When Static Variance Swap Replication Extends Beyond GBM

Summary

The document raises a modeling question about the standard static hedge for a plain vanilla variance swap. It observes that familiar derivations often assume geometric Brownian motion with constant drift and volatility, then asks whether the replication remains valid with stochastic, time-varying volatility or under other continuous price dynamics.

No derivation, answer, or empirical evidence is included. The post identifies an important scope issue: replication claims depend on assumptions about the underlying process, especially whether jumps are allowed. It should therefore be read as a question motivating analysis of variance swap replication, not as a proof that absence of jumps alone is sufficient. Practical conclusions require specifying the payoff, monitoring convention, and admissible dynamics.

Key ideas

• Standard variance swap replication is often derived under geometric Brownian motion with constant parameters.
• The post asks whether stochastic volatility is compatible with the static hedge.
• It also asks whether any continuous underlying dynamics suffice, provided there are no jumps.
• The document leaves these questions unanswered and supplies no evidence beyond the modeling concern.

Tags

# General assumptions for var swap replication


# General assumptions for var swap replication












I've seen claims that the standard static-hedge for a plain vanilla variance swap holds so long as the underlying doesn't jump, but every derivation I have seen begins by assuming the asset follows a GBM with fixed drift and volatility rates $\mu$ and $\sigma$. How general is the replication argument? Can $\sigma$ be stochastically time-varying? Can the underlying asset have any dynamics so long as it is without jumps?

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