Managing Skew Exposure in Forward-Starting Options
Summary
The note explains why hedging skew exposure in a forward-starting option differs from hedging an ordinary option. A forward-starting put may be analytically short skew, yet during the forward period its strike resets in proportion to the underlying price. This can keep its vega relatively stable after a price move, unlike a regular put, whose vega and skew exposure change dynamically as the underlying falls.
The answer describes hedging with ordinary options as difficult because those options carry both analytical and dynamic skew exposure. It recommends using options whose maturity matches the remaining forward-start period, rolling that maturity as time passes, and adjusting strikes with the underlying’s movement. The discussion is conceptual and tentative: it does not quantify hedge ratios, compare risk-reversal performance with alternatives, or provide empirical results. The answer also notes that forward-start option pricing is strongly affected by the term structure of skew.
Key ideas
- The term structure of skew has a strong effect on forward-start option pricing.
- A forward-starting put can be analytically short skew without having the same dynamic skew exposure as a regular put.
- Ordinary options can be imperfect hedges because they carry dynamic skew exposure of their own.
- A proposed hedge rolls option maturity with time and adjusts strike as the underlying moves.
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# Hedging Skew Risk in a Forward-Starting Option # Hedging Skew Risk in a Forward-Starting Option Suppose someone sells a $m$-year forward-starting option that kicks in $n$ month from now. If they are concerned about skew risk, could a risk reversal be an effective hedge? How would this approach compare to other potential hedging strategies, given the forward-starting nature of the option? What key factors should be considered when managing this exposure? ## Answer by João (score 1) https://quant.stackexchange.com/a/81994 For Forward Start Options the term structure of skew strongly impacts the pricing. Also there's a Paradox on Forward Start Options A short position in a $N$year $x$% put option forward starting in $(N-n)$ years is analytically short skew but has no dynamic skew exposure during the forward period. - A regular $N$year $x$% put is dynamically short skew: If the stock price drops, the position loses vega, increasing risk. - A forward-starting put is not dynamically short skew: If the stock price drops, the strike moves down proportionally, keeping vega stable. So this makes it much more difficult to hedge the exposure to forward starting options. Because you can only hedge with regular options (I don´t think cliquets, forward start variance swaps for example are the most suitable, but someone correct me), which are both analytically as well as dynamically short skew. You'll need to have two things in mind: - You'll need to hedge with options having a maturity equal to the term of the forward starting period, and continue to role this maturity forward as time lapses. - You'll also need to role the strike up if the share price moved up and role the strike down if the share price moved down. The book Dynamic Hedging Managing Vanilla and Exotic Options maybe have some input on forward volatility, don´t recall on having forward starting options there.
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