Need a favor from the community. Was interviewing a guy today and asked him a few intermediate options questions. Since he failed to answer any of them, I wanted to check if people find these questions overly difficult.
(1) When would you early ex an American call? Is there any uncertainty and how does it manifest? Is there a situation when you would early-X an American put?
(2) Why is it dangerous to delta-hedge a far-OTM options position? Which would would be more dangerous, long or short?
(3) Could you imagine a situation where a call will have delta greater than a 100%?
It would be really awesome if you can PM me the answers. I promise to post the right one here tomorrow, but I really would like to figure out how many people answer these right and what level they felt these question are.
Those are hard questions
Saw this too late to respond, but thanks for this, these were fun to think about. A few questions if you have time: 1. Got the put side, but was curious about the call side since in an ideal black scholes world where you could sell the option, the price would include the dividend and would generally be the better choice since you also don’t give up the extrinsic value (is it the case in practice that you often can’t find someone to take the other side in time to get the dividend?). 2. Got this one too, but I can see a possible confusion since there might be some path dependency to the positions (e.g. the argument clearly makes sense to me if the questions is whether you should go long an otm option and hedge it, but seems less valid relative to the short side if you imagine that you’re already long the option ). 3. Didn’t get this one at all, but if we assume sticky deltas and a steep enough skew then this seems possible (is there some no arbitrage argument for why this doesn’t make sense or is it just impractical).
Btw I’m a quant who used to price some slightly exotic commodity options so the put funding stuff was included in the first thing I read on American options, dividends were a non factor, and the not hedging long otm options came up in practice a couple of times.
PS. A bunch of people, mostly market makers, run a strategy where they go long and short American options prior to the ex-div date, hoping that the shorts will forego/foreget the early-X. If I recall correctly, a certain bank lost about 20 bucks on this exact strategy a few years back because they actually forgot to act on their side of the trade.
Yeah I thought about it some more and realized I was being an idiot on the call dividend stuff (that’s what I get for ignoring the q in my American option pricing models since I never had to deal with them).
On the hedging long otm options front I still think there’s an issue when expressed in expected value terms, but if I consider it in terms of sharpe ratios then it starts to make sense. Unhedged short vol strategies tend to have higher sharpe ratios most years, and in a scenario where you can adopt such a strategy without the tail risk I.e. by not being long very otm options, or simply limiting their downside volatility by not hedging them, then as long as the risk return ratios are what you care about the choice is obvious. Now maybe this could be interpreted as showing an issue with sharpe and similar ratios, but either way for traders who are judged and paid on them, anyone worth their salt would quickly realize that they’re better off not hedging or under hedging long otm options (thus this is maybe more a fit/experience question than a math question).
Still somewhat interested in your take on sticky deltas with regards to question 3, but I guess if we’re talking skew at all we’re already violating the constant vol assumptions of a vanilla bs world (and the answer you were looking for is clearly more salient when your goal is to filter for practical experience and not just their grasp of various models).
Ps: Interesting story, i can totally picture the risk and middle office guys who used to claim they were “integral to the desk” throwing smoke bombs and changing their resumes (assuming here that the traders involved were just fired immediately).
Generally agree, but could still picture a situation where maybe the sticky skew stuff could come up (e.g. price moves a lot in favor of your long call so it’s now at a strike far enough out of the money that it’s illiquid enough for bid ask spreads destroy any actual potential for executing the arbitrage but your model’s deltas still take skew into account, though I guess in that case it might be more natural to say that your model is bad then that delta is greater than 1 ).
Didn’t mean to insinuate anything about your candidate, I have no idea what he’s about (could easily picture a dood with his level of knowledge being a junior trader who landed his seat cus he was in the right place at the right time or as somebody who used options more as leveraged flat price plays than vol arb stuff), was more just thinking about my own experiences (the last place I worked sucked so this sort of blame passing ended up happening a lot, though options were usually not really a part of it).