Since we've been talking about negative option values. Are there any real world situations in which you'd get a negative implied volatility for a standard European option. I'm running the numbers for Shanghai warrants, and as things get close to exercise, I'm getting negative implied volatilities for some of them.

Want to describe what a negative volatility looks like, say in terms of a stock graph?I'm new at this game and can't imagine what it might be.

Collector wrote an article on negative vol..but that was a theoretical piece..he said negative vol is impossible...I think... im curious as to what neg vol is looking like....

Joseph, care to say how you "got" negative IVs? Negative vol is a vol of junk, doesn't make sense to happen.

QuoteOriginally posted by: mutleyJoseph, care to say how you "got" negative IVs? Negative vol is a vol of junk, doesn't make sense to happen.What seems to be happening is that the market value of a Shanghai put warrant seems to be less than the intrinsic value if you hold it to strike. Most likely answer is that I messed up in my code somewhere, but I was wondering if anyone had seen any such situations in real life.

When you hold it to maturity you mean? If so, could you ever imagine any rational investor holding on to it? It screams arbitrage & hence probably a bug in your code.

QuoteOriginally posted by: mutleyWhen you hold it to maturity you mean? If so, could you ever imagine any rational investor holding on to it? It screams arbitrage & hence probably a bug in your code.That's what I thought.....On the other hand, we are taking about Shanghai so the investors might be quite irrational.Anyway, I'll look harder for the bug in the code.....

I have seen energy options with several months left to maturity once trading for less than instinct.... this for deep in-the-money options.... reason was probably that some people that was long these options was in urgent need of cash...or alternatively they shorted such options to get in cash? This theoretically and practically implies negative vol I guess.... but market tend to think about such situations in different way, that is if deep in-the-money you adjust discount rate instead of vol, so implied discount rate was considerable higher than normal, or compared to for example at-the-moneys. Basically you got higher than normal return to buy such deep-in-the-money options (exchange traded so low credit risk).... but even then traders would take limited number of options due to binding up capital and risk limits.... most places have some notional limits... and people do not feel comfortable when someone suddenly dumps lots of options at "irrational" prices.... do such "irrational" prices imply something rational? Increased risk of default in clearing house etc...? it is always easy to see facts later on, but not in middle of battle field... so in such situations most players will do limited amounts and keep some bullets for later on (I am against any type of battle, except intelectual battles involving money in the market, if all wars was done in the option market many lifes would be saved, even if wealth not necessary had been evenly distributed , at least more people would buy option books instead of ammunition

We're talking about implied vols here so it is indeed possible to turn out negative since it is a derived value from prevailing market prices.But real volatility, on the other hand, may not turn negative because it does not make sense. So if we get negative implied vols, it's either you have problems with your model or the market is mispricing the option.

how would one make sense of implied volatility conceptually?

the effect of negative vol depends a lot on how your write your equations:whether S followsdS = rSdt + \sigma S dWor dS = rSdt - \sigma S dWhas zero effect on prices of options.It's only when you selectively change its sign in the BS formula that it has some effect.

"So if we get negative implied vols, it's either you have problems with your model or the market is mispricing the option."well not really mispricing the option, if you know one of the biggest players suddenly are going down and dumping options (even if exchange traded) and you know many players are going out of business then you would also have to ask credit risk questions you normally not would ask. And also you would ask is there even bigger arb opportunities coming along the next few days? Should I use all my capital now for getting excess 5% return next few months (taking close to no market risk, but possibly ssome "hidden" credit risk), or should I save capital for potentiaal much bigger arb opportunities in near future....of course with risk of all arb opportunities going away...Today when market still is over flooded with money this is possibly not an issue, but I remember the times when big banks had to work hard every day to fund their positions in overnight market, when nobody wanted to take longer credit exposure (on former AAA banks that suddenly had got multiple down grades) than over night....It is just that most theory is based on tonns of stated and unstated assumptions …in turbulent markets when things break down, you have to look at the whole picture not at isolated prices….for example to have reserves of cash can suddenly be very important....even if you make good returns you can for example get investorss doing redemptions. Not because they want to take out their money, but because they have to take out their money because they lost most if not all on other positions and got massive margin calls...of course to have deep pockets in such situations is very valuable... but what seams like an arb is not necessary an arb, except for a few deep-pocket players....

QuoteOriginally posted by: Collector"So if we get negative implied vols, it's either you have problems with your model or the market is mispricing the option."well not really mispricing the option, if you know one of the biggest players suddenly are going down and dumping options (even if exchange traded) and you know many players are going out of business then you would also have to ask credit risk questions you normally not would ask. And also you would ask is there even bigger arb opportunities coming along the next few days? Should I use all my capital now for getting excess 5% return next few months (taking close to no market risk, but possibly ssome "hidden" credit risk), or should I save capital for potentiaal much bigger arb opportunities in near future....of course with risk of all arb opportunities going away...Today when market still is over flooded with money this is possibly not an issue, but I remember the times when big banks had to work hard every day to fund their positions in overnight market, when nobody wanted to take longer credit exposure (on former AAA banks that suddenly had got multiple down grades) than over night....It is just that most theory is based on tonns of stated and unstated assumptions …in turbulent markets when things break down, you have to look at the whole picture not at isolated prices….for example to have reserves of cash can suddenly be very important....even if you make good returns you can for example get investorss doing redemptions. Not because they want to take out their money, but because they have to take out their money because they lost most if not all on other positions and got massive margin calls...of course to have deep pockets in such situations is very valuable... but what seams like an arb is not necessary an arb, except for a few deep-pocket players....I'm getting Collector's point. Somehow it seems that the option greeks as we know it (Delta, Gamma, Rho, Theta, Vega) is not enough to model every aspect of option pricing. In his example about credit risk considerations, since it is not part of conventional option pricing formulas, it's effect eventually finds it's way to implied volatility since it the only unobservable / derived variable. But if we explicitly put this in the model as a new variable, greek or as an adjsutment to your risk free rate (as pointed out by collector in another one of his previous posts), you might just have more rational implied volatility results. So this brings us to model 'misspecification' again.

Hmmmmm.... Interesting......One fact is that in order to issue a warrant in Shanghai you are required to superhedge. To issue a put warrant, you have to have on reserve cash which covers the warrant if the underlying goes to zero, that might keep people from issuing put warrants even if you had an obvious arb opportunity, and the reason the government requires superhedging is because no one has a model for pricing Shanghai warrants.Yikes, this could be really messy to model since the model changes the regulatory rules which changes the model.The first new Shanghai warrant expires on 8/30 and by 9/30 I hope to have a paper out that uses Carr and Wu (1998) to figure out the type of process (I expect that jumps will be important) and to coorelate changes in prices with regulatory changes.The one big public policy suggestion I have for the CSRC is to encourage companies to issue warrants with different strike prices. Even one or two more warrants at different strike prices will let you trace out the volatility smile (hard to trace a smile with two points. even harder to trace it with one), and once you have a smile curve it makes it much easier to figure out the pricing dynamics as well as giving you information that just isn't in the price of the underlying.

Riddle solved.Shanghai warrants have their strike prices reset whenever there is a dividend payment and there was one payment which I missed.