# Hedging a derivative

• Apr 8th 2008, 12:23 PM
Oli
Hedging a derivative
Quick question:
If an option is replicated by portfolio A, is it hedged by portfolio -A?
Or is there a portfolio of positive value that you can use to hedge the option?
• Apr 8th 2008, 12:45 PM
mathceleb
Quote:

Originally Posted by Oli
Quick question:
If an option is replicated by portfolio A, is it hedged by portfolio -A?
Or is there a portfolio of positive value that you can use to hedge the option?

I'm not much of a stock guy, but i asked around, as well as researched, does this help?

Black–Scholes - Wikipedia, the free encyclopedia
• Apr 21st 2008, 04:20 AM
gasbasis
If the cash flows of an option are exactly replicated by portfolio A, then yes, holding -A will offset its payoffs

But we're in the realm of science fiction here since A must be rebalanced continuously in order for it to work.
• Apr 21st 2008, 06:23 AM
colby2152
Quote:

Originally Posted by Oli
Quick question:
If an option is replicated by portfolio A, is it hedged by portfolio -A?
Or is there a portfolio of positive value that you can use to hedge the option?

If a negative call is a put, then, yes, your logic holds true. As gasbasis said though, you will have to continuously hedge every second, day, or whatever time period your option runs on to keep the entire portfolio in balance.
• Apr 21st 2008, 10:48 AM
gasbasis
Quote:

Originally Posted by colby2152
If a negative call is a put, then, yes, your logic holds true. As gasbasis said though, you will have to continuously hedge every second, day, or whatever time period your option runs on to keep the entire portfolio in balance.

A negative call isn't a put, but the act of writing a call. Holding a put option could conceivably make you delta neutral, but you'll have to deal with a lot of gamma so as a hedge it's not effective
• Apr 21st 2008, 10:54 AM
colby2152
Quote:

Originally Posted by gasbasis
A negative call isn't a put, but the act of writing a call. Holding a put option could conceivably make you delta neutral, but you'll have to deal with a lot of gamma so as a hedge it's not effective

Good point, but are we not delta hedging the portfolio?
• Apr 21st 2008, 12:07 PM
gasbasis
then why bother putting all those other nasty Greeks on your book with an option when you can do just fine with a linear instrument?