Hi , I am looking to approximate the time value of an option via the greeks -- a client of mine asserts that he should be able to approximate the BS value of an OTM option by multiplying theta * days to maturity and adding vega. I do not think this is the case -- theta for one is non linear over time, so we can't apply a straight line method to approximate the time value. Is it possible to use the greeks to approximate the value of an otm option ? Apologies for the basic question, I looked around and couldn't seem to find a resource that would help me answer this. Many thanks in advance!

Why would you have vega and theta, and not have the price?

I do have the price -- the debate is more theoretical than practical. Goal is to arrive at a quick approximation of the BS price via the greeks. I am wondering if, given greek values it is possible to back out the price of the vanilla option.

Well, you can approximate or back out the price time 1 for a change at time zero, which is precisely what the greeks do, of course it will only be a linear approximation of a non-linear function. IE/: (price time t)+ $Delta*(price change) + $Vega*(change in volatility)+ $theta*(number of periods) =price time t+s. Incorporate Gamma or other obscure greeks if you like, to complete the approximation.This is clearly not what you would like to do, you want to be given the greeks data and some how back out the price at time zero. Well, this can be done. Clearly delta is the instantaneous change in the option price given a change in the underlying, IE/ derivative with respect to price-> to undo integrate, but you get back to the BS equation this way. Also you will need not only the numerical value for delta, but data for the other option parameters. So, it is kind of pointless from a practical point of view, in my minds' eye, and Biblo makes a good point! Yeah I guess you could try to solve things numerically, if just given the greeks values, but the likelihood of infinite solutions, to the system of equations representing the approximation, is high. Just my take on things. Just use BS, or realize that BS is BS from a real world practical view point and move past it (LOL). How have you attempted to solve this problem? Am I way off? Please correct me if I am wrong.

Thank you takingalpha -- I see your point here, and indeed I can back out the t0 px via the greeks using the bs analytical formulas (though that requires a sprdsht) and agree with you that you can easily approximate the t+1 px given the greeks. But as far as I can see there is no numerical shorthand to quickly arrive at the option px at t0 given the t0 greeks. Thanks for the confirmation!