MATLAB FINANCIAL DERIVATIVES TOOLBOX Uživatelský manuál stáhnout pdf (Strana 102)

101

8.1.2 BSM Derivatives

From the same script as above, call a function with the name:

that returns the partial derivatives of the BSM formula (known as the Greek

letters) for both the call and the put value. The partial derivatives are:

delta:

e)d(NS/c

−

=∂∂

e)d(NS/p

−

−−=∂∂

theta:

)d(NrXe

sS)d(n

T/c

−

−−=∂∂

)d(NrXe

sS)d(n

T/p

−+−=∂∂

−

gamma:

TsS

)d(n

S/c

=∂∂

TsS

)d(n

S/p

=∂∂

vega: )d(nTSs/c

=∂∂ , )d(nTSs/p

=∂∂

rho: )d(NXTer/c

−

=∂∂ , )d(NXTer/p

−−=∂∂

−

where,

)z(n

−

represents the normal probability density function with mean zero and unity

standard deviation (the build in function is named as

f). The

s calling syntax should be:

“[Derivatives] =

s(S, X, T, vol, r, Index, dv)”

The function should make similar checks as before. The output of the

function

s should be a row vector if the input arguments are

single values or a two dimensional array if the input arguments are vectors

with the following format:

“Derivatives=[Delta, Theta, Gamma, Vega, Rho]”

1 2 ... 97 98 99 100 101 102 103 104 105 106 107 ... 118 119

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