Static Replication and Dynamic Rebalancing in Hedging
Summary
The document explains when a hedge can be established once and when it needs ongoing adjustment. Static hedging is possible when instruments can replicate a position’s payoff at inception; the payoff need not be linear. The example given is replicating a call with a put and a futures contract, which can remove contract risk if the replication is exact.
When using only the underlying to hedge, the response says that more frequent rebalancing reduces exposure to underlying price changes but raises trading costs. Infrequent hedging can mean setting delta once and leaving it unchanged, allowing delta exposure to build as spot moves. A super-hedge, such as shorting a future against a long call, can instead keep the combined payoff nonnegative, with its own trade-offs. The discussion is conceptual and gives no empirical comparison or detailed conditions for replication; the best choice depends on the hedge objective and available instruments.
Key ideas
- A payoff can be statically replicated even when it is nonlinear.
- More frequent underlying hedging reduces exposure to price moves but increases trading costs.
- A delta hedge set at inception can drift as the underlying moves.
- A super-hedge can bound payoff risk but has different costs and trade-offs.
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# Static vs Dynamic Hedging: when is each one used? # Static vs Dynamic Hedging: when is each one used? I understand that, in Static Hedging, you don't have to keep rebalancing the offsetting position(s) while in Dynamic Hedging you have to constantly keep re-adjusting it. What I'm not clear on is when is each one used? Is it that Static Hedging can only be used for linear payoffs while Dynamic Hedging is for non-linear ones? Or does it have to do with path-dependence of the payoffs? Also, can someone please recommend a good book about Static/Dynamic hedging? (something other than Taleb's which I found a bit chaotic to follow). Thanks. ## Answer by StackG (score 8, accepted) https://quant.stackexchange.com/a/59115 It depends a little bit what you're trying to do. - If you can statically replicate the payoff of a position at $t=0$, then putting on that hedge will insulate you from all risk coming from the contract. Payoff doesn't need to be linear - for example, you can perfectly replicate a call option using a put option and a futures contract - If you want to use only the underlying as a hedge, then the more frequently you re-hedge, the lower your exposure to underlying moves will be - but the strategy will be more costly as you need to trade more of the underlying to hedge - The limit of infrequent re-hedging would be to hedge your delta at inception and never again, or to super-hedge your position (eg. going short one future will cover a long call position, so payoff will always be positive), there are strengths and weaknesses to either approach but you'll build up delta due to spot moves over the lifetime of the trade My recommendation for a reference on static and dynamic hedging is this practitioner's textbook on vol trading (vol trading is all about your hedging strategy), and in particular he discusses the trade-offs between frequent and not-so-frequent re-hedging in detail.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.