Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a 3/2 Volatility Model
Abstract
This paper investigates the pricing and hedging of variance swaps under a 3/2 volatility model. Explicit pricing and hedging formulas of variance swaps are obtained under the benchmark approach, which only requires the existence of the num\'eraire portfolio. The growth optimal portfolio is the num\'eraire portfolio and used as num\'eraire together with the real world probability measure as pricing measure. This pricing concept provides minimal prices for variance swaps even when an equivalent risk neutral probability measure does not exist.
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