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

### Numerical solution to an implied vol equation

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 daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### Numerical solution to an implied vol equation 