Down-and-Out Binary Put Options

Down-and-Out Binary Put OptionsDown-and-out binary put options require that the strike be above the barrier else the strategy is trivial, in fact always worth zero! The strategy is always knocked-out before it can get in-the-money.

The strategy can be considered as a one-by-two put spread where the strategy is stopped out below the barrier. Alternatively the strategy could be looked at as a long binary put option with strike K, plus short a one touch put with strike B.

Either way, should you call the market too right then you will lose the premium since the barrier may get hit. So, for down and out binary put options to be a winner the speculator needs to not only get the market right in terms of direction, but also needs to have a good reason it is not going to dump out-of-sight! This may be because there is a major support level above the barrier which may inhibit a freefall.

Down and Out Binary Put w.r.t. Time

Fig.1 – Bund Down-and-Out Binary Put Options (K > B) FV w.r.t. Time to Expiry

The above example of down-and-out binary put options shows how it may be employed in the bund futures market traded on Eurex. For whatever reason the ECB may decide to put a lid on Bund yields which may involve central banks buying bunds just above the barrier of 136.00.

Figures 1 & 2 show the effect that changes in time to expiry and implied volatility have on this strategy. In general the higher the implied volatility and more time to expiry, the lower the value of the option as these factors will increase the likelihood of the strategy being knocked out. The assumption here is that the barrier and strike are fixed at 4.00 points apart, but by increasing the distance between the strike and barrier will impact on the effect of time to expiry and implied volatility.

Down-and-Out Binary Put Options

Fig.2 – Bund Down-and-Out Binary Put Options (K > B) FV w.r.t. Implied Volatility

Formula

where:

where:

and:

 

A similar circumstance actually took place in the late-Eighties in the UK after the privatisation of British Telecom. The UK government issued the stock at about £1.20 but yet another stock market collapse saw the stock tumble to the low 90p level. Amid the ludicrous squealing of the dumb investment fund managers who were immediately wearing a substantial loss the UK government announced that it would stand in the market and repurchase any stock at 86p. In effect the government was offering free put options with an 86p strike. So a few of us bought the stock and sold the calls one-to-one and immediately locked in the conversion. We locals made a killing, and the government a few months later knocked out the repurchased stock at £1.20 again…….happy days!

N.B. The UK government cannot always be counted on being good for its word when announcing it is going to stand in the market and support what it thinks is a sensible strategy. Take for example Chancellor Lamont’s stance in 1992 when announcing that the British Pound will not be booted out of the Euro: “We have a war chest of £10 billion(!) to defend Sterling with”. What a clown……he might as well announced a war chest of sixpence-halfpenny (less than a dime!) bearing in mind that just about every hedge fund in the world was betting against him. He then put rates up by 2% from 10% to 12% the following day which had absolutely no effect on the GBP, so Lamont stuck on his headmaster’s hat and told those of us in the market that if we didn’t ‘behave’ he would stick interest rates up a further 3% the following day. Of course, the government admitted defeat and announced the UK’s withdrawal (booted out!) from the European Exchange Rate Mechanism (now known as the Euro) that night. What a vainglorious buffoon!! But my best ever day trading………

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