Hi - like I said in my original post, these were part of a spread I had in place, not an outright buy. I held these into expiry and they expired worthless.
When the VIX goes from a 13 handle into the 50's in a week, you'd expect some off the charts high standard deviation moves in most underlying's including options. So the fact that your OTM put skyrocketed in value isn't surprising. I guess in your case what's more important is, what spread was the put a part of, and how did the spread do? Maybe you could provide more information. I'm curious why you'd hold anything to expiry.
The term you're looking for is "elasticity" or "gearing," although deep OTM options are really a vega play, not a delta play. https://en.wikipedia.org/wiki/Greeks_(finance) Lambda Lambda, , omega, , or elasticity [4] is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.
Thanks for replying - the rest of the position was nothing really particularly interesting. I had some 85% long puts that I bought earlier in the year with Dec15 expiry and they had been bleeding down in value so when the market dipped I took the opportunity to convert them into 95-85% put spreads and extend the duration for another 6 months for pretty much no cost. But that opened up the tail risk so I simply bought the one month 70% puts as a just-in-case safety net.