EuropeanBinomial: Price of a European Binomial Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a European Binomial Option

Description

The function computes the price of a European Binomial Option

Usage

EuropeanBinomial(s, K, r, b, v, t, n, pow, cap, type1, type2)  

Arguments

s	rice of underlying
K	strike price
r	risk free rate
b	cost of carry rate
v	volatility
t	time to maturity
n	number of time steps used for valuation
pow	power the power options are raised to
cap	cap is the cap on the payoff for any capped option
type1	Call or Put
type2	type of payoff

Details

It is capable of pricing any European option on a single asset, whose payoff is not path-dependent.

Value

Price of a European Binomial Option given the prcie of the underlying s, the strike price K, the risk free rate , the cost of carrying rate b, the volatility v, the time to maturiy of the option t, number of time steps used for valuation n, power the power options are raised to pow,the cap on the payoff for any capped option cap, the type of option type1, type of payoff type2

Author(s)

Colzani Luca, Magni Marta, Mancassola Gaia, Kakkanattu Jenson

References

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

Examples

EuropeanBinomial(100,90,0.05,0.02,0.3,0.5,3,2,50,"C","CPC")

## The function is currently defined as
function (s, K, r, b, v, t, n, pow, cap, type1, type2) 
{
    if (type1 == "C") {
        g <- 1
    }
    if (type1 == "P") {
        g <- -1
    }
    BinPayoff <- function(s, K, pow, cap, type2, g) {
        if (type2 == "PV") {
            BinPayoff <- max(g * (s - K), 0)
        }
        else if (type2 == "PC") {
            BinPayoff <- s^pow
        }
        else if (type2 == "CPC") {
            BinPayoff <- min(s^pow, cap)
        }
        else if (type2 == "PC") {
            BinPayoff <- g * (s/K)^pow
        }
        else if (type2 == "SPO") {
            BinPayoff <- max(g * (s^pow) - K, 0)
        }
        else if (type2 == "CPO") {
            BinPayoff <- min(max(g * (s^pow) - K, 0), cap)
        }
        else if (type2 == "POpt") {
            BinPayoff <- max((g * (s - K)), 0)^pow
        }
        else if (type2 == "CPOpt") {
            BinPayoff <- min(max(g * (s - K), 0)^pow, cap)
        }
        else if (type2 == "SO") {
            BinPayoff <- max(g * (sin(s) - K), 0)
        }
        else if (type2 == "CO") {
            BinPayoff <- max(g * (cos(s) - K), 0)
        }
        else if (type2 == "TO") {
            BinPayoff <- max(g * (tan(s) - K), 0)
        }
        else if (type2 == "LC") {
            BinPayoff <- log(s/K)
        }
        else if (type2 == "LO") {
            BinPayoff <- max(log(s/K), 0)
        }
        else if (type2 == "SQRTC") {
            BinPayoff <- sqrt(s/K)
        }
        else if (type2 == "SQRTO") {
            BinPayoff <- sqrt(max(g * (s - K), 0))
        }
    }
    dt <- t/n
    u <- exp(v * sqrt(dt))
    d <- 1/u
    p <- (exp(b * dt) - d)/(u - d)
    sum <- 0
    if (type1 == "C") {
        for (j in 0:n) {
            si <- s * u^j * d^(n - j)
            sum <- sum + choose(n, j) * p^j * (1 - p)^(n - j) * 
                BinPayoff(s, K, pow, cap, type2, g)
        }
    }
    if (type1 == "P") {
        for (j in 0:n) {
            si <- s * u^j * d^(n - j)
            sum <- sum + chose(n, j) * p^j * (1 - p)^(n - j) * 
                BinPayoff(type2, g, s, K, pow, cap)
        }
    }
    price <- exp(-r * t) * sum
    return(round(price, 2))
  }

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