MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur télécharger pdf (Page 103)

102

8.1.3 BSM Plots and Surfaces

Make the following plots:

• Two subplot figures, one for call options with T=0.15 and s=0.20, and

one for put options with T=0.25 and s=0.20 that plot S against all

partial derivatives. Give titles and axis names.

• A 3D surface of the c

BSM

and p

BSM

versus the S/X and T (note that in

order to create a smooth surface you should create a dense mesh-

grid) for the ranges:

120

.T.,S

≤

for:

100

.d,.r,.s,X

8.1.4 BSM Implied Volatility

The only unobservable parameter related with the BSM formula when we

deal with real world problems is the volatility measure, s (although as said

before it can be estimated via log-relative reruns of the underlying asset). It

is accustomed by options traders to observe a market value for a call or put

option and given the observed values of S, X, ?, r, and d, they derive the

value of s that equates the BSM estimate with the market quote. Such s

value is known as implied volatility. For instance, if c

mrk

is the market price of

a call option and S’, X’, T’, r’ and d’ are the observable parameters related

with the call option, then the BSM implied volatility, s

imp

, is that value of s

that minimizes the absolute error between c

mrk

and c

BSM

. Analytically this

problem is:

)'d,'r,s,'T,'X,'S(cc||)e(g|min

imp

BSMmrk

imp

−=

Alternatively, think this as solving the following equation:

|)d,r,s,T,X,S(cc

imp

BSMmrk

1 2 ... 98 99 100 101 102 103 104 105 106 107 108 ... 118 119

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