In the book Stock Market Wizards, author Jack Schwager interviewed a very intelligent options trader John Bender. I highly recommend you read the whole interview because it really explains some options concepts intuitively without the use of any math. Nonetheless, below are some very rich points that Bender makes on option pricing and risk taking. Sorry for the lengthy quotes, but reading them in their entirety paints the best picture (no one could really have explained skew or model fitting better).
On Random Walk Assumption of Black Scholes
Black Scholes assumes stocks follow a random walk, returns are normally distributed, which is not always a good model. John Bender gives an incredibly elegant counter to the random walk assumption by discussing how trading stops could actually accelerate the price movement of stocks and therefore make larger moves more probable than smaller moves. When reading this, I understood for the first time the overall beauty of 1x2 or 2x1 call spreads; you can also guess the reasons for skew in this passage. In the same way, if one were to bet against a cash merger (take the view that the merger would fall apart) via options, one could sell some put options near the current spot / deal price, but buy a higher quantity of downside put options which are more out of the money. News of a break-up of the deal would likely cause the stock to fall violently; hence, large movements are more likely than smaller movements in this case. Also, in the first paragraph, Bender discusses how stops might trigger a "slippery strike" effect; Paul Tudor Jones also spoke about his experience on the floor where he tried to force the price of a commodity through certain levels where there could be a lot of stop-loss orders.
"The best example I can think of involves the gold market rather than stocks. Back in 1993, after a thirteen-year slide, gold rebounded above the psychologically critical $400 level. A lot of the commodity trading advisors [money managers in the futures markets, called CTAs for short], who are mostly trend followers, jumped in on long side of gold, assuming that the long-term downtrend had been reversed. Most of these people use models that will stop out or reverse their long positions if prices go down by a certain amount. Because of the large number of CTAs in this trade and their stop-loss style of trading, I felt that a price decline could trigger a domino-effect selling wave. I knew from following these traders in the past that their stops were largely a function of market volatility. My perception was that if the market went back down to about the $390 level, their stops would start to get triggered, beginning a chain reaction.
I didn't want to sell the market at $405, which is where it was at the time, because there was still support at $400. I did, however, feel reasonably sure that there was almost no chance the market would trade down to $385 without setting off a huge calamity. Why? Because if the market traded to $385, you could be sure that the stops would have started to be triggered. And once the process was under way, it wasn't going to stop at $385. Therefore, you could afford to put on an option position that lost money if gold slowly traded down to $385-$390 and just sat there because it wasn't going to happen. Based on these expectations, I implemented a strategy that would lose if gold declined moderately and stayed there, but would make a lot of money if gold went down huge, and a little bit of money if gold prices held steady or went higher. As it turned out, Russia announced they were going to sell gold, and the market traded down gradually to $390 and then went almost immediately to $350 as each stop order kicked off the next stop order.
The Black-Scholes model doesn't make these types of distinctions. If gold is trading at $405, it assumes that the probability that it will be trading at $360 a month from now is tremendously smaller than the probability that it will be trading at $385. What I'm saying is that under the right circumstances, it might actually be more likely that gold will be trading at $360 than at $385. If my expectations, which assume nonrandom price behavior, are correct, it will imply profit opportunities because the market is pricing options on the assumption that price movements will be random."
On Fitting Prices to the Market
Sell-side bank traders can easily apply Bender's comments to their own lives. Most models will never be perfect, but in order to be prepared for client orders, flow desks and market makers continually "fit" their parameters to the market. Even if the pricing model is wrong/insufficient, one can still get the correct prices if one keeps tweaking inputs enough. As a result, it's important for one to know the short-comings in models and also if one parameter is compensating for another parameter in the pricing.
Schwager: Don't other firms such as Susquehanna [a company whose principal was interviewed in The New Market Wizards] also trade on models based on perceived mispricings implied by the standard Black-Scholes model?
Bender: When I was on the floor... I was typically trading on the other side of firms such as Susquehanna. They thought they had something special because they were using a pricing model that modified the Black-Scholes model. Basically, their modifications were trivial.
I call what they were doing TV set—type adjustments. Let's say I have an old-fashioned TV with an aerial. I turn it on, and the picture is not quite right. I know it's supposed to be Mickey Mouse, but one ear is fuzzy and he is a funny color green. What do I do? Do I sit down and calculate where my aerial should be relative to the location of the broadcast antenna? No, I don't do that. What I do is walk up to the TV, whack it a couple of times, and twist the aerial. What am I doing? I'm operating totally on feedback. I have never thought once about what is really going on. All I do is twist the aerial until the picture looks like what I think it should—until I see Mickey Mouse in all of his glory.
The market-making firms would make minor adjustments to the Black-Scholes model—the same way I twisted the aerial to get Mickey Mouse's skin color to be beige instead of green—until their model showed the same prices that were being traded on the floor. Then they would say, "Wow, we solved it; here is the model!" They would use this model to print out option price sheets and send in a bunch of kids, whom we called "sheet monkeys," to stand on the floor and make markets. But did they ever stop to think about what the right model would be instead of Black-Scholes?" No. They merely twisted the aerial on the TV set until the picture matched the picture on the floor.
This approach may be okay if you are a market maker and all you are trying to do is profit from the price spread between the bid and the offer rather than make statements about which options are fundamentally overpriced or underpriced. As a trader, however, I'm trying to put on positions that identify when the market is mispriced. I can't use a model like that. I need to figure out fundamentally what the real prices should be, not to re-create the prices on the floor.
Again, if you have the time, I would recommend you pick up a copy of the Stock Market Wizards book or try to find a copy of the interview.
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http://relavalue.blogspot.com/2013/12/investing-finance-book-recommendations.html
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