For the conventional call there is no limited upside, with the 45° profit line travelling upwards from –25 through breakeven, through 75, through 100 and upwards out of sight. But this increased potential profit comes at a cost, of course, because at any underlying price between A and B the conventional call performs less profitably than the upbet. At A, the upbet makes a 100% profit and turns a $25 bet into a $25 profit whereas the conventional option loses the full premium of $25.
Figure 1.7.1
Where the conventional call breaks even at an underlying price 25¢ higher than A, the upbet is worth 100 generating a profit of 300%. The difference between the conventional and binary’s profits subsequently diminishes until the underlying reaches B, where both conventional and upbet make a profit of $75. Above B the conventional call gains in value point for point with the underlying while the upbet is stuck on 100.
Figure 1.7.2
Fig 1.7.2 illustrates P&L profiles of the seller of the upbet and the writer of the conventional call. Here the profile of Fig 1.7.1 is reflected through the horizontal axis with the writer of the conventional losing less than the seller of the binary between A and B, but subsequently facing an unlimited loss scenario above B.
Downbets v Puts
Figs 1.7.3 and 1.7.4 illustrate the comparisons of long and short downbet/put expiry P&Ls.
Figure 1.7.3
Assuming the price of the downbet and put options are both 25 and the strike at A is $99, then the trader who bought the conventional put has a breakeven at C where the underlying is equal to $99 – 25¢ = $98.75.
The breakeven for the downbet buyer is at A, the strike, where the downbet is worth 50 and the buyer doubles his money. At B, an underlying of $98, both conventional put and downbet make a profit of 300%, but lower than $98 the conventional is now behaving like a short future.
The scale of Fig 1.7.4 might suggest that a short conventional put has a limited downside. It does, at the point where the stock is worth zero. If the downbet and put options are worth $10/pt, then with the underlying at zero, the maximum loss for the downbet would be limited to:
$10 ¥ ( 25 – 100 ) = – $750;
whereas the maximum loss for the conventional put would be:
$10 ¥ (0.00 – ( $99 – 25¢ ) = – $98,750.
Figure 1.7.4
The above comparisons between conventional calls, puts, upbets and downbets enable the user to further tailor the instrument to his market view. Furthermore, the combination of conventionals and binaries provides a highly sophisticated method of creating bespoke strategies for the imaginative and creative speculator.
1.8 Formulae
1.9 Summary
The probability of an event happening plus the probability of that same event not happening is 100%. Therefore, the probability that the share price at expiry ends up above $101, on $101, or below $101 must aggregate to 100%.
On comparing Fig 1.3.1 with Fig 1.6.2 and then Fig 1.3.2 with Fig 1.6.1 enables us to draw some interesting conclusions:
1. Selling an upbet for 40 is identical to buying a same strike, same expiry downbet for 60.
2. Buying an upbet for 40 is identical to selling a same strike, same expiry downbet for 60.
As a rule:
1. For the same strike and same expiry, BUYING an upbet for price X is the same as SELLING a downbet for 100 – X.
2. For the same strike and same expiry, SELLING an upbet for price Y is the same as BUYING a downbet for 100 – Y.
3. For the same strike and the same expiry the value of the upbet plus the value of the downbet must sum to 100. This rule may appear obvious and trivial but it absolutely differentiates binaries from conventional options as the section on vega demonstrates.
This chapter has covered the two most basic of binary instruments, the upbet and the downbet. The upbet and the downbet are the basic foundation blocks to which all financial instruments can be reduced.
1.10 Exercises
1. A bettor sells the out-of-the-money Comex Gold upbet at 28.2, $100 per point. What is the potential profit and loss?
2. The S&P Minis on the CME are trading at 1250. A punter fancies the market down. Should the aggressive gambler sell the 1350 upbet or buy the 1150 downbet?
3. The following prices are observed in the Forex $/€ binary options market for September expiry.
If the underlying exchange rate is trading at $119.35, what trade(s) are available to lock in a profit? What will the profit be?
1.11 Answers
1. Potential profit = 28.2 ¥ $100 = $2,820
Potential loss = (28.2 – 100) ¥ $100 = – $7,180
2. Buy the 1150 downbet since the emphasis is on the ‘aggressive’ gambler. Both bets are out-of-the-money and therefore worth less than 50. They both have strikes 100 from the underlying, so assuming a normal distribution, will be worth the same. Just say they were worth 25 each. Then selling the upbet can only ever realise a profit of 25 while buying the downbet at 25, will realise a profit of 75 should it win.
3. Firstly, the underlying in this case is irrelevant. Buying the upbet and the downbet will cost a total of 96.7 to yield a risk-free profit of 3.3, since the upbet and the downbet must aggregate to 100. Since this trade is risk-free ‘fill yer boots’ and do as many as possible, in this case $3,600 of each. Therefore: Profit = 3.3 ¥ $3600 = $11,880
2. Theta & Time Decay
2.0 Introduction
Theta is a ratio that measures how much the bet price will change due to the passing of time.
Theta is probably the easiest ‘greek’ to conceptually grasp and is possibly the most easily forecast since the passage of time itself moves in a reasonably uniform manner.
Bets on many financial instruments are now always ‘in-running’, i.e. there is always a market open on which to trade. These days there is a 24-hour market in foreign exchange trading so any bet on the future level of the $/£ rate is always ‘in-running’ with the theta constantly impacting on the price of bets. On other markets which operate in discrete time periods, where the market is open for a limited period of five days a week, market- makers will often use Monday’s theoretical prices on a Friday afternoon in order not to get too exposed to the weekend’s three-day time decay.
An understanding of time decay and theta is thus critical to the trading and risk management of binary options. The remainder of this section on theta will analyse the