SOA: Spread Option Approximation

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Spread Option Approximation

Description

The function computes an approximation of the price of a Spread Option

Usage

SOA(s1, s2, r, v1, v2, rho, t, b1, b2, K, q1, q2, type)

Arguments

s1	value of underlying 1
s2	value of underlying 2
r	risk free rate
v1	volatility asset 1
v2	volatility asset 2
rho	correlation btwn asset 1 and 2
t	time to maturity
b1	cost of carry asset 1
b2	cost of carry asset 2
K	strike price
q1	quantity of asset 1
q2	quantity of asset 2
type	call "C" or put "P"

Details

A European spread option can be valued using the standard Black and Scholes (1973) model by performing the following transformation, as originally shown by Kirk (1995)

Value

Approximation of the price of a Spread Option given value of underlying 1 s1, value of underlying 2 s2, risk free rate r, volatility asset 1 v1 , volatility asset 2 v2, correlation btwn asset 1 and 2 rho, time to maturity t, the cost of carry asset 1 b1, cost of carry asset 2 b2, strike price ,quantity of asset 1 q1, quantity of asset 2 q2 and the type 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

SOA(28,20,0.05,0.29,0.36,0.42,0.25,0,0,7,1,1,"C")

## The function is currently defined as
function (s1, s2, r, v1, v2, rho, t, b1, b2, K, q1, q2, type) 
{
    s <- (q1 * s1 * exp((b1 - r) * t))/(q2 * s2 * exp((b2 - r) * 
        t) + K * exp(-r * t))
    f <- (q2 * s2 * exp((b2 - r) * t))/(q2 * s2 * exp((b2 - r) * 
        t) + K * exp(-r * t))
    v <- sqrt(v1^2 + (v2 * f)^2 - 2 * rho * v1 * v2 * f)
    d1 <- (log(s) + (v^(2)/2) * t)/(v * sqrt(t))
    d2 <- d1 - v * sqrt(t)
    if (type == "C") {
        price <- (q2 * s2 * exp((b2 - r) * t) + K * exp(-r * 
            t)) * (s * pnorm(d1) - pnorm(d2))
    }
    if (type == "P") {
        price <- (q2 * s2 * exp((b2 - r) * t) + K * exp(-r * 
            t)) * (pnorm(-d2) - s * pnorm(-d1))
    }
    return(round(price, 2))
  }

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