EnergySwapoptions: Price of a Energy Swapoptions

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Energy Swapoptions

Description

compute the price of a energy swapoption

Usage

EnergySwapoptions(s, K, f, x, n, r, r_x, r_b, r_e, r_p, v, t, t_b, type)

Arguments

s	underlying price
K	strike price
f	foward/swap price observed in the market
x	number of compounding per year
n	number of settlements in the delivery period for the particular forward contracts
r	risK free rate
r_x	swap rate starting at the beginning of the delivery period and ending at the end of the delivery period with j compoundings per year, equal to the number of fixings in the delivery period.
r_b	risK -free continuous compounding zero coupon rate with t_b years to maturity
r_e	risK -free continuous compounding zero coupon rate with time to maturity equalto from now to the end of the delivery period
r_p	risK -free continuous compounding zero coupon rate with forward start at the option maturity t and ending at the beginning of the delivery period t_b
v	volatility
t	time to maturity of the option
t_b	the time to the beginning of the forward delivery period
type	type of option "C" Call or "P" Put

Details

European options on energy swaps, also called energy swaptions, are options that at maturity give a delivery of an energy swap at the strike price (but not necessarily physical delivery of any energy). The swap can have either financial or physical settlement. If a call swaption is in-the-money at maturity, the option has delivery of a swap. The payout from the option is thus not received immediately at expiration, but rather during the delivery period of the underlying swap (forward). The energy call swaption formula is derived from Haug, 2005a

Value

price of a Energy Swapotion given the underlying price s, strike price K, foward/swap price observed in the market f. the number of compounding per year x, the number of settlements in the delivery period for the particular forward contracts n, risK free rate r, swap rate starting at the beginning of the delivery period and ending at the end of the delivery period with j compoundings per year, equal to the number of fixings in the delivery period r_x , risK -free continuous compounding zero coupon rate with t_b years to maturity r_b, risK -free continuous compounding zero coupon rate with time to maturity equal to from now to the end of the delivery period r_e, risK -free continuous compounding zero coupon rate with forward start at the option maturity t and ending at the beginning of the delivery period t_b r_p, volatility v, time to maturity of the option t, the time to the beginning of the forward delivery period t_b, type of option "C" Call or "P" Put

Author(s)

Colzani Luca, Magni Marta, Mancassola Gaia, Kakkanattu Jenson

References

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

Examples

EnergySwapoptions(33,35,33,365,92,0.05,0.05,0.05,0.05,0.05,0.18,0.5,0.546,"C")
## The function is currently defined as
function (s, K, f, x, n, r, r_x, r_b, r_e, r_p, v, t, t_b, type) 
{
    Black76 <- function(s, K, f, r, v, t, type) {
        Black76 <- d1 <- (log(f/K) + (v^(2)/2) * t)/(v * sqrt(t))
        d2 <- d1 - v * sqrt(t)
        if (type == "C") {
            black76 <- exp(-r * t) * (f * pnorm(d1) - K * pnorm(d2))
        }
        if (type == "P") {
            black76 <- exp(-r * t) * (K * pnorm(-d2) - f * pnorm(-d1))
        }
        return(black76)
    }
    if (type == "C") {
        price <- (1 - (1/(1 + r_x/x)^n))/r_x * x/n * exp(-r_p * 
            (t_b - t)) * Black76(s, K , f, r, v, t,type)
    }
    if (type == "P") {
        price <- (1 - (1/(1 + r_x/x)^n))/r_x * x/n * exp(-r_p * 
            (t_b - t)) * Black76(s, K , f, r, v, t,type)
    }
    return(round(price, 2))
  }

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