implied: Black-Scholes implied volatility and price

Description Usage Arguments Format Details Value Note Examples

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

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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

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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.