My understanding of Delta is the change in the Option's price relative to the change in the underlying asset's price.
In the case of Treasury Future Options (ie those on CME), one intuitive way to do it is to shift interest rate curve (whatever curve the underlying asset depends on) by a certain amount, and then compute the prices of the underlying future contract, as well as the prices of the option itself, and find the ratio of the differences of those 2 types of prices. This will give me the 'Delta' of this option.
The trick of course is computing the price of the option in the above. And this is where option price modeling comes in.
But why would there be a 'market price' based delta? Whatever price that we need to find in the above methodology must be computed using a model, no?
How would one find a 'market price' based Delta ?