3 ms·

Former options trader here. This all checks out correctly, but there's maybe some intuition that enlightens it. BTW option traders are often called volatility t

Former options trader here. This all checks out correctly, but there's maybe some intuition that enlightens it. BTW option traders are often called volatility traders, because when you look at the formula there's this one free variable (all the rest are somehow given by the market). So when you're trading options, you're trading vol and the actual price is just a sort of formality. Thoughts: - Since you have a right but not an obligation to buy/sell, that creates asymmetry. Since it's asymmetric, a wider range of outcomes, ie higher vol (imagine your gaussian curve on top of the hockey stick), makes the option worth more. - Similarly having more time to expiry makes the option worth more, the range of outcomes is more spread out. - There's a whole bunch of Greeks that the books will go through, but the intuition is the same for all of them. You can work out what's good or bad for you from thinking about how the distribution of outcomes is affected by a change in whatever. - To trade the vol and not a mix of the vol and the direction, you flatten your delta by trading the underlying. If you do this at some point on the option price vs underlying price curve, you can get the graph to be flat, ie neutral to small price moves. But you can't make it flat everywhere with a hedge, because of course the graph is bendy. - Near the strike where the bend is in the hockey stick is where it curves the most. On one extreme the option is worthless, on the other it's the same as having the underlying. - As time passes it's got to get more curvey at the strike, less curvey on the sides. - Curveyness on the price graph is called gamma. This is the gamma that ended up biting with the GME squeeze, by the sound of it. The problem is if you are short options, the graph looks like an upside down parabola, so if the underlying moves up a lot you will be short and getting shorter. If it moves down a lot, you'll be getting longer and longer. This is bad. - It doesn't actually matter whether you are buying the right to buy or the right to sell. If you're buying, you have a positive gamma. But how? Well since owning a put and shorting a call of the same strike (or vice versa) should give you no curvature (looks like a straight line) they must have the same curvature. In the business people just call options with higher strikes than the current underlying price "calls" and options with lower strikes "puts" regardless of what they actually are. In-the-moneys just have some more premium attached to them, but act the same (in terms of everything other than delta) as their partner out-of-the-money option at that strike. - Why do people get short gamma, knowing that movement is bad for them? Of course the option costs something to the guy who buys them. As long as the movement isn't too much it might be worthwhile to be short. In fact, most of the time the movement isn't enough to justify the price.

JumpCrisscross 6y ago
(Thank you.)
blake1 6y ago
All good points. All I would add is that it costs money to flatten the delta every day, or delta hedging your option. Each time the stock changes direction, you pay the bid-ask spread. The number of times this happens is proportional in some way to the volatility—that free variable you mentioned—so you can speculate that the market's number is too high or low. If the market is too high on volatility: sell the option and you'll end up paying less in delta-hedging costs. If that market is too low on volatility: do the opposite.
FabHK 6y ago
> higher vol [...] makes the option worth more. > Similarly having more time to expiry makes the option worth more [...] These two observations become unified when one observes that the two variables sigma (vol) and (T-t) (time to expiry) only ever enter the Black-Scholes formula together, as sigma^2 (T-t) (which is the variance of the log return to expiry). (That leads to the observation that the unit of vol is 1/sqrt(time), normally a^(-1/2) [a=annum=year]). Next, you alluded to it, but let's make explicit the way to trade implied vol: Suppose (WLOG) that you think implied vol is too low. Then you buy it (buy cheap, sell expensive...) in the market (buy buying calls and/or puts). Now you're long gamma, but short theta, and long vol in two senses: a) if the stock doesn't move, but implied vol goes up, you can turn around and sell the option back for a profit. b) you can delta hedge the option. Every day, you lose money on theta, but gain money on the movements of the stock. If it doesn't move at all, you lose the theta. If the stock moves "as expected" (=as implied by the implied vol), you'll just break even. But if the stock moves more than expected (that is, realised vol is higher than the implied you bought it at), then you make money. If the market comes around to your estimate of the future vol, you can then sell the option at a profit, or you can hold it to the end and keep delta hedging, and that will be profitable if realised vol turns out to be higher than implied.

JumpCrisscross 6y ago

(Thank you.)

blake1 6y ago

All good points. All I would add is that it costs money to flatten the delta every day, or delta hedging your option. Each time the stock changes direction, you pay the bid-ask spread. The number of times this happens is proportional in some way to the volatility—that free variable you mentioned—so you can speculate that the market's number is too high or low. If the market is too high on volatility: sell the option and you'll end up paying less in delta-hedging costs. If that market is too low on volatility: do the opposite.

FabHK 6y ago

> higher vol [...] makes the option worth more. > Similarly having more time to expiry makes the option worth more [...] These two observations become unified when one observes that the two variables sigma (vol) and (T-t) (time to expiry) only ever enter the Black-Scholes formula together, as sigma^2 (T-t) (which is the variance of the log return to expiry). (That leads to the observation that the unit of vol is 1/sqrt(time), normally a^(-1/2) [a=annum=year]). Next, you alluded to it, but let's make explicit the way to trade implied vol: Suppose (WLOG) that you think implied vol is too low. Then you buy it (buy cheap, sell expensive...) in the market (buy buying calls and/or puts). Now you're long gamma, but short theta, and long vol in two senses: a) if the stock doesn't move, but implied vol goes up, you can turn around and sell the option back for a profit. b) you can delta hedge the option. Every day, you lose money on theta, but gain money on the movements of the stock. If it doesn't move at all, you lose the theta. If the stock moves "as expected" (=as implied by the implied vol), you'll just break even. But if the stock moves more than expected (that is, realised vol is higher than the implied you bought it at), then you make money. If the market comes around to your estimate of the future vol, you can then sell the option at a profit, or you can hold it to the end and keep delta hedging, and that will be profitable if realised vol turns out to be higher than implied.