no one is sure why you would expect that You seem to be confusing delta and the theoretical pricing. Delta is a derivative of the change in price on the underlying only....its not the other way around. Price is made up of a number of different elements - volatility, interest rates etc; determined by its strike and expiry. the delta simply shows you what to expect given a change in ONE particular parameter. Think of the extremes..... If you had a 1 month option delta, and a 6 month option same strike - would you expect the prices to be the same? Think about these in terms of if they were ITM (delta 1) and separately as OTM (Delta 0) by enough that the deltas where for all intensive purposes equal. would you expect the prices to be the same?
just as an FWIW- whenever struggling with some concept or idea I always set things to extremes to see what happens - it can be revealing. In this instance while you say delta is a function of volatility and time to expiry.....think about these scenarios with regards your original question (I rephrased). "Is your question - despite being different strikes, and despite being different expiries, given they have the same deltas, why dont they have the same price?" Expiry day.... underlying $50, the $30 strike and the $40 strike calls will have the same delta but different prices. Ex dividend day....(the night before anyone registered for dividend is entitled) underlying $50, the $30 call strike for this month and the $30 call strike for next month will likely have the same delta, and possibly the same price, as it might be worth exercising both to collect the dividend (this will depend on the dividend amounts, vola and interest rates of course). Hope this helps. /////////////// Kinggyppo - good link. Thanks.
Folks, why all the fluff on this thread when the answer to the OP's original question can simply be written down on 1 line, or coded into Excel in one formula? Even adding the skew modeling is not hard (for index skews) and can be explained in a few comments. Draft730, get your Black Scholes formulas in front of you and just follow your nose - I promise it's not hard. If you want to also model the index skews then my question would be, do you understand the basics here or do you need education?