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divingwai
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Posts: 3
Joined: January 17th, 2010, 5:37 am

Numerical solution to an implied vol equation

October 27th, 2010, 1:18 am

I built a model in volatility, the formula looks like "vol = a +b*skew + c*kurt + d*adjust" , where a,b,c,d are all known in advanceI would like to fit my formula to the market data, since i have 3 unknowns (skew,kurt,adjust), how can i find them throught non-linear programming? any well-known algorithm?From market data, I can make such equationcall price = BS_c(S1,K1,r,q,vol_call) = BS_c(S1,K1,r,q,skew,kurt,adjust) put price = BS_p(S2,K2,r,q,vol_put) = BS_p(S2,K2,r,q,skew,kurt,adjust) straddle price = BS_c(S1,K,r,q,skew,kurt,adjust) + put price, 0 = BS_p(S2,K,r,q,skew,kurt,adjust) - put price In short, I would like to solve for skew, kurt, adjust, so that all equations are satisfied, who can advise?call price = BS_c(S,K1,r,q,skew,kurt,adjust) put price = BS_p(S,K2,r,q,skew,kurt,adjust) straddle price = BS_c(S,K,r,q,skew,kurt,adjust) + put, 0 = BS_p(S,K,r,q,skew,kurt,adjust) - put* bold words are unknown
 
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daveangel
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Joined: October 20th, 2003, 4:05 pm

Numerical solution to an implied vol equation

October 27th, 2010, 9:24 am

levenberg-marquadt or nelder-mead
knowledge comes, wisdom lingers
 
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tagoma
Posts: 18849
Joined: February 21st, 2010, 12:58 pm

Numerical solution to an implied vol equation

December 1st, 2010, 10:26 pm

it seems to me that the LM algorithm is the more popular of both methods mentioned by daveangel.anyway, both are well-documented on the web.you can implement the LM algorithm with quantlib.or, you may use the c++ code available there : http://www.ics.forth.gr/~lourakis/levma ... .divingwai, you keep us updated on your projects ?