# perpetual: Perpetual American options In derivmkts: Functions and R Code to Accompany Derivatives Markets

## Description

`callperpetual` and `putperpetual` compute prices of perpetual American options. The functions optionally return the exercise barriers (the prices at which the options are optimally exercised).

## Usage

 ```1 2``` ```callperpetual(s, k, v, r, d, showbarrier) putperpetual(s, k, v, r, d, showbarrier) ```

## Arguments

 `s` Price of the underlying asset `k` Strike price `v` Volatility of the asset price, defined as the annualized standard deviation of the continuously-compounded return `r` Annual continuously-compounded risk-free interest rate `d` Dividend yield, annualized, continuously-compounded `showbarrier` Boolean (FALSE). If TRUE, the option price and exercise barrier are returned as a list

## Details

Returns a scalar or vector of option prices, depending on the inputs

`callperpetual(s, k, v, r, tt, d)`

## Value

Option price, and optionally the optimal exercise barrier.

## Note

If the dividend yield is zero, a perpetual call is never exercised. The pricing function in this case will return the stock price, which is the limiting option price as the dividend yield goes to zero. Similarly, if the risk-free rate is zero, a perpetual put is never exercised. The pricing function will return the strike price in this case, which is the limiting value of the pricing function as the interest rate approaches zero.

## Examples

 ```1 2 3 4``` ```s=40; k=40; v=0.30; r=0.08; d=0.02; callperpetual(s, k, v, r, d) putperpetual(s, c(35, 40, 45), v, r, d, showbarrier=TRUE) ```

derivmkts documentation built on June 6, 2019, 5:03 p.m.