impliedVolatility {FMStable}

Computations Regarding Value of Options for Log Normal Distributions

Description

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

Usage

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) 

Arguments

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 price is given is a call option.

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.

Details

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.

Value

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.

See Also

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.

Examples

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))