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Ex derivs trader here. If you want to understand this, here's a short explanation. 1. Options have asymmetric payoff. One way you win, the other way you don't
by lordnacho 6y ago
Ex derivs trader here. If you want to understand this, here's a short explanation.
1. Options have asymmetric payoff. One way you win, the other way you don't lose, assuming you are the buyer. The opposite is true for the seller.
2. Because of the asymmetry, movement is positive for the owner. So the option is priced based on how much movement is expected. There's a distinction here between vega and gamma, which are both movement related. Vega is sensitivity to the appraised future volatility, which means the option has more of that if it's long dated. Gamma is (2nd deriv) sensitivity to movement in the current price, so you'll have more of that if you're near the expiry.
3. As an options market maker, you are not in it to guess which way the underlying stock goes, you are in it to gain an edge in pricing that movement risk. So you hedge it when you trade an option with someone. If you buy a call, you sell some underlying so that your delta is flat. (Delta is just the 1st order price sensitivity)
4. If you flattened your delta, you can imagine the gamma making your local PnL vs price a parabola. If you are long the option you'll make money when the price moves either way, and you'll be needing to buy low and sell high to get back to flat delta. (Incidentally this is also why we don't really care whether it was literally a put or a call, as in the right to buy or sell. The 2nd order is the same, so has the same effect on your PnL when the price moves.)
5. The opposite is a less nice position to be in. The more the price moves, the more wrong your position is. In fact, the more it runs away, the more you have to push it the wrong way, because you'll be selling into a falling market or buying a rising one.
6. Natural question is, why would anyone ever be short gamma then? Well, you're going to charge people for their gamma, and if things turn out right you'll have charged them more than it's worth in terms of potential movement that they can buy low and sell high on.
7. So what happens with squeezes? Well sometimes that gamma gets so out of hand, there's some player with a huge wrong position squirming to flatten his position, but he is pushing it further and further away with each trade. Note that near expiry, a lot of things get hairy. You can imagine the gamma gets really spiky near the strike, because the time value is coming out of the price, and so you have a discontinuity at that corner. Also with binaries, knock-outs, and other simple non-vanilla options, you get some weirdness that can momentarily cause some large sensitivities. I've seen more than a few days where someone is defending some level and the price action looks odd.
8. Isn't the pressure the opposite for someone else somewhere? Technically yes, but often incentives are not the same for different agents. Different players have different risk tolerances, and they have different business models. For instance if someone has taken a load of options and shoved them into a structured product, maybe they're not quite as worried about hedging it as someone who doesn't have that customer flow. Or someone just has some cash to take a punt on the option, and they don't care if it expires worthles. Remember it's not just the two people who traded the option, there's the market in the underlying as well. Interestingly that means you can trade an option with me and we can both make money.
- anonymouse008 6y agoExcellent and beautiful explanation. I've been wondering if Elon's TSLA comp package was designed with this in mind. It really would be perfect SEC like move.
- im3w1l 6y agoI haven't seen so much information explained so briefly since Rudin, kudos!
- beezle 6y agoOn your points: 1/ Vega is sensitivity of option price to change in level of implied volatility. Appraised is an unusual word choice. You'll have more gamma if the asset price is near the strike price of the option. But gamma can actually be lower near expiration for the same strike if its fairly out of the money - gamma will only be higher for at/near the money options. 6/ Market makers buy and sell volatility and outside of retail, prices are usually quoted in vol terms. That's not to say that professionals can't do some crazy things trying to hedge risk, including theta (time) and rho (interest rates) but the original trade is a vol trade first and foremost. My slightly different explanation: Delta is the 1st deriv change in price of the option wrt the value of the underlying asset. Gamma is the 2nd deriv, ie the rate of change of delta. As expiration approaches, gamma gets very like a dirac delta function, centered at the strike price. Easy to understand - moments before expiration a call option value is either worthless or exactly (Underlying - Strike price) Thus a delta of either 0 or 1 (-1 if you are short) with gamma equal to delta. As the original poster explained, traders hedge by buying or selling the delta amount of the underlying (if delta is 0.5, you do 50% of your notional contract size). As the underlying moves, the short trader needs to buy when the underlying rises (his negative delta is increasing) or sell when it falls (his delta is decreasing so less hedge needed) to maintain a 'neutral' position wrt to small changes in the price of the underlying. Recall, gamma is the rate of change of the delta and so determines how much the hedge needs to change. On day of expiration at the money strikes have very high gamma and thus subject the short option trader to large whipsaw risk - the need to add or remove a hedge aproaching 100% while chasing the underlying. The art is really in deciding when to hedge on/hedge off and how much, regardless of the formulaic delta and gamma values at the current underlying price.