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These are extension questions to Joshi's Quant Interview Book.

(1) Given the choice between two different static replicating portfolios that match an option's payoff, what criteria would you use to decide between the two?

-- The first things that come to my mind are the following:

(i) Which replicating portfolio has cheaper transaction costs.

(ii) Which replicating portfolio has 'simpler' instruments (these would be more liquid and should have lower spreads; makes more sense to have a static replicating portfolio of calls and puts rather than of exotic options, for example)

Are there other criterion that I am missing?

(2) What are some of the practical problems of dynamic replication?

Besides things like T-costs from daily rebalancing etc., what else is there to mention here?

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Would argue that point 1.i and 1.ii are the same. Transaction costs/market impact are synonymous in my opinion - and simpler usually means more liquid.

Issues with dynamic replication include jump risk leading to imperfect replication. Also argue that when not dealing with a prime you can have to post margin for the hedging side if it's not able to be cross-collateralised with your option position. Sometimes stocks are unable to be shorted (have to use options, less liquid, higher tx cost) or are prohibitively expensive to short. If using futures to replicate longer duration options then the far futs can be less liquid, but using the front month can incur basis risk.

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  • $\begingroup$ Thank for your answer. Just two quick points: (1) What did you mean by 'when not dealing with a prime' and by 'cross-collateralised with your option position'. I know when posting margin, you can offer collateral but what do you mean by cross-collateralize? $\endgroup$ Commented Mar 14, 2023 at 7:27
  • $\begingroup$ A prime is a prime broker. Among other things, they can give you access to multiple exchanges through their system and allow trades on different venues to offset one another. I.e long/short the same asset on different exchanges where they're mispriced. If you as an individual were trading alone then you may not have this ability. Cross-collateralised just means that positions can collateralise one another. So your option position P/L and hedge P/L would be mixed and count towards one another, allowing for efficient delta hedging. This is a common problem in new classes like crypto. $\endgroup$ Commented Mar 14, 2023 at 8:45

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