Hi,
I’m trying to analyze the risk position of one of our option traders. I asked why the portfolio’s delta has decreased significantly during the last month. He replied:
“delta was decreased due to gamma effect caused by the increase in interest rates (portfolio is short volatility).”
Could someone explain what does this mean? Please explain it as you would be speaking to a golden retriever, as it is not my smarts that got me this position.
At least part of the reason for your lack of understanding is that his reply is nonsense.
Delta measures how fast an option’s price changes when the price of the underlying (stock, say) changes. Gamma measures how fast an option’s delta changes when the price of the underlying changes. But gamma doesn’t cause delta to change; it simply measures it.
When options are far out of the money, their price doesn’t change much when the price of the underlying changes, so delta is near zero. Furthermore, delta doesn’t change much, so gamma is near zero.
When options are far in the money, their price changes a lot when the price of the underlying changes: nearly one-for-one for calls and negative-one-for-one for puts; delta is near 1 for calls and near −1 for puts. But delta doesn’t change much, so gamma is near zero.
Things get more exciting when the option is close to the money. When that’s the case, a price change in the underlying will cause a change in the price of the option, and also result in a change in the delta of the option: it’s the area in which the delta for a call is transitioning from near zero to near +1, and the delta for a put is transitioning from near −1 to near zero. Because delta is changing (increasing, in fact, when the price of the underlying increases), gamma is positive. But gamma is not causing the change in delta; it’s merely measuring it. The change in delta is caused by a change in the price of the underlying (and the nonlinear nature of the payoff for the option).
When interest rates increase, the price of a call option will increase and the price of a put option will decrease. However, delta won’t change much merely because interest rates change. A little, but not much.
The real answer about why delta changed is that the price of the underlying changed on options that were close to at-the-money. If you have access to the data, look at the price(s) of the underlying(s) and the strike prices on the options.
I hope that that helped.
Thanks a lot for your thorough reply. I really appreciate it. I’ll try to my wrap my head around this during the next couple days.
I read somewhere that there is a thing called “gamma trap”. Do you know what it is and is it related to this situation?
I just read about the gamma trap.
It’s related to your original question in that it’s a nonsensical way of trying to explain a phenomenon: trying to make the explainer sound a lot more sophisticated than they really are.
The gamma trap occurs when you’re short gamma and the price of the underlying moves a lot: you can lose a lot of money.
Options have positive gamma, as I mentioned. So . . . if you’re short options (calls or puts or both), you’re short gamma; i.e., your position has negative gamma. If you’re short puts and the price of the underlying goes down a lot, you’re in trouble; if you’re short calls and the price of the underlying goes up a lot, you’re in trouble. The trouble is caused by the change in the price of the underlying coupled with your short option position; it’s not caused by negative gamma: you would have the same problem if gamma were zero.
Sigh.
If you can’t dazzle them with brilliance, something something… 
I have another question related to a similar analysis but on a different desk, which deals just interest rate caps, floors and vanilla swaps in EUR. We use CVaR for risk management purposes. It’s basically just an average of tail dates. The net delta risk across all buckets (0-40YR) is basically zero. The head of trading (the same dude as in the earlier example) said that “there isn’t almost no curve risk”.
Yet, last week when the euribor rose in the short end of the curve and significantly in the 2Y-10Y buckets, but interest rate delta’s contribution to total CVAR increased by 40%, but our net delta decreased.
I guess what I’m trying to say, is that, I don’t understand how these three things can happen simultaneously: