MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur télécharger pdf (Page 105)

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arguments precede the optional ones (the optional are “dv”, “maxNumIter”

and “tol”).

Use as inputs the initial data from the loaded txt file (without considering s).

The function should make similar checking like previous functions with the

additional that:

• If not specified, “maxNumIter” should be equal to 100.

• If not specified, “tol” should be 1e-5.

• At the beginning of the function, it should be tested whether with a

small value of s (e.g. s=0.001) the c

BSM

and p

BSM

are greater than c

mrk

and p

mrk

respectively; if such condition holds (it can be observed in

practice as an arbitrage result), an implied volatility value that

minimizes |g(e)| does not exist, so the function should return a

“NaN” value.

• To help the algorithm convergence rate and to save computing time,

the starting values for the algorithm should be given from the

following approximation suggested by Bharadia, Christofides and

Salkin [3]:

for call options:













−

dXe

mrk

imp

, and,

for put options:













−

dXe

mrk

imp

with,

)XeS(.d

rT−

−= 50

To use the implied volatility function, replace the volatility column of

the options data that were previously loaded from the text file with

random values taken from a uniform distribution on the interval [0,1]

(use the build in function:

d). Afterwards, use the

e to find

the theoretical values for calls and puts. In the following, use the

l to verify that the implied volatility is quite close with

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