They aren't included in any model known to man? You're incorrect. I am familiar with Taleb's work. I also know his hedge fund (which buys extremely OTM options in the hopes of getting that black swan) is doing horribly, whereas funds (LJM for example) that sell OTM options are doing great. LJM has been making money selling S&P options for 15 years. Taleb has been losing money since his fund's inception. If you can properly compute the odds of an event happening, it doesn't matter which side of the bet you take. How do you think a bookie makes his living? 1) He makes a best guess of an event occuring. (You can't tell me you can compute the odds of an option expiring ITM any better than a bookie can compute the odds of the Red Sox beating the Yankees) 2) He adds vig to take his profit 3) He will happily take either side of the bet. 4) He adjusts the odds as he sees how the public is betting. 5) He hedges by betting on a secondary market. Sound familiar? A market maker selling options: 1) Makes a guess about the option expiring ITM using his best probability model. 2) He adds a spread to take his profit 3) He will happily take either side of the bet 4) He adjusts the prices based upon whether he is buying or selling too many of a particular option. 5) He hedges by buying/selling deltas or gammas. To avoid looping this debate ad nauseum, let me see if I can summarize our points of view... I argued that it's not just the risk/reward that measures the value of a bet but the probability of it winning. A bet to win $20 and lose $1000 which will win 99.5% of the time is a great bet. You argued that it's impossible to compute the odds because no "model known to man" accounts for fat tails, therefore selling options is a losing proposition. Sound right?
I have said no such thing. Are you even reading my posts. Never in my ET history have i said that there is an edge in buying over selling or vice versa. All i am saying, for the third time now in this thread, is that generally people misuse probabilities in the context of selling cheap gamma. Just because a bet may "appear" winning when you compare probability of expiring OTM with the payoff ratio doesn't always mean you will have expectancy after a large enough sample. Some of the reasons for this i have already mentioned in my previous posts. If you think you have a model that accounts for fat tails and can sustain several consecutive VAR shocks in negatively skewed bets, that is fine. Prosperous trading to you.
OK...here is my twisted take on odds and probs...Once I wrote an "arb" race track's system , which did the following : 1. Take a win odds on horse A ( lets say its 3:1) 2. Take a win odds on horse B ( 8:1) 3. mathematical calculate the odds of exacta ( horse A comes first , B second , lets say it 25:1) 4. Compare math's odds of 25:1 to ACTUAL odds on exacta , and place a bet if price is > 25:1 , which happened many , many , many times. Why its happens ? because the SAME public that just awarded horses A and B with odds of 3:1 and 8:1 (hence , exacta odds 25:1) in the WIN money pool , placed completely diff exacta odds in EXACTA pool. Notice , WIN pool is always much larger then exacta pool . It also has much large $ distribution per entry ( 8 horse race has 8 WIN entry , but 56 possible exacta combinations). So far its easy , now about options... If OTM or FOTM or FFFFFOTM skew is exists , which vols ( odds of which pool ) should one use when calculates probs to reach/close ? Heavy volume weighted ATM's ? Front month only ? OTM ?
I like the arb you described. I guess the short answer to your vol question is "neither". We already know the standard distribution does a pretty poor job of modeling equity behavior (hence the reason for volatility smiles in the first place). There are a variety of jump models which take into account leptokurtosis and flatten out the smile. But, changing volatility needs to be included as well (GARCH, for example). GARCH + a jump distribution is a reasonable start at getting a vastly superior probability model, in my opinion. I have no problem selling options as long as the odds are in my favor and I can survive improbable events. At the moment, there are plenty of opportunities where the price of a long-shot option (and occasionally even the near money option) has been bid up enough to give you the statistical edge. Maverick's view is pretty widespread and causes an edge to exist. If no one is willing to sell a call, but everyone is happy to buy one, the price goes up. Just look at the vol smile for the S&P options--really expensive puts, very cheap calls. Supply and demand overwhelms statistics in some surprising ways.
Vol smile has nothing to do with a statistical edge. And a litte FYI for ya, for more people are selling the S&P options, then buying them, especially the put skew. And as far as selling options when the odds are in your favor, this statement is full of holes as you will never know the true odds or probability of the trade. This is the rub of the options pricing model. You can model volatility and stochastic volatility very well, even price jumps. But you cannot model fat tails effectively.
This is pretty much the definition of probability. What are the "true odds"? Red Sox are 5:1 underdogs for the world series in '07. Why 5:1? Why not even money? Why not 500:1? What are the odds their pitching staff gets injured early in the season? Their best hitter gets traded? Your statement still holds, "You will never know the true odds or probability" So, why have bookies existed (and made awfully good money) for the last 2,000+ years? Because they have a probability model they believe in. I have a probability model I believe in. You don't have to believe it--it's my model, not yours. But I'm very happy to keep taking the money of people who overpay for options month after month. And to do so in a way that will allow me to survive the series of improbable events. There are hedge funds that have been around for 20 years that do the same thing. To each his own.
Just to set the record straight, that is not what bookies do as I have many friends that are very successful bookies. Bookies make a 2 sided market. Bookies do not speculate on outcomes. Their goal is to make a line that will draw the most 2 sided action. That is where they make the most money. If they are leaning too heavy on one side, they will lay it off on the Vegas books. I just wanted to clear that up. As to all these funds that have been selling premium for 20 years. LOL. Look, there have probably been close 30k funds since 1970. Of which maybe 2 or 3 are around today that have been selling premium. Gotta love those odds! Or as Taleb would say, you put enough monkeys behind a typewriter and one of them will write the "Iliad". And lastly, how much money you have made in the past has no bearing on how much you will make in the future. Only a fool makes such a claim. I also love the assumption that people are overpaying for options. Overpaying compared to what?
That's what I've been saying ALL ALONG. If you get the odds right, you make a two sided market! If people are overpaying, you sell them options, if they're undercharging, you buy options from them! You responded that you can never know the odds, therefore you can't decide which side of the market to be on. If that's the case, why are you trading options at all? If you believe no one can compute the odds at all, the only options you should be trading are at-the-moneys . If this is your trading strategy, fine, otherwise you are implicitly computing the odds every time you buy or sell. What is your model based on? Or as Taleb would say, you put enough monkeys behind a typewriter and one of them will write the "Iliad". I fail to see why Taleb is such a hero. His fund is a dismal failure proving people, in general, *overpay* for options. The odds are against him. And lastly, how much money you have made in the past has no bearing on how much you will make in the future. Only a fool makes such a claim. I also love the assumption that people are overpaying for options. Overpaying compared to what? Where did I say that the previous roll of the dice affects the next? I'm pretty sure that's what I've been saying all along as well. Overpaying compared to a model you believe in. I'm pretty sure I said that too. Putting words in my mouth and then arguing with them makes this whole discussion pointless.