What is the difference between a variance swap and a volatility swap?
By Matthew Alvarez
What is the difference between a variance swap and a volatility swap?
As you know both var swap & vol swap are traded on vol. The difference comes in convexity. Although variance swap payoffs are linear with variance they are convex with volatility. Because of the convexity, a variance swap will always outperform a contract linear in volatility of the same strike.
Is variance and volatility the same?
While variance captures the dispersion of returns around the mean of an asset in general, volatility is a measure of that variance bounded by a specific period of time.
How does a Vol swap work?
What Is a Volatility Swap? A volatility swap is a forward contract with a payoff based on the realized volatility of the underlying asset. They settle in cash based on the difference between the realized volatility and the volatility strike or pre-determined fixed volatility level.
What is an FX Vol swap?
In FX derivatives: A volatility (vol) swap is a forward contract on the realized volatility of spot over an agreed period. A variance (var) swap is a forward contract on the realized variance of spot over an agreed period.
Does variance swap have Delta?
The delta of a variance swap is its price sensitivity to the movement of the underlying asset: ≡ ∂ V ∂ So . The purpose of this short article is to derive an analytic formula for a variance swap delta. It shows that the delta is determined by the volatility skew and the vega of vanilla options only.
Is Vol standard deviation or variance?
Volatility is Usually Standard Deviation, Not Variance Of course, variance and standard deviation are very closely related (standard deviation is the square root of variance), but the common interpretation of volatility is standard deviation of returns, and not variance.
Does Black Scholes use standard deviation or variance?
A test of the Black-Scholes formula is via the implied standard deviation. Consider a real option selling at a particular price. Using the Black-Scholes formula, calculate what standard deviation is needed to yield this price.
Why do variance swaps have Delta?
The reason for the variance swap having delta is the presence of the skew in implied volatility (for details, see de Weert (2008), Chapter 23): as the spot price goes down, the at-the-money implied volatility will grow up and hence increase the variance swap price.
Does a variance swap have gamma?
The Greeks of the variance swap can then be calculated by differentiating Pt. Since the dollar gamma is achieved by scaling the gamma by the spot squared, this gives a constant dollar gamma as expected. In particular, if the variance strike doesn’t change, theta remains constant.
What is the difference between variance swap and volatility swap?
The replication of a volatility swap is not as simple as that of a variance swap. Variance arises naturally in the P&L of hedged options, which depends linearly on variance. Volatility on the other hand should be viewed as a derivative of variance.
How do you replicate a volatility swap with unit notional?
An approximate strategy replicates a volatility swap with unit notional by a variance swap with notional of 1/ (2. Kvol ), where Kvol is the volatility strike of the volatility swap.
How much is the portfolio worth for a variance swap?
The total value of the portfolio is the sum of all option position prices and amounts to about $40,000 for this variance swap. We now calculate the fair variance and the associated risk statistics for the variance swap using the worksheet “Fair Var”.
Why is the fair strike of a variance swap higher?
The fair strike of a variance swap is slightly higher than that of a volatility swap. This is to compensate for the fact that variance is convex in volatility, as illustrated in Exhibit 2 in the next page. Identical strikes for the two in- struments would otherwise lead to an arbitrage.
