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, lowvol, highvol,
.tol=.Machine$double.eps^0.5) bsputimpvol(s, k, r, tt, d, price, lowvol, highvol, .tol=.Machine$double.eps^0.5)
bscallimps(s, k, v, r, tt, d, price, lower=0.0001, upper=1e06,
.tol=.Machine$double.eps^0.5) bsputimps(s, k, v, r, tt, d, price, lower=0.0001, upper=1e06, .tol=.Machine$double.eps^0.5)


### Arguments

 s Stock price k Strike price of the option 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 lowvol minimum implied volatility highvol maximum implied volatility .tol numerical tolerance for zero-finding function 'uniroot' v Volatility of the stock, defined as the annualized standard deviation of the continuously-compounded return lower minimum stock price in implied price calculation upper maximum stock price in implied price calculation

### 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 0.2.5 Index]