MATLAB FINANCIAL DERIVATIVES TOOLBOX Uživatelský manuál stáhnout pdf (Strana 104)

103

for s

imp

. It is known that such equation has no analytic solution, so to solve

it someone has to implement a numerical root-finding algorithm. The most

well known root finding algorithm for the implied volatility problem is the

Newton-Raphson method.

The Newton method is very simple and quite fast method. It can be

summarized in three steps:

• Step #1: give an initial guess for

imp

(e.g. 10

imp

= )

• Step #2: perform an algorithm iteration, k, based on the following

formula:

⇒

∂

−

−=−=

−−

)e('g

)e(g

BSM

BSMmrk

imp

BSM

BSMmrk

imp

∂

−

−1

for k=1,2,3,….

• Step #3: If |g(e)|<e then stop and return

imp

s , otherwise go to Step

#2 and perform one more iteration, k, of the algorithm (the e is the

desire accuracy, usually set to a very small quantity)

Write a function with the following calling syntax:

“[ImpliedVol]=

l(Qmrk, S, X, T, r, Index, dv, maxNumIter, tol)”

where “Qmrk” is the market quote of a call or put option. “maxNumIter”

represents the number of iterations and “tol” the desire accuracy (it is a

stopping criterion related with the absolute difference of market option value

and BSM estimate). “Index” is a single string with values “CALL” and “PUT”

(or any other combination that delivers the required word meaning) that is

used to distinguish between calls and puts as before. Note that all input

1 2 ... 99 100 101 102 103 104 105 106 107 108 109 ... 118 119

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