Description Usage Arguments Format Details Value Note Examples

`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.

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)
``` |

`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 |

An object of class `numeric`

of length 1.

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

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

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.

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)
``` |

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