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<p>This paper shows the relationship between the forward start volatility swap price and the forward start zero vanna implied volatility of forward start options in rough volatility models. It is shown that in the short time-to-maturity limit the approximation error in the leading term of the correlated case with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H\in (0,\frac{1}{2})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> does not depend on the time to forward start date, but only on the difference between the maturity date and forward start date and on the Hurst parameter <i>H</i>.</p>

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Forward Start Volatility Swaps in Rough Volatility Models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月30日

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  • Elisa Alòs,
  • Frido Rolloos,
  • Kenichiro Shiraya

摘要

This paper shows the relationship between the forward start volatility swap price and the forward start zero vanna implied volatility of forward start options in rough volatility models. It is shown that in the short time-to-maturity limit the approximation error in the leading term of the correlated case with \(H\in (0,\frac{1}{2})\) H ∈ ( 0 , 1 2 ) does not depend on the time to forward start date, but only on the difference between the maturity date and forward start date and on the Hurst parameter H.