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Financial module >> Financial module > bsimpvol

bsimpvol

Compute the implied volatility in a Black and Scholes framework. The function computes the volatility by equating the theoretical value of an option (with both constant riskless interest rate and volatility) to its market value.

SYNOPSIS

[sigmaC,sigmaP]=bsimpvol(option,S,K,r,T,sigma0);

Description

Compute the Black and Scholes implied volatility

Parameters

option

the market price of an option (either put or call)

S

current price of the underlying asset

K

strike price of the option

r
riskless interest rate (assumed to be constant until the maturity)
T
time to maturity; it must be in the same time unit of measure as the riskless interest rate (if the riskless interest rate is annual, then an option with maturity of 3 months must have T=3/12)
sigma0
the value of the volatility the solver must start from (it is a guess value)

Output

sigmaC

implicit volatility of a call option; the function writes "Call: good convergence" if the solver finds a good value for the implicit volatility, instead it writes "Call: bad convergence"

sigmaP
implicit volatility of a put option; the function writes "Put: good convergence" if the solver finds a good value for the implicit volatility, instead it writes "Put: bad convergence"

Example

We assume that an option (eithe call or put) is worth 1.09 euros on the market. It is written on an asset whose value is 25 euros, with a strike price of 25 euros. If the (annual) riskless interest rate is 0.001 and the time to maturity is 3 months, then the implicit volatility is computed with the following command.

-->[sigmaC,sigmaP]=bsimpvol(1.09,25,25,0.001,3/12,0.1)

Call: good convergence

Put: good convergence

sigmaP = 0.2193413

sigmaC = 0.2180861

Authors

Francesco Menoncin - Brescia University - 2010

See Also


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