An Option with a Negative Value?
A recent post in the Wilmott forums asked "Can an option have a negative value?"
Conceptually, an option with a negative value does not make sense. A negative value means that the option seller (writer) pays the option buyer. This results into a "free lunch" as described by one of the posters (waiter222). The option buyer will always win out in this case. He can exercise and make money when "in-the-money". He also has an instant gain even when the option expires worthless due to the initial cash flow. Indeed it is unfair.
Mathematically, an option value cannot be less than zero as well. (Please correct me if I'm wrong). I've played with several scenarios using the Black-Scholes and Binomial methods and the least value of an option is zero ("worthless").
But it is possible for an option position (note that I'm talking about an option position) to have a negative value when doing mark-to-market valuation. Marking-to-market is getting the close out (unwind) value of the position. And it can result into a loss (negative value). Here's an example, an option writer sells an option for $5. After some time, the value of an option at the same strike and expiration date rises to $6. This could mean that the option is getting more "in-the-money" and the possibility of an exercise increases. This is bad news for the option seller. The value of his position is obtained by assuming an offsetting transaction (he buys an option at $6) . The net result is -$1.
The point that I'm getting at here is that is quite unthinkable to have negative option value. So far no one has disputed that fact. But depending on one's position (P&L standpoint), the treatment of that option can be negative or positive depending on whether you treat is as an asset or liability. Does this make sense?
Tags: finance derivatives options valuation
2 comments:
Your example confuses negative P&L with negative implied vol. By definition, BS has a sqrt(sigma) in it, so I'm curious what you pulled this one out of.
It's POSSIBLE that a term structure of vol implies a negative forward variance of the asset, perhaps that's what you meant to say. Negative forward variance occurs when sigma1^2*t1 > sigma2^2*t2 (and t2>t1). What does that mean philosophically? It means your vol curve is screwy and you can arb it if you think that vols will drop back in line eventually.
Thanks for the comment. I never talked about negative implied vols in the article. I'm talking about the possibility of treating option values as gains or losses (asset or liability) on an accounting standpoint. It's purely about P&L.
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