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

Brushing up on my math skills...

I'm somewhat amazed on how I got myself into the world of Financial Derivatives. I do not have a quantitative degree (I majored in Management Economics) and didn't pay much attention to my math and statistics classes in college. Yet I find financial markets (derivatives in particular) fascinating. And becoming knowledgeable in them actually gave me an edge in the industry.

Looking back, it seems that I chose the wrong college course. But my interest in the subject matter and the willingness to learn did not stop me from attaining my goal. Although not for quants, the CFA program gave me a good background on the financial markets in general; as well as valuation methods for plain vanilla derivatives.

I searched the net for papers. Marketing and research papers published by the big banks are of great help. Sites like DefaultRisk has loads of papers on Risk Management and Derivatives. But reading them is no simple feat as most of them are written by PhDs or PhD students. My lack of academic foundation in mathematics do get in the way, especially when I encounter a lot of greek symbols.

Finding like-minded individuals to discuss topics of interests and ask for advice also did a lot of good. I am an active member of Wilmott -- an online community of quants (Username: Jomni). At first, I was the one asking questions, and now I give answers and advice myself (on topics that are not mathematically deep).

I never stop reading. Part II of the PRMIA Professional Risk Managers' Handbook is a good refresher on quantitative finance topics. It covers Matrix Algebra, Differential and Integral Calculus, Probability, and Statistics. Other good books would be Hull's Options, Futures and Other Derivatives and Paul Wilmott on Quantitative Finance.

Tags: derivatives finance math quant books cfa