i know this is an old thread but there may still be some people reading it. one alternative to calculating the iv and
greeks is to use a black-scholes pricing model and calculate the iv using the newton-rhapson method. you can't
solve black-scholes for iv but you have all the other inputs for calculating the option fair value. the technique is to pick
an iv value, use it to calculate the option price and then depending on the value, adjust the iv until you get
the correct option price. you assume the iv is, say between 0 and 100, to make the math easy to understand.
you pick 1/2 the range, or 50, and use that in the b-s model. if the fair value is above the known option price,
you know the iv you picked is too high. you now know the iv is between 0 and 50 so again you pick 1/2
the range and solve for the fair price. using this you can quickly converge on the iv. once you have the
iv all the other greeks should be accurate, or as accurate as any model can be.