Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model

Details Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model

2010-07-18

arxiv.org/abs/1007.2968v2

Economy

Quantitative Finance

Pricing of Securities

23 pages, 5 figures

Scientific paper

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\'{e}raire portfolio. The growth optimal portfolio is the num\'{e}raire portfolio and used as num\'{e}raire 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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