Sizing Option Positions to a Target Portfolio Volatility

Summary

The note asks how to size option positions so a strategy reaches a chosen long-run daily volatility. It considers strangles and risk reversals, and compares sizing from the historical P&L volatility of one unit, from implied-volatility and vega estimates, or from a decomposition of P&L into delta, gamma, vega, and theta exposures. It also raises the challenge of modeling how implied volatility changes with the underlying and how the Greek contributions co-vary.

The document is a question rather than a completed method: it supplies no recommendation, calculation, or empirical evidence. Its useful framing is that position risk should account for the combined and changing Greek exposures, rather than assuming vega alone determines volatility, especially for non-delta-neutral positions. Any sizing procedure would need a defined horizon, a model for joint market moves and volatility changes, and validation against realized strategy P&L; those details remain unspecified here.

Key ideas

• Historical P&L volatility of a unit option strategy is one candidate basis for position sizing.
• Vega-based sizing may be inadequate when a strategy has meaningful delta exposure.
• Option P&L reflects interacting delta, gamma, vega, and theta effects.
• Estimating joint Greek changes and their covariances is a central unresolved modeling question.

Tags

# Volatility targeting / sizing for option strategies


# Volatility targeting / sizing for option strategies












I am trying to work out how to properly size an option strategy to a given target volatility.

Assuming I have \$100 capital and I would like to have a strategy's long-run daily volatility to be \$1 (e.g. buy 1-month 25-delta strangle or risk-reversal). If all the greeks are available, what's the proper procedure to size the daily positions?

For example, I can think of a few possibilities:

- estimate the historical volatility of 1 unit strangle/RR and try to size that to \$1.

- estimate the historical volatility of the 1M ATM implied vol, and target position's vega volatility to be $1. But this seems only applicable for positions targeting neutral delta.

- given an option's return pnl can be sum all the greeks pnl (delta/vega/gamma/theta), we could estimate the historical volatility of the underlying, then compute the position volatility together with daily greeks. The tricky part seems to be estimating the vega change due to underlying change. Perhaps use regression here? And how about the "covariance" between all the greeks?

I am new to this space and helpful recommendation/suggestions are welcome. Thank you.

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