# Eachway Puts

Eachway puts pay out for a win and a place. Eachway puts consist of two strikes so that at expiry, if the underlying is below the lower strike, the eachway put settles at 100. Between the strikes the eachway put settles at 25, but could be any number depending on the ratio, e.g. 100:40:0. Above the upper strike the bet settles at 0.

If the asset price is exactly the same as a strike price then the settlement price is the arithmetic mean of the above and below settlement price. So in the case of settlement prices of the ratio 100:40:0 the ‘dead heat’ settlement prices would be (100 + 40)/2 = 70 and (40 + 0)/2 = 20. Alternatively, 100:25:0 ratio would have dead heat settlement prices of 62.5 and 12.5.

### Eachway Put Valuation

The eachway put is calculated as:

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

where K1 is the lower strike and K2 the upper strike.

R1 > R2 and R1 + R2 = 1

### Eachway Puts at Expiry

Figure 1a shows the underlying between the two strikes settling at 50, while if the underlying price is below the lower strike the eachway put settles at 100. The at-the-money settlement values are now:

(100 + 50)/2 = 75 and (50 + 0)/2 = 25

Figures 1b shows the eachway put with the intermediate settlement values of 25. Here at-the-money settlements are:

(100 + 25)/2 = 62.5 and (25 + 0)/2 = 12.5

Binary options structures have now gone from the binary put options three, not two, outcomes to an eachway put with five outcomes. To avoid semantics maybe these eachway puts should be referred to as ‘quinquery’ options. Yes, silly! Far  better to just acknowledge that binary options are not just ‘Over’ and ‘Under’s.

### Eachway Puts over Time

Figures 2a and 2b provide the 98.50/101.00 eachway puts with ratios 100:50:0 and 100:25:0.

In both illustrations the 25-day profile shows the shallowest gradient and lowest gearing. The eachway put gamma will be constantly extremely low for this option with a long time to expiry. Figure 2a – Eachway Put FV w.r.t. Time to Expiry 100-50-0

With Figure 2, in general the gearing is reduced around the upper strike but increased at the lower strike. As the ratio tends towards 100:0:0 the gearing at the top  strike will be zero and at the lower strike that of the binary put option.

### Eachway Puts and Volatility

In this section the 100:50:0 and 100:25:0 eachway puts with 10 days to expiry are compared over the same range of volatilities.