Losing Money When There is No Volatilty

It is common knowledge that there is more risk when there is more volatility. But it is also possible to lose (a lot of) money in the absence of volatility as well. This case was illustrated in a recent article published by Financial Engineering News. It was reported that Credit Suisse recently lost $120 million in Korean Derivatives -- particularly reverse convertible bonds.

A conventional convertible bond offers lower interest rates but gives the investors an option to call a company's stock. The bondholder is effectively the owner of the option and the issuer is the option writer. A reverse convertible bond gives investors higher interest rates but gives the issuer the right to put shares to the investor. In this case, the bondholder is the seller of the option and the issuer is the option buyer. When volatility increases, option prices increase as well. This added value stems from a higher possibility of going in-the-money. Conversely, a decrease in volatility will lower the option value. So if Credit Suisse was the one who "bought" the stock options via the reverse convertible structure, a decrease in volatility will decrease option value and will result into a mark-to-market loss on their end.

Now as market makers (structurers), shouldn't Credit Suisse be hedging their exposure? The problem with this particular structure is that the option is not based on one stock. It issued reverse convertibles on a number of shares. Hedging proved to be quite difficult and luck was not on their side, as stated in the article:

The problem however came in the hedging. Credit Suisse no longer had a single put option, nor did it have a portfolio of put options, since it could exercise its put into only one share. Instead it had an option on an option, a put option under which it could choose the share on which the option would be exercised. This instrument could be reasonably hedged by an appropriate portfolio of the shares provided volatility remained approximately constant, but it was effectively unhedgeable against a sharp change in volatility. If volatility in Korean shares had increased, there would be no problem; Credit Suisse’s multiple put option would be more valuable. There was, however, no effective way to hedge against a decline in volatility, which is what happened.

The lessons that we can learn here are the following:

1) You can lose when there is less volatility -- particularly in options since volatility is explicitly included in valuation.
2) When building a structure, one should know how to hedge it properly.

Tags: derivatives financial engineering investments valuation volatility structured products options

An Option with a Negative Implied Volatility?

Previously, we talked about cases when an option will have a negative value. This time, it was asked in Wilmott if there are real-life cases where options have negative implied vols.

Here's my take on the subject matter:

Since implied volatilities are derived values, based on observed market parameters and a model or formula, it is indeed possible to have negative results. But does it make sense? Intuitively, we would think that the volatility measure should only be positive and it does not make sense if negative. I think negative implied vols are a result of either a misspecification in the model, or mispricing by the market (an arbitrage opportunity, as mutley pointed out).

Tags: finance derivatives options valuation volatility

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