implied: Black-Scholes implied volatility and price

In derivmkts: Functions and R Code to Accompany Derivatives Markets

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)

derivmkts documentation built on April 11, 2022, 5:10 p.m.