GARO: Price of a Geometric Average Rate Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Geometric Average Rate Option

Description

compute the price of a geometric average rate option

Usage

  GARO( s, K, r, b, v, t, type )

Arguments

s	underlying value
K	strike price]
r	risk free rate
b	cost of carrying rate
v	volatility
t	maturity of the option [years]
type	call "C" or put "P"

Details

The geometric average rate option is a specific Asian option and therefore depends on an average price of the underlier. Here this average is calculated geometrically.We price the option using the formula by Kemna and Vorst (1990), where the geometric average option can be priced as a standard option by changing the volatility and cost-of-carry term

Value

price of a geometric average rate option call or put given the price of the underlying S, K the strike price, r the risk free rate, b cost of carrying rate, v volatilitity , t the maturity of the option [years] 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

GARO(80,85,0.05,0.08,0.2,0.25,"P")


## The function is currently defined as
function (s, K, r, b, v, t, type) 
{
    b_a <- 0.5 * (b - (v^2/6))
    v_a <- v/sqrt(3)
    d1 <- (log(s/K) + (b_a + (v_a^2)/2) * t)/(v_a * sqrt(t))
    d2 <- d1 - v_a * sqrt(t)
    if (type == "C") {
        price <- s * exp((b_a - r) * t) * pnorm(d1) - K * exp(-r * 
            t) * pnorm(d2)
    }
    if (type == "P") {
        price <- K * exp(-r * t) * pnorm(-d2) - s * exp((b_a - 
            r) * t) * pnorm(-d1)
    }
    return(round(price, 2))
  }

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