In previous sessions we took a very brief look at exotic contracts and introduced the concept of derivative strategies. In the current session we will take a deeper look and quickly walk through instances and examples of a range of exotic contracts such as Digital, Barrier, Asian (Asian we have covered but we’ll go out and expand that family by introducing other members that go by the name of Bermuda and Mid-Atlantic), Lookback, Quanto, Compound option, chooser options, Ladder and Shouts. All variations on contracts that allow a customer to do a hand full of things that we’d addressed earlier such as adding yield, limiting downside, providing structured protection, and reducing cost.
Let us start with the first instrument in the family which is a Digital contract (aka Binary, Bet, All or Nothing, Cash or Nothing options).
A digital contract is also known as a Bet option. If you go back to the example of a call, a call allows its buyer to the right but not the obligation to buy something at a future date at a price that has been agreed upon today. A digital contract, a binary option or a bet option comes in two variations. The first is known as an Asset or Nothing and the second is known as a Cash or Nothing [option].
If you take the example of a call, let’s say you’ve bought a call on gold that gives you the right to buy gold once it cross $1700. Gold right now is at $1600 and change and your call option gives you the right to buy Gold at a price of $1700. You will only exercise it if prices are above $1700. So if you compare this, if you think in terms of the dynamics, if you have a simple call option you will only exercise at 1700 [Step 1]. When you exercise it you pay 1700 [Step 2] , when you exercise it and pay 1700 you will receive your single ounce of Gold [Step 3]. Correct. That’s the structure for a regular call option. If you do an Asset or Nothing Option, the asset or nothing option says that if Gold exceeds 1700, so if Gold crosses a hypothetical barrier where it crosses 1700, you will receive an ounce of Gold. You will directly jump to (this is step one, this is step 2, this is step 3) Step 3 without having the need or the requirement of paying 1700. That’s the Asset of Nothing for you. If you did Cash or Nothing, let’s say you agreed on a price and that price was, for the sake of argument 1700, then if Gold crossed 1700, you will receive this payment of 1700. You will not receive the asset you will actually receive this payment.
What you are actually saying is that compared to a call contract a digital option or a binary option has two settings. One is asset or nothing where you receive the underlying for free, the other is cash or nothing where you receive a pre-agreed amount of cash if the condition that drives/ defines the bet is true, comes true or comes to pass.
There is a very interest relationship between a call option and an asset or nothing and a cash or nothing option. This relationship is covered in most basic derivative texts and if we get time we will try to cover or introduce this in a more advanced course on this topic. In fact if you are interested, if you go to any of our derivative pricing or quant risk management courses on financetrainingcourse.com there are actually a handful of course where this relationship is adequately defined.
Coming back to our family of exotics, a digital option is a bet option which allows you to receive a prize which may be the underlying asset in a certain quantity or cash in a certain quantity if a certain condition comes to pass.
A barrier option is an option that primarily gets used to reduce the out-of-pocket cost to a client and a customer.
These are options and contracts that are also known as sudden death. A customer comes to you and says “you are in the process of selling me this call option and the out of pocket premium for me is very expensive, say I’m paying 3% of notional. I can’t afford to pay this. Is there any you can do to reduce this cost?”
You go back to the customer and say “Listen, when we discussed your risk profile you mentioned that [if] prices are ever going to fall below this level”, let’s say if you talk about Gold the example that we gave earlier, let’s say Gold is here at 1600, you don’t think gold is ever going to cross the threshold of 1400. What I can do is that I can reduce this cost by a bit if we agree to the following condition. Your option with work, function, behave like a regular option throughout its life, unless and until gold touches 1400. And the minute Gold touches this barrier 1400, this option will cease to exist.
The client can come back and say, “You know, this makes sense. If Gold touches 1400 I don’t think I am interested in buying, I don’t think it will ever go back to 1700. So yes if it touches 1400 kill the option. If that means that you can reduce the premium by a certain amount go ahead and reduce it”. Or the client may come and say, “This [threshold] is too low, why don’t we bring it up to 1450”, or “this is too high why don’t you bring it down to 1300 or even 1200.” As you move this barrier, this threshold, you’ll find that prices/ the premium that you are charging the customer will also go up and down, because effectively, in essence what you are doing is if this is the distribution of values, in essence, you are telling the customer that my full call option covers the entire distribution but if you want to save a few cents then let’s take this piece out. My revised distribution for a barrier or a sudden death option excludes this part because the minute you touch this part the option will cease to exist.
You can flip this and say that the option will only come into existence if prices touch 1400, or the option will only come into existence if the prices touch 1800. You can create a structure where you only have one barrier. From a pricing point of view, if prices touch this barrier on the downside, so that if prices go down it will cease to exist, in which case it is a Down and Out. If prices touch this barrier the option will come into existence in which case it is a Down and In. Or you may set the barrier above the current price, and actually go out and say that if prices touch this barrier the option will cease to exist, in which case it is an Up and Out. Or if prices touch this barrier it will come into existence, in which case it is an Up and In. So Down and Out, Down and In, Up and Out, Up and In. That defines the barrier option.
The third family, the Asian option, the averaging option that we discussed earlier, allows you to reduce volatility. If you remember the example of the Asian that we gave earlier, the client comes in and says that I don’t really care about where prices are at a given point in time. All I really care about is that the average provides me some protection and that’s what I am happy with. This was an Asian, if you compare that with an American. An American allows you to exercise at any point in time throughout the life. Compare this with an European option where the European option only gives you the right to exercise only at maturity, an Asian also only gives you the right to exercise only at maturity but because you are averaging it out, the benefit of exercising earlier sort of gets averaged out. A Bermuda option or a mid- Atlantic option sort of sits in between in the sense that it says that you can exercise this option at some pre-defined and pre-agreed upon points- at this point you can exercise these option. So you are sort of sitting between Europe and America hence the term mid-Atlantic.
Among the family of options that we have looked at, a look back option is the Bentley. It’s the most expensive product that you can buy there. The way it works is, if you do a regular call, a call says my payoff profile is Max(ST – X, 0). In a look back option you basically, if this is the date on which it is expiring and this is the time frame over which it existed, at expiry I will look back and pick the price where I had the maximum payback. If it is a call, then price I use is going to be this number, if it is a put the minimum value that I will use is going to be this number. Whatever maximizes my payoff that is the value I am going to use in a look back option.
A Quanto option is a very different variation. The primary objective behind a Quanto is to eliminate or reduce what we call FX risk. For example, if I want to take exposure on the Indian stock exchange or on the Indonesian stock exchange or on the Australian stock exchange. I have a financial security that I have purchased in India, in Indonesia, in Australia, but rather than being impacted by changes in FX or Exchange rate, my primary concern is that what will be my net return, net of any FX or exchange rate variation. That is exactly what a Quanto option does. A Quanto option strips out the FX piece, strips out the exchange piece. The return it offers/ provides you is, if you are a US dollar investor, it will give you the return in US dollar terms, if you are an Australian dollar investor, it will give you a return in AUD terms. You may take exposure in any given market India, Indonesia, Australian, Pakistan, Middle East or elsewhere but the return that you get is denominated in the native currency terms that you are investing in.
Chooser and compound options are options that have very interesting variations from a structuring point of view.
If I start off with a chooser option, there are instances where we expect markets to go up or come down. And the approach of the strategy that we choose when markets go up is obviously going to be a call option and when markets went down it will be a put option. Within the terms of option strategies, if you are not sure of the direction of the market, you know that something is going to happen, something is going to break and when that happens, prices are either going to go up or come down, but you don’t know which direction. Within the strategy world, we go out and buy a call option to cover the upside and we also go out and buy a put option to cover the downside, and in this specific case the V that we see here is known as a straddle.
A chooser option allows us to get the same desired result that a straddle achieves but at a slightly lower cost. A chooser option basically says that if you are standing here, this is let’s say six months before the expiry date, at the three month point in time when the news that you expect to break has broken I will give you the right to choose. You can buy a call or a put. Depending on the direction the market has gone and this is post the event you were waiting for, depending on the direction of that event you can decide to buy a call or a put. This option is going to be more expensive than a vanilla call or put, but is going to be less expensive than a straddle, going back to the theme of reducing cost. Again a chooser option is an exotic contract, you can’t buy it off the shelf. It is something that is generally bought over the counter and is backed by a team who have gone out and structured the note/ transaction for you and going to manage the risk for their account.
Going back, we’ve looked at Lookback, Quanto and Chooser. Let’s try the Compound option now. Think about this Call on a call, Call on a Put, Put on a call and a put on a put. A call on a call is, I have a right to buy a call. Call on a put is, I have a right to buy a put but not the obligation. A put on a calls is, I have the right to sell a call. A put on a put is I have the right to sell a put. It’s effectively, if you look at a call on a call, its effectively an option on an option. Call on a call, Call on a Put, Put on a call and a put on a put. Being an option on an option that’s where the term compound originates.
Lookback, Quanto, Compound and Chooser, in addition to Digital, Barrier, Asian, Bermudas. These are the contracts that we have studied so far within our list of derivative contract families. Moving on we’ve got two more that are a variation on the Look back option we looked at earlier. If you remember in the Look back option we said prices go up, prices come down… and my primary worry as an investor is to see what I can do to maximize my return. When we introduced the concept of a look back option we said that the option picks up the maximum value that maximizes your pay off and that value is that value that is used in calculating your payoff. We also said that the look back option is a Bentley of all options the most expensive contract that you can buy. What can you do to get a similar profile but at a lower cost?
One variation that you can play with you can actually go out and define ladders, or thresholds, or ranges, and you can tell your client that listen I have got four ladders here which effectively means that if at expiry I calculate your payoff, your payoff is going to be the maximum ladder that was breached, which in this case, let’s say your option is going to expire in this range, at this point in time. At this point in time how many ladders have you breached. You breached this, here, you’ve breached this, here… you’ve breached all 4 levels. However, at expiry the price that you touched was this number here. If you have a ladder option, a ladder option gives you the benefit, very simple benefit that says that at expiry I am going to simply take ST the price at expiry and I’m going to compare it with Ladder level 1, 2, 3 and 4 and I’m going to take the maximum of these. When I say ladder level 1, 2, 3 and 4 these are ladder levels breached, so I’ve breached it here, here and here. And if I do this comparison, if I take this ST and compare it to L1, L2, L3 and L4, then I can clearly see that L4 is the last level that was breached and certainly higher than ST. Hence the payoff when it is calculated is simply going to be Max (L4 – X, 0). Think of it as a high watermark. If you touch that high water mark, you are going to live with that high water mark. If you haven’t touched you’ll take the next highest high water mark and if none of them have been breached then you are stuck with ST. But if you touch or cross or go above a certain threshold at any point in time then your payoff will be linked to that level, that threshold.
A look back option was the Bentley, a Ladder option is sort of a close approximation. As you increase the number of ladders, and as they become thinner and finer the cost of a ladder option should come close to a Lookback. If you can afford neither a Lookback nor a ladder and you want to do a variation, a variation basically says I take the same payoff profile and if I touch this point because I understand the market very well, because I have such a keen eye as to how the market is going to move, I think that this is the maximum threshold that prices will touch, will breach, so I can shout at this point in time and say I pick this level. At expiry when my pay off profile is calculated here because this level and this threshold is higher than the threshold, this level will be used to calculate my payoff. I can shout here and I can be completely wrong, and when payoff comes prices may have expired here or here. Again it’s the level that I’ve picked that will be used in calculating my payoff.
Very quickly, going back to the original list of exotic options. We’ve now gone through the concept of Digital, Barrier, Asian and Bermudas, Lookback, Quanto, Compound, Chooser options, Ladder and Shouts. I hope you have found this useful. I understand that this is a very brief and quick introduction to the concept of exotic options but I think it is enough to get you started or get you thinking about the underlying mechanism at play in some of these structures.
We’ll certainly do a much more detailed and a much more hands-on session on exotic options on a later date. Till then appreciate the time you have spent with us. This is Jawwad Ahmed Farid signing off for financetrainingcourse.com. Thank you very much for your time.