Eachway Tunnel Gamma

Eachway Tunnel Gamma iconEachway tunnel gamma is the metric that describes the change in the delta of an eachway tunnel due to a change in the underlying price. It is the second derivative of the eachway tunnel (ET) and first derivative of the eachway tunnel delta with respect to a change in underlying price. It is depicted as:

\Gamma = \frac{d\Delta}{dS}

where  \Gamma is gamma and \Delta is the tunnel delta.

Evaluating ET Gamma

The eachway tunnel gamma can be constructed from the digital call gamma.

Eachway Tunnel Gamma = R1 x Digital Call Gamma(K1) + R2 x Digital Call Gamma(K2)

– R2 x Digital Call Gamma(K3) – R1 x Digital Call Gamma(K4)

where K1, K2, K3 & K4 are lowest strike to highest strike, and

where R1 + R2 = 1 and R1 < R2 and R2 = 1 – R1.

Eachway Tunnel Gamma Over Time

As a conventional options market-maker of 20 years standing I would have to admit that it is not possible to use the following illustrations of gamma to hedge with. The oscillations above and below zero make this Greek interesting if not of much practical use.

Eachway Tunnel Gamma
Figure 1a – Eachway Tunnel Gamma w.r.t. Time to Expiry 100-40-0

 

Eachway Tunnel Gamma
Figure 1b – Eachway Tunnel Gamma w.r.t. Time to Expiry 100-25-0

 

European Digitals Eachway Tunnel Eachway Tunnel Delta Eachway Tunnel Theta Eachway Tunnel Vega

Eachway Tunnel Gamma and Volatility

Figures 2a and 2b suggest yet again that the eachway tunnel gamma is of little value as volatility hits extreme lows. In these two cases any volatility lower than 6% is likely to be of very limited use.

Eachway Tunnel Gamma
Figure 2a – Eachway Tunnel Gamma w.r.t. Volatility 100-40-0

 

Eachway Tunnel Gamma
Figure 2b – Eachway Tunnel Gamma w.r.t. Volatility 100-25-0

Yet if you compare both scales it becomes evident that the 0.25 rebate requires the wider range in order to include all volatility profiles of ±6%. Bearing in mind that the value of the eachway tunnel is constrained to the range 0.0 → 1.0 an absolute value of >1.0 is unrealistic. Yet this is no different for other Greeks at extreme variables, e.g. conventional theta can very often wildly over exaggerate the daily time decay.

Summary

  • A highly volatile Greek when time to expiry and/or implied volatility are exceptionally low.
  • Can generate unrealistic scenarios that, if included into a portfolio of options, can lead to most misleading data.
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