Tunnel Options Gamma

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Tunnel options gamma is the metric that describes the change in the delta of a tunnel option due to a change in the underlying price. It is the second derivative of the tunnel and first derivative of the 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.

Tunnel Gamma Over Time

Options gamma is crucial in risk management and the tunnel gamma is no different. Figure 1 illustrates the tunnel gamma over a range of time to expiry.

Tunnel Options Gamma
Figure 1 – Tunnel Options Gamma w.r.t. Time to Expiry

The blue 25-day and 8-day profiles are pretty flat which is no surprise since those respective profiles of Figure 1 of tunnel delta are also flat.

The 2-day profile is negative between the strikes and positive outside the strikes.

The 0.5 and 0.1 gamma profiles provide such switchback ride it would be pointless even attempting sustainable risk management.

The point about binary options is that, unlike conventional options, the writer has limited loss. This advantage is only accorded the conventional optional buyer as the short conventional call writer has potential unlimited losses. The limited risk nature of binary options often throw up these gyrating risk metrics. Yet they are probably only of interest to wholesale FX traders since for retail, binaries always offer capped risk trading.

Tunnel Gamma and Volatility

Figure 2 shows more dramatic gamma profiles…….

Tunnel Options Gamma
Figure 2 – Tunnel Options Gamma w.r.t. Volatility

…..but the scale shows even less risk. The gamma scale (-1.0 to +1.0) encompasses all profiles (except for the unrealistic 2.0%) which suggests minimum exposure to changes in volatility.

By: Hamish Raw

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