Variance Swap Model Dependence Beyond Continuous Diffusion

Summary

The document asks how interest rates and dividends affect variance-swap pricing and delta when replication uses a finite set of options rather than a continuous strip. It contrasts this practical setting with a simplified, zero-rate framework in which continuous option replication makes the payoff appear sensitive only to volatility. The underlying issue is that finite replication leaves exposure to forward prices, which depend on rates and dividends.

The response provides only a brief conceptual qualification: once the continuous-diffusion assumption is relaxed, variance-swap pricing is no longer model independent. It points toward an analysis of jump effects, but does not explain the direction or size of rate and dividend impacts, derive a pricing relation, or answer the delta-sign question. Those specifics cannot be inferred from the material provided and require a fuller treatment of the replication assumptions and model.

Key ideas

• Continuous option replication under simplified assumptions can make variance-swap value appear volatility focused.
• A finite set of options can leave forward-price exposure in the replication.
• Forward prices are affected by interest rates and dividends.
• Relaxing the continuous-diffusion assumption removes model independence from variance-swap pricing.
• The response does not determine the sign of variance-swap delta or quantify rate and dividend effects.

Tags

# Variance Swap : dividends and rates


# Variance Swap : dividends and rates












In a simplified world you can assume that the var swap is replicated by a continuous set of calls and puts and interest rates are equal to zero. So your PNL is only sensitive to the volatility. But in reality, you don't have a continous set of options, and your PNL is sensitive to the forwards so rates and div have an impact on your pricing. How do rates and div impact the pricing of the var swap? And why, intuitively? Also what is the signe of the delta of a var swap?

Thank you!

## Answer by Ezy (score 1)

https://quant.stackexchange.com/a/42897

See this article for the impact of jumps on varswaps

http://www.columbia.edu/~mnb2/broadie/Assets/variance_swaps_jumps_200903.pdf

In general as soon as you leave the assumption of a continuous diffusion the price of varswap is no longer model independent.

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