implied {derivmkts} R Documentation

## Black-Scholes implied volatility and price

### 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

```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

```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)

```

[Package derivmkts version 0.2.4 Index]