Interpreting Incremental PnL in a Variance Swap

Summary

The document presents a proposed interval PnL expression for a variance swap: squared log return minus implied variance multiplied by the interval length. It defines the return over consecutive times and asks how this expression follows when the position is risk managed at a fixed implied volatility. The expression frames realized variance accrual against a fixed variance benchmark, making the distinction between realized and implied variance central to understanding the trade.

The text does not provide a derivation, evidence, or a worked example; it is a question rather than a complete explanation. Interpreting the formula requires attention to contract conventions, units, annualization, and the assumptions used to approximate or replicate variance exposure. The interval expression alone does not specify whether it represents a normalized payoff, a hedged mark-to-market change, or the full PnL of an actual variance swap position.

Key ideas

• The proposed interval payoff compares squared log return with implied variance accrued over the interval.
• The volatility input is held fixed in the expression.
• The document asks for a derivation but does not supply one.
• Contract conventions and scaling affect how the expression maps to traded PnL.

Tags

# VarSwap PnL formula


# VarSwap PnL formula












I came across this formula for the varswap PNL: let $r_i$ be the log return over $[t_i,t_{i+1}]$ and suppose we risk manage the VS at a fixed implied volatility sigma, the PnL of (the payoff) over time interval $[t_i,t_{i+1}]$ is: $$ r_i^2-\sigma^2*\Delta T\ $$ Do you know how the author gets this formula?

Thanks!

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