1. Why does it seem that some options with no apparent extrinsic value has a theta attached to them? For example, yesterday I saw NFLX Jan 20' 12 120P being worth $33.9. After some calculation, I found the put had an extrinsic value of $0.12. Next, theta was exactly -0.04. Since the option expires in 13 days, that means it will lose a total of -0.52 according to the theta number. But clearly this is impossible, seeing as the extrinsic value is only $0.12. So what am I missing? 2. It seems the theta gets even more out of whack on options closer to expiry. Some of the NFLX Jan 06' 12 options has over the last couple of days, had thetas ranging from -1.00 to -15.00 and probably even higher than that. For example I once saw a put option worth 0.15 or so having a theta of -1.00. Clearly impossible. 3. Next, a question about gamma scalping. Say you are long gamma. Is it correct that the P/L you make per hedge is equal to 1/2*gamma*S^2 (S being spot movement). So if I'm delta neutral when the spot is at 15, I will then have made 1/2*gamma*0.75^2 once spot has moved to 15.75 or 14.25? And then when I re-hedge, I lock in this profit? 4. Assuming I short an ATM straddle. The spot then moves $10. One option is now DITM, whilst the other is DOTM. Lucky for me, I delta hedged every $1 spot movement. So despite the stock moving $10, I am still delta neutral. Since I hedged every $1, I have now lost a total of 1/2*gamma*S^2 * 10. Now here's the question: Since gamma is higher when an option is ATM, the delta hedges I make closer to ATM is going to incur more losses than the hedges I make closer to OTM/ITM. The same goes for theta. Since theta is higher ATM, I am going to make more money while the option is ATM vs when the option is OTM/ITM. But here's the problem. Theta, unlike gamma, occurs in a nonlinear and unpredictable fashion. In fact, the loss I incur from delta hedging at any spesific point in time, may or may not be offset by the theta at that spesific point in time. Am I right that this is a problem? 5. Working from the question above, one way I see this can be solved is to sell ATM straddles, and combine them with selling more OTM/ITM straddles at equidistant moneyness. This way I get an equal theta exposure accross the board, such that my theta over 24 hrs will always be approx. the same, and thus the theta gain I have will be more predictable. Obviously my gamma exposure as well will stay the same at all levels. Now the only problem is what I said in my first couple of questions. ITM options have little extrinsic value, so shorting them won't gain me any premium despite theta saying it should. 6. Continuing from above, I am hoping we can have a discussion on how exactly theta manifests itself. To be honest, I am rather mystified by the concept of theta. Hopefuly someone can explain it and answer my questions. Thanks
I am not going to address all of your concerns but 1. The Greeks are not derived via laws of nature, like gravity. There is some fudge in there. They are more an expectation than an actuality. http://www.investopedia.com/articles/optioninvestor/04/121604.asp#axzz1iqGoRwIx 2. With respect to your puzzlement with the value of theta, the value of theta is not constant over the life of the contract. The value of theta will change each day as the contract approaches expiration.
1. I realize they are more of an expectation. The question is when can you expect them to be right? Why isn't extrinsic value respected in the calculation of theta via Black-Scholes? It would be quite easy to integrate a function that disallows theta to be above extrinsic value. Why hasn't any options platform done this? 2. Yes, the theta gets higher and higher each day towards expiration. However, since the stock fluctuates up and down accross different strikes intraday, the theta number of one spesific strike will also fluctuate a lot intraday. However the theta fluctuation may or may not be realized, because theta occurs abruptly and nonlinear. On the other hand, gamma fluctuations will always be realized, because gamma is linear and predictable. This can be a problem when gamma scalping.
The way each Greek is calculated is to make assumptions about all the other Greeks, hold them constant, and back out the isolated variable. There is always error here, but for most positions, observation suggests that these calculations are good approximations. The truth is that option pricing has an element of art in it. For example, theta is time value in days. Is it a 24 hr day, or only when the market is open? Let's assume 24 hr. Then does the option price decay theta/24 per hour? Not really. And on and on. I doubt theta is ever above extrinsic value, ceterus paribus. In your example, with 13 days left to expiration, you are assuming that the theta will be the same for all 13 days. Actually, it will get progressively smaller as expiration approaches. You can't just multiple 13 x .04. The theta will be much smaller than .04 near expiration. Bottom line - No financial market moves exactly like any formula says it should.
Theta is non-linear so multiplying today's value by the number of days remaining is inaccurate. Also, today's theta represents all other market values remaining the same. If they are, you won't see that daily amount of $ change in the UL (theta). If not, it may be more or less. The gamma scalping formulas are above my pay grade. But vis vis GS-ing a long straddle at 15, yes, you lock in the gain on the shares bot (or shorted) but the time decay is working against you... as will any IV drop.
Looking at IB options chain data, as mentioned in my first post, calculated theta is actually above extrinsic value for all options that are very near expiration and even for some options that are further from expiration, spesifically DITM/DOTM options. All other options seem somewhat accurately priced in accordance with extrinsic value. Next, it seems theta increases towards expiration for all strikes. Working from these two points, the conclusion I am reaching is that all options eventually reach a strike that is far enough ITM/OTM and/or a point in time where the theta part of Black-Scholes is no longer valid. This point can be seen to occur when theta*days to expiry reaches a value higher than the options extrinsic value. Let me know what you guys think of this. Again I'm new to this so my observations may be wrong. Hm, I could have sworn theta increases towards expiration. TBH I've never seen any long-term options have higher thetas than near-term ones, even at DITM/DOTM strikes. Then again this is all based on my own observations, and since I'm new they are probably wrong anyways And yes as you say, theres the factor of other greeks influencing theta as well... Yeah, theta is working against you long gamma. But can also work for you when short gamma. Vega can be an issue, but I usually hedge vega risk with var swaps or calendar spreads in a ratio that makes me vega neutral.
I'm a novice with most of the Greeks. When I've gamma scalped, it's been really simple... usually UL versus a long option leg, sometimes adding something short that's OTM in order to reduce some of the time decay. What I have noticed is that at times, IB's data is erratic and therefore unreliable. I checked the deltas of the bid and ask but that didn't account for the occasional weird fluctuations. To compensate for this, the night before, I would print a hard copy of the UL's price and the delta of my options at increments of say 25 cts. ranging a few dollars in each direction.
Yeah, to be honest, I've been thinking a lot of the problems I see has to do with IBs data feed....I know it's extremely unreliable for charts and T&S since it's aggregated. Wouldn't surprise me if something is up with the options feed as well. Also, does anyone know how to make IB TWS calculate total portfolio greeks? I cant seem to make it work, and its a pain in the ass having to use a calculator everytime I want to rebalance something.
#1 and #2 Theta is not constant through time. It's a function of implied vol, moneyness, and time to maturity. It will be related to gamma as it can be viewed as the cost of owning gamma. It's predictable as much as the amount of gamma you are running is predictable. Out of the money options have higher theta now than close to expiration. (you can view this as the option having less and less chance of "being an option" as a particular outcome (in the money or out of the money) will be very likely). ATM money options have theta that increases as you approach expiry because the "optionness" in the option is very high. Anything can happen. As a result you have a lot of gamma beause a move in the underlying has potentially a huge effect on the new probability of it being in the money and there is little time for this to change. #3 Correct #4 Theta and gamma are related so you don't really have a problem. The problem you have is that suppose you are short 100 straddles. If the straddles are away from the money then you will have low gamma and theta so your potential gain or loss will be small. If they were at the money your potential gain or loss will be huge for the same size in contact terms. #5 Correct. Look up synthetic replication of a variance swap. #6 Many ways to look at theta. You can look at theta as the cost for getting an asymetric payout. You can look at theta as a fixed vs floating swap (fixed (implied) vs floating (realized) volatility). You can look at theta as the cost of dynamically creating an option via delta hedging. In the end it's all really the same thing.
Thanks newwurldmn, this answers a lot of my questions. However, regarding #5, say I want to replicate a variance swap. What I'll do is basically short straddles all over the place, at equidistant moneyness, say $5 or so between each straddle. Now here's the thing. The straddle I short ATM is going to earn me an extrinsic value of for example $5 in total. But the straddles I short ITM/OTM, are going to earn me extrinsic values of less than $5, and it gets lesser and lesser the more in/out of the money the short straddle is. And if price now moves to one of my deep short straddles, and it becomes ATM, it's extrinsic value is going to increase beyond the initial extrinsic value I shorted it at. Won't this give me a disadvantage? Theta will obviously also increase as it comes closer to ATM, but as far as I see, that theta increase won't benefit me in any way, because I don't have enough extrinsic value to realize the theta. People who shorted it while it was ATM on the other hand, have enough extrinsic value to realize the theta. Or am I overthinking it?