Description Usage Arguments Details Value See Also Examples

Computes values of European-style call and put options over assets whose future price is expected to follow a log normal distribution.

1 2 3 4 5 | ```
BSOptionValue(spot, strike, expiry, volatility,
intRate=0, carryCost=0, Call=TRUE)
ImpliedVol(spot, strike, expiry, price, intRate=0, carryCost=0,
Call=TRUE, ImpliedVolLowerBound=.01, ImpliedVolUpperBound=1, tol=1.e-9)
lnorm.param(mean, sd)
``` |

`spot` |
The current price of a security. |

`strike` |
The strike price for an option. |

`expiry` |
The time when an option may be exercised. (We are only dealing with European options which have a single date on which they may be exercised.) |

`volatility` |
The volatility of the price of a security per unit time. This is the standard deviation of the logarithm of price. |

`price` |
The price for an option. This is used as an input parameter when computing the implied volatility. |

`intRate` |
The interest rate. |

`carryCost` |
The carrying cost for a security. This may be negative when a security is expected to pay a dividend. |

`Call` |
Logical: Whether the option for which a |

`ImpliedVolLowerBound` |
Lower bound used when searching for the inplied volatility. |

`ImpliedVolUpperBound` |
Upper bound used when searching for the inplied volatility. |

`tol` |
Tolerance specifying accuracy of search for implied volatility. |

`mean` |
The mean of a quantity which has a lognormal distribution. |

`sd` |
The standard deviation of a quantity which has a lognormal distribution. |

The lognormal distribution is
the limit of finite moment log stable distributions as `alpha`

tends to
2. The function `lnorm.param`

finds the mean and standard
deviation of a lognormal distribution on the log scale given the mean
and standard deviation on the raw scale. The function
`BSOptionValue`

finds the value of a European call or put option.
The function `ImpliedVol`

allows computation of the implied
volatility, which is the volatility on the logarithmic scale which
matches the value of an option to a specified price.

`impVol`

returns the implied volatility when the value of options
is computed using a finite moment log stable distribution.
`approx.impVol`

returns an approximation to the implied volatility.
`lnorm.param`

returns the mean and standard deviation of the
underlying normal distribution.

Option prices computed using the log normal model can be
compared to those computed for the finite moment log stable model
using `putFMstable`

and `callFMstable`

.

1 2 3 | ```
lnorm.param(mean=5, sd=.8)
BSOptionValue(spot=4, strike=c(4, 4.5), expiry=.5, volatility=.15)
ImpliedVol(spot=4, strike=c(4, 4.5), expiry=.5, price=c(.18,.025))
``` |

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