Skip to content
All library documents

Choosing Strike for Delta-Hedged Gamma Trading

Article Quant Q&A · Author: Mane
Read the original

Summary

The note considers which call strike to use when a trader expects realized volatility to exceed implied volatility and plans to delta hedge, aiming for gamma gains to outweigh option decay. It explains that the approximate gamma contribution to daily profit and loss is proportional to gamma times the squared underlying price move, so a strike with higher gamma may capture more from realized movement.

Under the European Black–Scholes assumptions, gamma is highest when d1 is zero, at a strike slightly above the forward level according to the stated formula; this is near, though not exactly, at the money. The note therefore favors a near-the-money option. It does not compare the full effects of strike choice on theta, hedge frequency, transaction costs, or the probability and size of price moves. The conclusion depends on the model assumptions and is a simplified guide rather than a complete trading rule.

Key ideas

  • A delta-hedged long option can benefit when realized volatility exceeds implied volatility, if gamma gains outweigh decay.
  • The approximate daily gamma profit and loss scales with gamma and the squared underlying price move.
  • In Black–Scholes, call gamma peaks near the money, with the exact strike depending on forward, volatility, and time.
  • The strike comparison omits costs and other position risks, so it does not establish profitability.

Tags

OptionsVolatilityDerivatives pricing
Full text
# How does gamma trading depend on $K$?


# How does gamma trading depend on $K$?












If we think realized vol > implied vol, then we might go ahead and delta hedge a call, hoping that profits from gamma outweigh the decay.

Question: What should $K$ be on the call? ATM? If so, why? What happens if its OTM/ITM?

## Answer by FinanceGuyThatCantCode (score 2)

https://quant.stackexchange.com/a/33277

There is much more to exploit when gamma is highest. Your daily gamma PnL is $0.5\Gamma(X_t-X_{t-1})^2$, so you would probably prefer to have $\Gamma$ highest which is near the money. To be precise, $\Gamma$ is highest when $d1=0$ which occurs for $K=Fe^{0.5\sigma^2t}$. Of course, I am assuming a European option and that the Black Scholes model is correct of course - either way, close to ATM is what you want.

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.