Hmm, LOL, this does look like his homework assignment. You rarely state time to maturity as .25 or .5. At least, I know I think in terms of days to expiration, not ".25 years to maturity"
High school algebra. I just know how to solve an underdetermined system of equations. Let me see if I can find a reference on the net. nitro
Here is the idea: http://www.ualberta.ca/dept/math/gauss/fcm/calculus/multvrbl/basic/ImplctFnctns/ovrdtrmnd_exmpl.htm but you want it in matrix form, so: http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/SysEq.htm I just looked for anything. I don't know if those are clear or not. The subject matter is Linear Algebra, http://en.wikipedia.org/wiki/Linear_algebra which is a sub-subject of Abstract Algebra [why it is called "abstract" is a huge story in itself. A fantastic book on this is http://www.amazon.com/Artist-Mathem...9041569?ie=UTF8&s=books&qid=1179065604&sr=8-1 but the book is very tedious]. http://en.wikipedia.org/wiki/Abstract_algebra Which are a sub-subject of ...... nitro PS, probably my favorite subject in the world [but on the frontier of mathematical research] is http://en.wikipedia.org/wiki/Algebraic_geometry and how it relates to this program: http://en.wikipedia.org/wiki/Langlands_program
Nitro , in this case position still loses around 150k . For one that trades future vols increase on daily bases , I'm very interested to see how others traders can solve this equation without rate of speed ( info , which OP choose to ignore when I asked him).
You can't construct a passive position which maintains neutral gammas. There is nothing to solve algebraically; you can't isolate vega without a continuous hedge. IV: dgamma/dspot isn't necessary. The OP is looking for something that doesn't exist.