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Math Help - Hedging a derivative

  1. #1
    Oli
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    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?
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  2. #2
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    Quote Originally Posted by Oli View Post
    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?

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  3. #3
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    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.
    Last edited by gasbasis; April 21st 2008 at 03:22 AM. Reason: clarification
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  4. #4
    GAMMA Mathematics
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    Quote Originally Posted by Oli View Post
    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.
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    Quote Originally Posted by colby2152 View Post
    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
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    GAMMA Mathematics
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    Quote Originally Posted by gasbasis View Post
    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?
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  7. #7
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    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?
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