# implied: Black-Scholes implied volatility and price In derivmkts: Functions and R Code to Accompany Derivatives Markets

## Description

`bscallimpvol` and `bsputimpvol` compute Black-Scholes implied volatilties. The functions `bscallimps` and `bsputimps`, compute stock prices implied by a given option price, volatility and option characteristics.

## Usage

 ```1 2 3 4``` ```bscallimpvol(s, k, r, tt, d, price) bsputimpvol(s, k, r, tt, d, price) bscallimps(s, k, v, r, tt, d, price) bsputimps(s, k, v, r, tt, d, price) ```

## Arguments

 `s` Stock price `k` Strike price of the option `v` Volatility of the stock, defined as the annualized standard deviation of the continuously-compounded return `r` Annual continuously-compounded risk-free interest rate `tt` Time to maturity in years `d` Dividend yield, annualized, continuously-compounded `price` Option price when computing an implied value

## Format

An object of class `numeric` of length 1.

## Details

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

## Value

Implied volatility (for the "impvol" functions) or implied stock price (for the "impS") functions.

## Note

Implied volatilties and stock prices do not exist if the price of the option exceeds no-arbitrage bounds. For example, if the interest rate is non-negative, a 40 strike put cannot have a price exceeding \$40.

## Examples

 ```1 2 3 4 5``` ```s=40; k=40; v=0.30; r=0.08; tt=0.25; d=0; bscallimpvol(s, k, r, tt, d, 4) bsputimpvol(s, k, r, tt, d, 4) bscallimps(s, k, v, r, tt, d, 4) bsputimps(s, k, v, r, tt, d, 4) ```

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