# Eachway Call

The eachway call option pays out for a win and a place. This bet consists of two strikes so that at expiry, if the underlying is above the higher strike, the bet settles at 100. Between the strikes the settlement value is a variable, for example 0:25:100, 0:40:100, 0:50:100, etc..

### Eachway Call Valuation

The Eachway Call is calculated as:

Eachway Call    =    R1 x Binary Call(K1) + R2 x Binary Call(K2)

where K1 is the lower strike and K2 the upper strike binary call option. R is the ratio: R1 + R2 = 1 and R2 ≥ R1.

R1 (x 100) is the settlement value between the strikes.

### At Expiry

Figure 1a shows the underlying between the two strikes settling at 40, while if the underlying price is below the lower strike the eachway call settles at zero.

Figures 1b shows the eachway call with the intermediate settlement values of 25.

As usual, if the underlying price settled on either of the strikes then the mean of the adjacent settlement prices would be used for settling the strategy, i.e. 20 and 70 for the lower and higher strikes respectively for Figure 1a, while 12.5 and 62.5 for Figure 1b.

Therefore, this particular binary options strategy is certainly not an all-or-nothing bet since it is possible to have five different settlement prices. The eachway could be perceived as a strategy that pays out a secondary settlement price for, in gambling parlance, ‘a place’.

The eachway call provides a second bite at the cherry in the case where the speculator forecasts the market inexactly. In the example of Figure 1a, maybe the asset price is moving upwards as forecast by the eachway call buyer but not quite at the pace required to get it over the line for the strategy to settle at 100. The secondary settlement price provides the consolation of calling the market right but getting the momentum wrong.

### Eachway Call Over Time

Figures 2a and 2b provide the 99.00/101.00 eachway call over a range of time to expiry to illustrate how the price profiles behave over time. The 8-day profile at 98.00 possesses a shallow gradient, thereby defining a low delta which reflects low gearing.

In the above illustration at 98.00 the eachway call is worth 10.99 compared with the same eachway call below of 7.64. Both options would would generate a handsome return if the asset price at expiry was above 99.00, i.e. (40 – 10.99)/10.99 = 264% return for above and (25 – 7.64)/7.64 = 227% for below.

If the asset price over the eight days rose to above 101.00 at expiry the returns jump to (100 – 10.99)/10.99 = 810% and (100 – 7.64)/7.64 = 1029%. On the other hand the 25-day profiles are more of a ‘slow burner’ with very low gearing. Midway between the strikes at 100.00 and 25 days to expiry the 0:40:100 is worth 46.61 and the 0:25:100 option is worth 42.15. This means that the 0:40:100 option at 100.00 with 25 days to expiry can look forward to losing only 6.61 if the asset price remained unchanged to expiry in contrast to the 17.15 of the 0:25:100 spec. eachway.

As time to expiry falls to the last day and less the profile slowly becomes steeper and only with 0.1-days to expiry does the profile resemble the settlement price profile of Figure 1. This creates some interesting eachway call theta profiles.

### Volatility

In this section the 0:40:100 and 0:25:100 ratio’d eachway calls with 5 days to expiry are compared over the same range of volatilities.

One of the interesting features of a single binary call is that if out-of-the-money then an increase in volatility increases the call value. This is referred to as positive vega. Correspondingly, if the call is in-the-money then an increase in volatility lowers the call value. This is because when out-of-the-money a ‘vol’ increase means a higher probability of the call becoming in-the-money while the in-the-money call finds that a ‘vol’ increase means a higher probability of the call becoming out-of-the-money.

In the above two examples the price profiles cross each other between the strikes, but with the 0.25.100 ratio’d eachway call having this conjunction closer to the higher weighted 101.00 strike than the 0.40.100 ratio’d eachway call.

In effect, one would expect the volatility to have no impact on the eachway call value if the ratio was 0.50.100 and the asset price was midway between the strikes. This would equate to a zero eachway call vega. As the ratio gets increasingly skewed toward the upper strike then a change in volatility has decreasing effect on the eachway call value.

When the asset price is above the upper strike, with the ratio 0.25.100 the volatility’s effect on the eachway call is now very much like a single 101.00 call.

By: Hamish Raw

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