Daily Delta Hedging in Static Option Replication of Variance Swaps
Summary
The document explains the role of the underlying asset position in a variance swap replication strategy. A short variance swap can be hedged with a strip of options across strikes, often represented in practice by an at-the-money straddle together with out-of-the-money puts and calls. The option portfolio is initially close to delta neutral, but its delta changes as the underlying price moves.
To maintain the hedge, the trader adjusts the underlying position, returning the combined portfolio to delta neutrality at each daily observation or close. Because the option strip is long gamma, an upward move tends to leave it with positive market exposure, prompting a sale of the underlying; downward moves lead to the corresponding adjustment. The accumulated hedge trades are described as capturing realized variance over the swap period. The discussion is a conceptual answer rather than a full derivation: it assumes daily observations and gives no transaction costs, discrete-strike approximation analysis, or treatment of jumps and other replication errors.
Key ideas
- A short variance swap can be hedged with a portfolio of options spanning strikes.
- The option portfolio is usually close to delta neutral at inception, but its delta changes with the underlying price.
- Daily adjustments in the underlying offset the changing delta of the long-gamma option hedge.
- The accumulated dynamic hedge activity is intended to capture realized variance over the contract period.
- The explanation is conceptual and does not quantify costs or replication errors.
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Full text
# varswap replication doubt # varswap replication doubt I have a doubt regarding the varswap replication- I know the portfolio of options with proper weights is a static one, and that there is a dynamic position required in underlying. My confusion is whether this dynamic position in underlying relates to delta hedging of the options i.e. are you required to calculate net delta of your portfolio of options and hedge that? I think it somehow relates to delta hedging as we are finally able to capture difference between implied and realized vol, but cant get my head around it. ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/39430 Well I've never actually traded a var swap but I see no answers so I'll give it a shot. If you are short a var swap, your hedge is to buy options of all strikes. In practice, you buy a ATM straddle and some otm puts of various strikes and some otm calls of various strikes. Initially, this is close to delta neutral. Suppose the payoff of the variance swap is calculated from daily observations of the underlying. Then, you need to get back to delta neutral at the close of business on each day. Thus, if the market has gone up, your portfolio of hedge options has gotten long the market (since it is long gamma), so you need to sell the market to get back to flat. You do this every day. At the end of the trade your hedging activity has realized the actual variance of the stock during the period, which was your goal. ## Answer by user34971 (score 1) https://quant.stackexchange.com/a/53841 Take a look at the following note which explains that indeed the dynamic position in the underlying is from delta hedging the options. I actually still have to complete the note with showing that the aggregate delta of the options portfolio is $1/S_t$, but I have not had time yet. F. Rolloos, Delta Hedging and Variance Swap Replication
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