CPO: Price of a Capped Power Option

In Lcolzani98/OptionPricingFunctions: Option Pricing Functions

Price of a Capped Power Option

Description

The function computes the price of a Capped Power Option

Usage

CPO(s, K, r, b, v, p, c, t, type)

Arguments

s	price of the underlying
K	strike price
r	risK free interest rate
b	cost of carrying rate
v	volatility
p	power
c	maximum predefined level of the payoff
t	maturity
type	call "C" or put "P"

Details

Power option is an option whose payoff is based on the price of an underlying asset raised to a power. It is designed to allow the buyer (holder) to take a leveraged view on a specific asset or its volatility. A capped option caps the maximum possible profit for its holder. When the underlying asset closes at or beyond a specified price, the option automatically exercises We use the Esser (2003) gives the closed-form solution to price the option

Value

Price of a Capped Power Option given the price of the underlying s, the strike price K, the risk free rate r, the cost of carrying rate b, the volatility v, the time to maturity t 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

CPO(100,100,0.1,0.07,0.1,2,30 ,0.5,"C")
## The function is currently defined as
function (s, K, r, b, v, p, c, t, type) 
{
    e1 <- ((log(s/K^(1/p)) + (b + (p - 0.5) * v^(2))) * t)/(v * 
        sqrt(t))
    e2 <- e1 - p * v * sqrt(t)
    if (type == "C") {
        e3 <- ((log(s/(c + K)^(1/p))) + (b + (p - 0.5) * v^(2)) * 
            t)/(v * sqrt(t))
        e4 <- e3 - p * v * sqrt(t)
        price <- s^(p) * exp(((p - 1) * (r + p * v^(2)/2) - p * 
            (r - b)) * t) * (pnorm(e1) - pnorm(e3)) - exp(-r * 
            t) * (K * pnorm(e2) - (c + K) * pnorm(e4))
    }
    if (type == "P") {
        e3 <- ((log(s/(K - c)^(1/p))) + (b + (p - 0.5) * v^(2)) * 
            t)/(v * sqrt(t))
        e4 <- e3 - p * v * sqrt(t)
        price <- exp(-r * t) * (K * pnorm(-e2) - (K - c) * pnorm(-e4)) - 
            s^(p) * exp(((p - 1) * (r + p * v^(2)/2) - p * (r - 
                b)) * t) * (pnorm(-e1) - pnorm(-e2))
    }
    return(round(price, 2))
  }

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