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Arithmetic variance swaps
journal contribution
posted on 2023-06-09, 02:28 authored by Stamatis Leontsinis, Carol AlexanderCarol AlexanderBiases in standard variance swap rates can induce substantial deviations below market rates. Defining realised variance as the sum of squared price (not log-price) changes yields an `arithmetic' variance swap with no such biases. Its fair value has advantages over the standard variance swap rate: no discrete-monitoring or jump biases; and the same value applies for any monitoring frequency, even irregular monitoring and to any underlying, including those taking zero or negative values. We derive the fair-value for the arithmetic variance swap and compare with the standard variance swap rate by: analysing errors introduced by interpolation and integration techniques; numerical experiments for approximation accuracy; and using 23 years of FTSE 100 options data to explore the empirical properties of arithmetic variance (and higher-moment) swaps. The FTSE 100 variance risk has a strong negative correlation with the implied third moment, which can be captured using a higher-moment arithmetic swap.
History
Publication status
- Published
File Version
- Accepted version
Journal
Quantitative FinanceISSN
1469-7688Publisher
Taylor & FrancisExternal DOI
Issue
4Volume
17Page range
551-569Department affiliated with
- Business and Management Publications
Full text available
- Yes
Peer reviewed?
- Yes