SWPTN: Price of a Swaption

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Swaption

Description

The function computes the price of a Swaption

Usage

SWPTN(t_1, f, K, r, t, v, u, type)

Arguments

t_1	tenor of swap in years
f	forward price of underlying swap
K	strike price
r	risk free rate
t	time to expiration
v	volatility
u	number of compoundings per year
type	call "C" or put "P"

Details

It is usual to distinguish between the following: Payer Swaption The right but not the obligation to pay the fixed rate and receive the floating rate in the underlying swap. Receiver Swaption The right but not the obligation to receive the fixed rate and pay the floating rate in the underlying swap.

Value

Price of a Swaption given tenor of swap in years t_1, forward price of underlying swap f, the strike price K, risk free rate r, time to expiration t,the volatility v, number of compoundings per year u 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

SWPTN(4,0.07,0.075,0.06,2,0.2,2,"C")
## The function is currently defined as
function (t_1, f, K, r, t, v, u, type) 
{
    d1 <- (log(f/K) + (v^(2)/2) * t)/(v * sqrt(t))
    d2 <- d1 - v * sqrt(t)
    if (type == "C") {
        price <- ((1 - (1/(1 + f/u)^(t_1 * u)))/f) * exp(-r * 
            t) * (f * pnorm(d1) - K * pnorm(d2))
    }
    if (type == "P") {
        price <- ((1 - (1/(1 + f/u)^(t_1 * u)))/f) * exp(-r * 
            t) * (K * pnorm(-d2) - f * pnorm(-d1))
    }
    return(round(price, 2))
  }

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