Choosing Static Replication and Managing Dynamic Hedge Risks

Summary

This discussion considers how to choose between static portfolios that reproduce an option payoff and what can go wrong with dynamic replication. For static alternatives, it highlights transaction costs and instrument simplicity: simpler, more liquid instruments are generally expected to have narrower spreads and lower trading costs. The answer treats these considerations as closely related through liquidity and market impact.

For dynamic replication, the answer identifies several practical risks beyond frequent rebalancing costs. Market jumps can prevent a hedge from matching the option payoff; margin may be required for the hedge if it cannot be cross-collateralized with the option; and short-sale constraints can force a switch to less liquid, more costly options. Longer-dated futures may also be less liquid, while using nearer contracts can introduce basis risk. These are qualitative considerations, with no comparison data or universal ranking; the appropriate replication depends on instruments, financing, liquidity, and market conditions.

Key ideas

• Static replication choices can be compared by trading costs and instrument liquidity.
• Simpler instruments are often more liquid and may reduce spreads and market impact.
• Jumps can cause dynamic hedges to replicate option payoffs imperfectly.
• Margin and short-sale constraints can make dynamic hedging harder or more costly.
• Futures replication can involve a tradeoff between liquidity in distant contracts and basis risk in nearer contracts.

Tags

# Static vs Dynamic Replication


# Static vs Dynamic Replication












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?

## Answer by Newquant (score 0, accepted)

https://quant.stackexchange.com/a/74921

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.