Is your gamma, vega and theta neutral position giving you a delta risk? I had built similar position in the past, and it survived the vega risk very well. However, it was very difficult for me to close the position because of a higher bid-ask spread that usually comes with a higher volatility. What is a better way to close this type of multilegged position to reduce the slippage. To close the whole position, i ended up with a small loss even my calculator showed i had a decent gain.
Be carefull with interest rates you're using. Option models are based on the assumption that, you're able to borrow and lend money using the same interest rate (even for banks it's not true). Are option models based on that assumption, or is that just a common misconception? I would say that if a lender uses his own rate, and a borrower uses his own rate, then everybody gets the right price and the model works as intended. Yes, that does result in a different "fair price" perhaps for the buyer and the seller, but nothing wrong with that. The third problem is that different interest rates lead to different implied volatilities for the same market price. Which one will give you a correct information about volatility ? You can't have different expected standard deviations for the same price at the same time. Aren't you playing devil's advocate here MAW? You and I have agreed in the past that the implied volatility doesn't really imply much about actual volatility - that it's better thought of as the "adjusted price" of an option. As for GARCH - I probably should have said that Hoadley provides tools that allow you to calculate volatility over a past period of time, using closing prices, high-low prices, or high-low-close prices. Admittedly that doesn't tell you where volatility is going, but it tells you where it's been. And if you look in another thread maw - I think the straddles thread - you will be happy to see that I have quoted from "the bible." It seems that the bible's author, Espen Haug, has come down on both sides of the issue of how much option pricing models are used - claiming as co-author of one article that they are entirely unused, and claiming in his book that they are the most-used mathematical models the world has ever seen. Like the author of that other Bible, Haug works in mysterious ways!
All right, well, Taleb and Haug are Ph.D.'s and I'm not so if they tell me I only think I've been using these models extensively for the past 25 years and that I really wasn't - who am I to argue? To me, they're just playing games with language - and I fail to see the point. I can play that game too. I can define "using a hammer" as driving nails under 1 inch long. By that definition, if you're using a hammer to drive nails 2 inches long, you're not really using a hammer, even if you think you are. I could even come up with a historical reason to justify my definition. Maybe I could show that when hammers were invented, nails never exceeded 1 inch in length. So all the 2-inch-nail-driving people today who think they are using hammers are mistaken, because the inventor of the hammer never knew hammers could be used that way. I could do that, but why? What's the point? Unless of course I'm in academia and have to "publish or perish." In that case I might have an incentive to play such silly intellectual games. That's what Taleb and Haug do in their article. They create a ridiculously narrow definition of what it means to "use" an option pricing model and then show that - according to their artificially restrictive definition - nobody actually "uses" pricing models. So even if I use option pricing models a hundred times a day to make critical option trading decisions, by their definition I'm not "actually using" a pricing model. But whatever Haug's definition of "use" is, I still wonder how he reconciles that nobody actually "uses" these models in his paper, but that more people "use" these models than any other mathematical tool according to his book.
Dmo, The fact that a model is wrong doesn't prevent people to still use it. Basically, if you're using something like Black-Sholes or Cox Ross Rubinstein framework, your assumption is that volatility is a constant. How can we imagine to calculate Vega, that is the first derivative an option price with respect to volatility, ie volatility variation rate, that way ? Variation rate of something that is a constant, is always....zero. Dave, for sure volatility is not constant, and for an option trader that's what make money. But it's irrelevant with model framework. why don't we talk about constant interest rate that is implied in option pricing? As for Vega, the same for Rhô. There is no such a thing than a steady volatility and a steady interest rate in real life. Options were traded before option pricing models were built, with heuristic rules and tricks. Models are tools and nothing more.
I've re-read the article by Taleb and Haug, and I still see only intellectual masturbation. Since I see nothing but specious arguments and distortion in the article from start to finish, it's hard to know where to begin explaining why. But here's a smattering. - One major criticism is that the BS model is derived from a "thought experiment" involving dynamic hedging. Dynamic hedging is impossible in reality. Therefore the entire model is built on a fallacy and no one can possibly use it as its authors conceived it. Well, I can think of another Nobel prizewinner who was famous for his thought experiments - Albert Einstein. His involved such absurdities as people running at the speed of light. From these "silly" thought experiments Einstein had some of the deepest insights anyone's ever had, which have found wide practical application in astronomy, warfare, and others. Would you say that an astronomer calculating how much a planet bends light is not "really using" Einstein's work because he cannot run at the speed of light? By the same token, the insights arrived at through the thought experiment using dynamic hedging have found wide application among option and derivative traders, even though the thought experiment that produced the insights cannot be replicated in the real world. - Another criticism is that the existence of put-call parity makes the BS formula unnecessary. Even before BS, "Based on simple arbitrage principles [option traders] were able to hedge options more robustly than with Black-Scholes-Merton." That works great for pricing the put if you already know the price of the call at the same strike, and vice versa. But what if you're dealing with illiquid options and don't have a price for either the put or the call? You'll need a pricing model. - I guess my favorite criticism is that we don't "really use" the model, even if we think we're using it. Doesn't this remind you of Bill Clinton's "It depends on what the definition of 'is' is." If this is the intellectual level of Taleb's case, then why even bother to discuss it? On a personal level, I guess I find the whole article offensive because I first stepped into an option pit in 1984 with a grand total of $15,000 in my account. I've managed to increase it since then, but would not have been able to do so without the BS and Whaley pricing models. I must have made hundreds of thousands of markets in my life, risking lots of money each time. I am the furthest thing from a seat-of-the-pants option trader you can imagine, so every time I made a market, I relied totally on a pricing model. The models have not let me down. When I was on the floor I would take the opposite position of whatever the public was doing. As a result, my positions grew randomly into an incomprehensible mish-mash of 5,000 to 6,000 long and short options at every strike and in every month. I was able to manage that incredible jumble with almost surgical precision using the BS and Whaley models. The model has worked. The model bought me the house I live in. The model has provided me with a living for 25 years. So if I "never really used it," okay, sure, whatever.
Please Dmo, replace this article with the context. Both claim that Black and Scholes only steal an 1900's option model, Bachelier's, and never thank Ed Thorp to be the one who derives the actual form. They were happy then to accept the one million dollar for the Nobelprize's formulae. Take a look at Bachelier's formulae (1900), I'm sure you will change you mind. You then would take another look at Nelson (1904), Sprenkle(1964), Boness(1964), Samuelson(1965)...well before Black and Scholes and every prices are near, sometimes the same as the Black and Scholes ones. No one made a assumption like continuous dynamic hedging.