Interesting perspective on volty as function of strike. Here is my "theory/law" on it. If the market goes down faster than it goes up, one would expect (short term) volty to be higher at strike ATM-1, and lower at strike ATM+1. (you can replace -1 and +1 by -epsilon of + epsilon). Volty at strike ATM-2 should be greater than volty at strike ATM-1, because on the way down if underlying reaches ATM-1 strike, strike ATM-2 will be its immediate next down strike, and the at the money reasoning applies. By the process of induction, Volty should be increasing at lower strikes. The induction can alternatively be viewed as an anticipatory process in determining the right voltys. What do you think of this "theory/proof/law" of skew?
do you ever reread what you write? i recommend a proof reader. you said: "for the occasional short straddle" and those are not naked? sure you can tell me that you have a futures position and/or fly's, etc in your book; but no matter what they are naked. even wide spreads are imo essentially naked as the dd will be huge nonetheless. lastly, can you honestly post that you never had at least one dd from short premium? i know i have. my point in all this is to point out that although some here; including yourself still must use short gamma to bring home the bacon. isn't that true, optioncoach? i believe from all my trading that one must have a deep book that uses short premium as the main driver of profits. this post stays on topic also regarding the safety of naked options too!
The speed of moves up vs down is not what drives the skew. Look at natgas - down 40% in less than 2 months - and the otm calls STILL are at a premium to the otm puts. Or silver - down 36% in a month and again, the otm calls still are at a premium to the otm puts. You cannot understand the skew by looking at math or price patterns or distributions of the underlying. That's barking up the wrong tree entirely. If you want to understand the skew of any contract, ask yourself "Who are the participants in this market? What are their financial interests? What scenario is their greatest fear? What scenario will be a relief? What scenario will bring out their greed?"
And you need a proof reader as well since I said I would not recommend naked options to a newbie. You have said nothing to contradict this but claimed I am hypocritical. Do I have short straddles on the index once in a while? Sure in small numbers to play volatiltiy and often I FLY it off. It is not hypocritical for someone with experience to say to a newbie not to trade naked options. But I do not NEED short gamma to bring home the bacon. Been doing just fine with FLYs and Calendars and some directional bets. No one NEEEEEDS short premium to make money, it is just one of many strategies.
Hi tyrant, There is no possible abitrage due to transaction cost, slippage, cost of carry..and parity for european style options. My point is some people who own a pure SP portfolio hedge themself with puts. That's insurance reason. They own SP, they hedge SP. But over there, there are a lot of people who may own a portfolio that is not a pure replication of SP. Those people buy (or sell) puts on SP like a bet. They just want an exposure to a global market, even it's not correleted with their own exposure. As if you pay an insurance for your neighbour car, 'cause if your home burnt, his car would experience the same. There is a psychologic element. One way to be hedge if you own pure SP exposure like SP futures could be a cash extraction. You sell your future and you buy a deep in the money call. Say future is around 1200, you sell it and buy a 1100 call. But people won't do that way because if you pay a 1100 call with a spot at 1200, you have to pay right now the intrinsic value 100. They prefer, for the same final payoff, to pay the symmetric put (strike 1100) and to purchase the future. Psychologically, one doesn't see the same constraint. Transaction costs and liquidity holes keep in mind. Regards
The vol of vol, volga/ vomma or convexity of vega are some reasons for deep and out options to be price higher than a BS suggest. Fat tails are in proportion of vol of vol, and become more important as maturity decreases. Correlation between vol and asset price change a smile into a smirk. But my point of view is about transaction costs as you hedge an option. First a call is not a put (it holds just for forex options). They have different possible final payoffs, are differently impacted by cost of carry and interest rate. If you need to see that, take a look at a theta for a call and the symmetric (the same strike) put. Price it with an interest rate of 2%, and do it with an interest rate of 8%. The result is obvious. So I will explain for a call, and call-put parity will be set for the related put. If you want to hedge a deep in the money call, it will be more expensive than an out the money one. As you can avoid to hedge a small bet, a deep out of the money call, the risk if you don't with a deep in the money one is much more important. You will incur the risk of losing part of intrinsic value of your call. So there is a constaint that you can't skip. The more deep in the money, the more expensive transaction costs and slippage for hedging purpose. If you are deep in the money, gamma and vega are small. Hence, gamma scalping will be a very difficult game 'cause delta won't move until the spot will become closer the strike. The most deep in the money call, the higher cost. That cost will be embedded in option price and deep in the money call will exhibit a higher implied volatility. I don't know you, so I could not answer. Who knows? Do you?
Quote from MasterAtWork: The vol of vol, volga/ vomma or convexity of vega are some reasons for deep and out options to be price higher than a BS suggest. Fat tails are in proportion of vol of vol, and become more important as maturity decreases. Correlation between vol and asset price change a smile into a smirk. OTM calls/ITM puts trade under ATM and ITM call/OTM put vols and therefore have greater convexity/dgamma and dvega. Your "fat tails" implies a smile, yet we have a smirk, hence cheap gamma/vega as shown in the slope of dgamma/dvega on the upside strikes. "Correlation between vol and asset price change a smile to a smirk" It sounds to me as though you're making an argument for portfolio insurance based upon historical precedent. But my point of view is about transaction costs as you hedge an option. [snipped] [Conclusion] The most deep in the money call, the higher cost. That cost will be embedded in option price and deep in the money call will exhibit a higher implied volatility. If so, deep itm puts would carry a premium as well and the vol-surface would reflect a smile, not a smirk. It's the basis of your arguments. Your arguments are in opposition.
No, because if you read what i've written, a put is not a call. There is no symmetry except for forex options. So, my arguments are not in opposition. Smile and smirk are related with correlation between asset prices and volatility. It's not an immutable situation. It varies as market sentiment varies. Try to price your option with a stochastic volatility model and you will see a smile. If you put a negative correlation between asset and volty you will see a smirk, a positive one, you will see the opposite smirk.