 - v * sqrt(t)
     if(type == "C"){
    
    price <- exp(-r*t)*(f*pnorm(d1) - K*pnorm(d2))
    
  }
  
  if(type == "P"){
    
    price <- exp(-r*t)*(K*pnorm(d1) - f*pnorm(d2))
    
  }
  
  return(round(price,4))
  }

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