Derman’s Volatility Approximation Under Linear Skew

Summary

The document introduces Emanuel Derman’s volatility approximation for a volatility swap under an assumed linear volatility skew. It describes the approximation as assuming a linear put skew and a flat call skew, with applicability focused on strikes relatively near the money. The stated inputs are at-the-money forward volatility, the slope of the skew, and the swap’s maturity.

The author asks what the skew slope represents and requests an explanation, but the document supplies no formula, derivation, numerical example, or answer. It therefore identifies the approximation’s assumptions and named inputs without teaching how to calculate the estimate or interpret its output. The near-the-money qualification and simplified skew shape are important limits; the text does not establish how the approximation behaves for distant strikes or more complex volatility surfaces.

Key ideas

• The approximation is presented for a volatility swap when volatility skew is treated as linear near the money.
• Its stated assumptions are a linear put skew and a flat call skew.
• The listed inputs are at-the-money forward volatility, skew slope, and swap maturity.
• The document asks what the skew slope means but does not provide a definition or calculation.

Tags

# Emanuel Derman Volatility Approximation


# Emanuel Derman Volatility Approximation












Can someone please explain Emanuel Derman's volatility approximation as given below? Under Linear Skew

If skew is assumed to be linear, at least for strikes relatively close to the money, then Derman’s approximation can be used.

Derman’s approximation assumes a linear put skew and a flat call skew. It is a function of three variables, namely:

1)ATM (forward) volatility. 2)Slope of the skew. 3)Maturity of the swap.

I would also like to understand what slope of the skew signifies.

Reference from here: https://bookdown.org/maxime_debellefroid/MyBook/variance-swaps.html

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.