Once again, a variance swap is not just the log contract. It's the log contract plus dynamically hedged $1 worth of stock.- Greeks of a variance swap (under B-S): Vega decreases linearly with time; Delta zero (but...); dollar Gamma constant.
- Two disadvantages of straddle (even if delta-hedged), as compared to variance swap, are that 1) volatility exposure rapidly diminishes as soon as asset price moves away from strike; and 2) path dependence of P&L.
- Due to these subtle differences between variance swap and delta-hedged straddle, the combination of the two is a neat way to trade the variance convexity. However the moving-underlying problem is still present and the delta-hedged straddle leg of this trade has to be periodically re-struck.
- Taking a step back, the reason why volatility capturing using vanilla option (or a porfolio of them) depends on path is that the Gamma of the option/options changes as underlying moves.
- Interest rate term structure has a short end (short rate) that is quite stable; on the other hand the short end of the variance term structure can move substantially and abruptly.
Reference: JP Morgan Variance Swap
Further readings: Correlation trading, volatility skew trading using Gamma swap
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