Yes, that's the correct graph. (Thank you for posting it.) And the graph is what it is. My question is: what are the real world results - compared with buying the ATM fly? What I am wondering is: 1) If it's true that the ATM and FOTM options are undervalued in the real world and if the OTM (1,2 sigma) are overpriced and 2) If it's true that buying the ATM buetterfly (per quoted article) is profitable Can we conclude that one can do better by buying the OTM flies, rather than the ATM fly? Mark
Thanks, I'll look it up. Another good one is Taleb's "Dynamic Hedging" - not too much math, and great explainations of some complex topics. Your point about using a simple model is well explored in Derman's autobiography "My life as a Quant" - a fairly interesting look at one of the pioneers in this area. Gives some neat insight into Fischer Black.
Yip, I've thought about this a bit more, and I'll try to explain better: I've stolen this example from John Hull's textbook. Assume the value of a stock is $20 and pays no dividend. At the end of three months, the stock price will be either $22 or $18. We need to value a European call option with a $21 strike and 3 months to expiry. This option can have only two possible values in three months: if the stock price is $22, the option is worth $1, if the stock price is $18, the option is worth nothing . To price this call option, we can undertake static/dynamic replication whereby we set up a hypothetical trade consisting of the option and the stock, in a way such that there is no uncertainty about the value of the portfolio at the end of three months. Since the portfolio has no risk, the return earned by this portfolio must be the risk-free rate. Imagine the trade initially is long X shares of stock, and short 1 call option. We can compute X so that the position is risk free at inception. If the stock goes up to $22 or down to $18, then the value of the portfolio is: stock goes up = $22X − 1 stock goes down = $18X − 0 So, if we choose X = .25, then the value of the portfolio is if stock goes up = $22X − 1 = $4.50 if stock goes down = $18X − 0 = $4.50 Whether the stock moves up or down, the value of the portfolio is $4.50. The correct value for X (eg.g the delta) is 0.25 to make this option a risk free equivalent to payouts from owning the stock A risk-free portfolio must earn the risk free rate ("the law of one price" i.e 2 securities with the same pay-out must have the same price). If the current risk-free rate is 12%, then the value of the position today must be the present value of $4.50 (the future value), or 4.50 Ã e^(−.12Ã.25) = 4.367 This, I hope, demonstrates why the risk free rate is used to calculate prices. The variance/std dev of stock movements is used when we aren't certain about the final payoff (e.g. when we aren't certain that at 3 months the stock price will be $18 or $21).
I agree with you in Hull's textbook. John Hull text was the one that I started before seriously trading options. If you read Hull's book carefully, you'll realize that he started with the markov process, and if one really solves it using the geometric Brownian motion, u should be the mean return of the stock, and sigma should be the standard deviation of the stock. He then jumped to use the risk-free portfolio and so u became the risk-free rate. To me, it means there are 2 different approaches for getting the model based on two different assumptions. The first assumption is the brownian process, and the second assumption is that all participants are rational, and smart enough and so no arbitrage assumption. If I start from the first assumption, and solve the geometric brownian process without looking at the risk neural argument, I will get a conclusion that I should use the average return of the market for u. After the no arbitrage argument, I was confused because I totally agree with the no arbitrage argument, and I don't understand why it doesn't agree with the solution obtained from solving the brownian process. I believe if I can find an explanation, it might give me a better insight in trading options. I might have something, but I don't have enough experience to back up my current explanation. [edit] Hull's book is the only theorectical book that I have ever read. Perhaps I should read "BS and beyond".
You are onto something that very few traders understand, much less employ in their day to day market bets. Statistics and all the different variations of pricing mechanisms out there are best used to reject trade ideas rather than to support them.
I am curious about this exit rule for the butterfly strat they tested: "3. If the spread is still open on the Friday that is one week before options expiration, exit at the close." The P/L curve of the fly changes dramatically during the last week of the trade. They have a graph of the classic pointy hat P/L graph and talk about the great risk/reward for the butterfly. Then they structure the trade so that it exits before that risk/reward profile is ever reached. Instead they opt for a slightly wider and much lower shape P/L profile. No wonder they got a better w/l% but only a 1.2/1.0 win/loss ratio. I don't have the numbers to test and see which is better. But the authors didn't test the premise they setup in the beginning of the article.
I've got all of the posts from this forum archived, there are plenty of recent examples of options trading 'lingo' that without referenced examples could otherwise be catagorized as 'babble' from knowledgeable traders. And then someone like Sailing comes along and gives solid examples of trade setups that decipher the 'lingo' into normal trading terminology, along with adjustments that can take place in order to refine the positions as the trades progress toward expiration. I don't know if the use of this 'lingo' is a deliberate attempt to cloak the underlying trading strategy, or if the 'lingo' is just commonly communicated setups among the 'in the know' crowd. (Being a suspicious sort of person, I tend to think that the use of 'lingo' may be designed to foster insecurity among the normal retail trader, driving them to the 'safe haven' of 'knowledgable' prop firms.) In any case, looks like it just takes patience for us 'out of the loop' folks to get the proper translation. FWIW... I've got to rank high among unsophisticated traders, but I've done OK for 40+- years trading lots of different equities and derivities. I 'fired' my last employer 8 years ago and am worth more now than I was then. My advice... don't let the 'babble' intimidate you. Listen to people like Phil (and others) who have a clear, consistant and unambigious message about managing trades. And when you see 'lingo' that you cannot quickly decipher with tools like google, then be suspicious. I'm off the soap box now. Sorry for the diversion.