Serving the Quantitative Finance Community

 
User avatar
kfp22
Topic Author
Posts: 3
Joined: October 8th, 2014, 1:34 pm

Cash delta vs Forward delta?

June 25th, 2018, 8:14 am

In Taleb's book "Dynamic Hedging", I came across the following paragraph about cash vs forward delta in the context of options management.
I am totally lost and hope you can help me out on this ...
What is the definition of cash delta and forward delta? What does Taleb mean by transforming the future exposure into cash exposure? What is it for?
Thanks a lot



"CONFUSION: DELTA BY THE CASH OR BY THE FORWARD
 
The delta as expressed by the Black-Scholes-Merton formula concerns the
amount of cash the operator needs to execute to offset an option position.
For all European options, however, the real exposure lies in the forward.
Nevertheless, operators prefer to see the cash delta as they generally
hedge themselves with it. It is easier to monitor on a screen and quote in the
market. When they deal with options on futures or use the futures as a
hedge, they need to use a different delta fit to the exact period in the future.
The difference between the two is sometimes far from trivial. Operators
often must deal with questions like this one: An option that is close to the
money in the forward trades at 50% delta. What is the cash delta?
The answer is to transform the potential future exposure into a cash ex-
posure through the delta of a forward. This can be done by discounting the
forward exposure using the cash-future growth rate as a discounting factor.
Therefore, the delta of the cash will be the discounted value of that number.
The discounting method will depend on the underlying security of the op-
tion, as will be described. "
 
frolloos
Posts: 752
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

Re: Cash delta vs Forward delta?

June 25th, 2018, 9:56 am

Me thinks it's a very long-winded way to say that you can hedge an option either using the future or the underlying (i.e. "cash") instrument.

And this question should be in the student forum.