Newbie question on premium

[sharpie458]

I was looking at UNG puts today when it was trading at $9.25 a share and I noticed something odd about the $9 and $10 strikes. The implied premium of the $9 put seems to be more than the premium of the $10 put. How could this be? I understand that the $10 strike is in the money by 75 cents but why would this translate to such a huge discount in premiums, are NG prices considered to be that bearish long term by the writers?

The prices in question are:

UNG APRIL 2010 $10 PUT $1.70 (with UNG stock trading at $9.25/share)

UNG APRIL 2010 $9 PUT $1.10 (with UNG stock trading at $9.25/share)

The breakeven for the $10 call would be $8.30 and the breakeven for the $9 put would be at $7.90. Insinuating from that the premium for the $10 strike put would be $1.10 and that for the $9 strike put would be $1.60. This is the part that puzzles me, I know that the $10 strike is in the money by 75 cents and the $9 is out of the money by 25 cents but still does that justify such a massive a premium increase for the $9 put of about 50 cents(in premium)?

It just seems to me that the $9 put is priced too high, conversely the $10 could be priced too low but I doubt that is the case because writers don't make such blunders and if they did the market would suck up the mistake like a vaccum. So what exactly is going on here, why is the $9 put so overpriced?

 

[Martinghoul]

I don't think there's anything overpriced here... It all seems relatively fair value, even when you assume flat vol (which is not unreasonable as both strikes are relatively close to ATM).

 

[Dommo]

I think the quoted prices are perfectly consistent with spot and a reasonable volatility smile. I'm ignoring interest rates and dividends here, but if you look at option value as:

Option value = intrinsic value + time value
where, for a put, intrinsic value = Max(strike - spot, 0)

Strike 10 - intrinsic value = 0.75, so time value = 0.95 (total 1.70)
Strike 9 - intrinsic value = 0, so time value = 1.10 (total 1.10)

This looks reasonable to me - the smile just implies a higher volatility for the $9 strike.

 

[Martinghoul]

The vol for the $9 strike is actually a little lower than for the $10 strike. That's the way it should be, as the $9 strike is closer to ATM.

 

[sharpie458]

First of all, the historic price low for UNG is $9.01. It has never ever gone lower than that, ever. Now the $9 strike might be closer to ATM but I was thinking more towards the chances of the price of UNG stock itself dropping $ 0.20 further and causing immense pain to the writer of the $10 put and dropping the same $0.20 and causing no pain at all to the holder of the $9 put. In other words the risk of UNG dropping to the breakeven(for the put's buyer) of a $9 put are almost negligible compared to the chances of UNG dropping further in the money(as it would with every penny drop in stock price) for those with a $10 put.

From what I understand, a put imparts a risk onto the seller that they may have to suffer monetary damage the further down that an equity price goes from the time the option was underwritten. To compensate for that risk the writer charges a risk premium.

Keeping that in mind one would infer that the further south the market price tumbles from the strike price, the greater the damage to the writer. The difference between the market price and the strike price in the case of an itm put would be mostly irrelevent as it would be factored in at the time of writing as well as the various times of trading and retrading the option. Now this is the part I don't get, that if this put was written when UNG stock was trading above $10 then the chances of UNG stock dipping below $10 would obviously be quite a lot more than the price of UNG dipping below $9. Hence the risk premium charged by the underwriters for a $10 put should most definately be more than the risk premium they charge for a $9 put. Just looking at the price of the $9 put I got the idea that comparatively speaking, if one ignores the 75 cents in-the-money cost of the $10 put the $10 put is a bargin, premium wise compared to the $9 put.

Actually I would tend more to think that the $9 put is ridiculously overpriced. Maybe it didn't have a chance to correct itself after the big dip in UNG price over the last few days?

 

[Martinghoul]

I don't see how any of this is relevant... You're thinking of options all wrong. Just try to think of the normal distribution centered arnd $9.25 and things should become clear.

Assuming a simple Black-Scholes world, where both strikes have the same vol (say 51.633%), the fair value of the $9 put is $1.10, while the fair value of the $10 strike is $1.695. The half tick extra comes from the skew.

 

[sharpie458]

Well I'm not speaking about options in general here but specifically UNG options. From what I gather, UNG stock is basically backed up in large part by professionally placed futures contracts on natural gas itself. This means that all the stock that goes into UNG is collateralized by a share in physical reserves of natural gas. Now unlike loans, off which banks make money, physical natural gas can go up and down in value but it cannot go up in flames into nothingness as CIT stock did because well, NG will always be worth something to someone since it is constantly being consumed in the US.

Now the price of NG itself has steadily been declining but it can never really go below the cost of production because then nobody would bother producing it lol. Hence, with the price of NG being a wee bit over the cost of production right now my feeling is that the price of UNG stock is extremely unlikely to dip below $9 because nobody who has a stock of something tangible like natural gas will sell it much below market in a panic, it's just not going to happen. Hence I just don't understand why the risk premium for the $9 put is higher than that for the $10 put since UNG is so unlikely to dip very far below $9 anytime in the next few months.

So it seems like me that the writers did all the math right, but sort of missed the forest so to speak. At least in the case of UNG. Now I may be wrong about the riskyness of UNG stock of course but assuming I am right then the $9 price is impossible to breach anytime soon.

 

[Martinghoul]

So you're suggesting that the zero bound loosely implied in standard Black-Scholes is not applicable here. I have done some very simple analysis...

I don't know anything about the cost of NatGas production, so I did it simply. UNG US didn't exist during the previous US recession, so I used the actual spot Henry Hub prices, which the UNG, ultimately, is supposed to reflect (you could also use NG futures, with the same result). According to the historical futures/spot prices, NatGas fell to as low as 50% of its current price (not inflation adjusted). What this suggests is that UNG could easily go as low as $4.60, even with the reasonably benign assumption that the current recession is not worse than the one in 2001/2.

Now if you believe that UNG price can never go below than, say, $7, you should be buying ratio put spreads, e.g. 8.00 - 7.00 1x2s. This will allow you to fade the shape of the skew and the normal distributions that are implied by the Black-Scholes pricing of low strike puts. You should be careful, though, since large strategies based on 'it can't happen, because it had never happened before' can blow up in a most spectacular fashion. They blow up not because they're necessarily wrong, but rather because people's pockets are not deep enough to withstand the mark-to-mkt.

As to NatGas per se, as I understand it, there's currently a glut of supply. Moreover, gas can also easily go up in flames into nothingness, which is, apparently, what happens annually to immense volumes of gas (equivalent to a quarter of US annual consumption).

 

[sharpie458]

That's a lot of good info to digest, I am not too good with options terminology so some of it went over my head but I get the gist of what you are saying, that $9 is not so strong a barrier that it cannot be broken with impunity as the slow and steady price decay creeps up into the high $8 zone.

What I have done so far is to just buy a $10 put on one contract and also grabbed the equivalent stock, 100 shares. This was more of an experiment to see if this combo behaves as I think it should. Both positions are "hedging" each other and the hope is that a wild upswing in stock might occur to over $9.50 over the next few days or perhaps even over $10 at which point I will drop the UNG stock and either hold the put or drop it at the same time.

What I am hoping for and to a tiny degree also observing is that as the price of UNG stock moves up the stock seems to gain slightly more than what the put loses. If UNG decides to not move decisively in the next few days I will just liquidate both positions by Friday or Monday at the latest for fear of the put starting to decay.

 

[Martinghoul]

In general, I always try to draw graphs of distributions in my head whenever I think about these things (you can also actually generate these implied risk-normal distributions by differentiating the option prices wrt strikes). It makes everything a lot more intuitive.

For example, what you're suggesting is that at some point (whether it be $9 or $4) the left tail of the normal distribution collapses and that's not priced in by the mkt. Not only that, but the mkt even prices in a heavy left tail (that's what the skew implies).

If you disagree, as I mentioned, you'll need to sell lots of low strike puts. That's a difficult and dangerous thing to do, which brings us back to why these options are so expensive.

 

[arabianights]

don't worry sharpie i have a photo of martin receiving fellatio from a horse which is yours for a bag of UTG puts

 

[Martinghoul]

don't worry sharpie i have a photo of martin receiving fellatio from a horse which is yours for a bag of UTG puts

Oh no! Where did you get that, you *******? I was sure I had all those destroyed !

 

[arabianights]

from the horse

 

[noitop]

Does anyone know why an atmf call option is not 50 delta but slightly more? Seems that it has something to do with the lognormality of price distributions but how does the dynamic work?

 

[Martinghoul]

Does anyone know why an atmf call option is not 50 delta but slightly more? Seems that it has something to do with the lognormality of price distributions but how does the dynamic work?

Picture the normal distribution arnd the price... Is the right side of the distribution exactly the same as the left side? Therein lies your answer.

 

[noitop]

Picture the normal distribution arnd the price... Is the right side of the distribution exactly the same as the left side? Therein lies your answer.

Hi Martinghoul, thanks alot for the prompt response. The lognorm dist has a longer right tail but if I just look at the distribution, how do I tell where the atmf falls? If it fell more to the right side, the effect of the longer right tail would be negated? Besides looking at the equation of d1 and hence N(d1), how can I tell a little more intuitively? does it have anythign to do with the mean of the lognorm px dist being more to the left and therefore the atmf = to tt mean?

 

[Martinghoul]

Hi Martinghoul, thanks alot for the prompt response. The lognorm dist has a longer right tail but if I just look at the distribution, how do I tell where the atmf falls? If it fell more to the right side, the effect of the longer right tail would be negated? Besides looking at the equation of d1 and hence N(d1), how can I tell a little more intuitively? does it have anythign to do with the mean of the lognorm px dist being more to the left and therefore the atmf = to tt mean?

Nah, that's an entirely different effect... For the moment, let's assume that ATM = ATMF and the distribution is centered arnd it. No matter how you slice it, the left side of the distribution will look different from the right one.

 

[Cadavre]

I used a trading program I got from here and ran the matrices on both your UNG puts (PI and PJ), using today's chain with the market for the underlying at 8.84$. The manufacturer offers a free copy of their legacy platform that includes a CBOE Chain reader and a portfolio with a mark up to market feature. They also offer a free IV calculator that produces a forward price smile for sticky delta and theta pricing, as well as American and European Bisection and Smile IVs. It is very important to use an American IV when evaluating American put options.

Why did the market favor the higher strike?
There's a theoretical price for an option and there is the market price. A factor known as implied volatility corrects the theoretical price to the market price and can be used to estimate the future spot, or market, value of the premium under a range of different stock prices (price steps) and dates (date steps). The historical volatility is a real volatility and measures noises in the market for the underlying. The HV for UNG 56%.

The reason for the disparity in the spread of the 9 to 10 April Put is most likely the sellers notion that the market price of the underlying, UNG, would decline, making the 10$ put more attractive, therefore supporting an argument for a better premium or ask for the option. And, in fact that is what happened. It is important to research the news related to the underlying and currency exchanges. The US market seems to have an inverse relation with the USD (dollar index) and it bumped up a couple of basis points today while the DOW declined in early trading:

The chain reader also produces an IV for all the call/put pairs in the chain. The IV for the 10$ April Put my last read was 52.20%, while the 9$ April put shoes an IV (at the chain price) of 50.90$ (the ATM IV at the time I read the chain). That's a 1.3% disparity in IV. I should also note that the chain reader shows parity favoring the call as well as attractive reverse conversion put ITM call OTM yields for the UNG strikes you're looking at (which I have no understanding of but have heard are used to prospect for arbitrage opportunities).

 

[Martinghoul]

AAAAAAAAH! Cadavre, please stop... What you're saying is horribly wrong on so many levels.

 

[Cadavre]

AAAAAAAAH! Cadavre, please stop... What you're saying is horribly wrong on so many levels.

My specialty is learning from my mistakes, naivety, errors and omissions. I don't claim any special knowledge or expertise - so please help me understand so I can grow. Your general disclaimer has my attention. Could you be more specific?