http://www.finpipe.com/exoptions.htm
an introduction to exotic options
This article will provide a brief overview of exotic options. We have already talked about so-called "plain vanilla options", the simple puts and calls that are priced in the exchange-traded markets and the over-the-counter markets for equities, fixed income, foreign exchange and commodities. Exotic options are either variations on the payoff profiles of the plain vanilla options or they are wholly different kinds of products with optionality embedded in them. The exotic options market is most developed in the foreign exchange market so we will restrict ourselves here to using foreign exchange examples, although we could easily talk about any of the other asset classes.
Barrier Options
A barrier option is like a plain vanilla option but with one exception: the presence of one or two trigger prices. If the trigger price is touched at any time before maturity, it causes an option with pre-determined characteristics to come into existence (in the case of a knock-in option) or it will cause an existing option to cease to exist (in the case of a knock-out option).
There are single barrier options and double barrier options. A double barrier option has barriers on either side of the strike (i.e. one trigger price is greater than the strike and the other trigger price is less than the strike). A single barrier option has one barrier that may be either greater than or less than the strike price. Why would we ever buy an option with a barrier on it? Because it is cheaper than buying the plain vanilla option and we have a specific view about the path that spot will take over the lifetime of the structure.
Intuitively, barrier options should be cheaper than their plain vanilla counterparts because they risk either not being knocked in or being knocked out. A double knockout option is cheaper than a single knockout option because the double knockout has two trigger prices either of which could knock the option out of existence. How much cheaper a barrier option is compared to the plain vanilla option depends on the location of the trigger.
First, let us think of the case where the barrier is out-of-the-money with respect to the strike. Consider the example of a plain vanilla 1.55 US dollar Call/Canadian dollar put that gives the holder the right to buy USD against Canadian dollars at a rate of 1.55 for 1 month's maturity. Spot is currently trading at 1.54. Consider now the 1.55 US dollar call/Canadian dollar put expiring in 1 month that has a knockout trigger at 1.50. The knockout option will be cheaper than the plain vanilla option because it might get knocked out and the holder of the option should be compensated for this risk with a lower up front premium. However, it is not very likely that 1.50 will trade, so the difference in price is not that great. If we move the trigger to 1.53, the knockout option becomes considerably cheaper than the plain vanilla option because 1.53 is much more likely to trade in the next month.
Note that for a given trigger, we would expect the difference in price between the plain vanilla price and the knockout price to increase with moves higher in implied volatility. A higher implied volatility means that spot is more likely to trade at the trigger than if spot were less volatile. A greater likelihood of trading at the trigger means a greater likelihood of getting knocked out.
The reverse logic applies to knock-in options. The knock-in 1 month 1.55 US dollar call with a trigger of 1.53 will be more expensive than the 1 month 1.55 US dollar call with a knock-in trigger of 1.50 because 1.53 is more likely to trade. If we own the 1 month 1.55 US dollar call/Canadian dollar put that knocks out at 1.53 and we also own the 1 month 1.55 US dollar call/Canadian dollar put that knocks in at 1.53, the combined position is equivalent to owning the plain vanilla 1 month 1.55 US dollar call.
Now, turn to the case where the barrier is in-the-money with respect to the strike. Imagine that the spot US dollar/Canadian dollar exchange rate is trading at 1.54. Consider the price of a 1 month 1.50 US dollar call/Canadian dollar put. This option has quite a bit of intrinsic value to it, already. Its premium will be at least 0.04 Canadian dollar cents/US dollar notional. The price of a 1 month 1.50 US dollar call/Canadian dollar put that knocks out at 1.56 is much cheaper than the plain vanilla 1 month 1.50 US dollar call because of the likelihood of spot trading as high as 1.56. In the blink of an eye, 0.06 Canadian dollar cents/US dollar notional worth of intrinsic value could be knocked out if spot were to trade at 1.56. A knock out option in which the barrier is in-the-money with respect to the strike is called a reverse knockout option. A knock-in option in which the barrier is in-the-money with respect to the strike is called a reverse knockin option.
How do we make money with this position? We buy the cheaper 1 month 1.50 US dollar call/Canadian dollar put that knocks out at 1.56 if we believe that spot will be contained within a narrow range around the current spot. Ideally, spot drifts higher very slowly, ending up just under 1.56 at expiry (say at 1.5580) without ever trading that level. We exercise the option, buying our US dollars against Canadian dollars at 1.50 and sell them simultaneously in the spot market, locking in 0.5580 Canadian dollar cents/US dollar notional. The higher the implied volatility at the time the option is priced, the cheaper the knock out option with the in-the-money trigger will be, compared to the similar plain vanilla option.
Higher implied volatilities suggest a greater probability of triggering the barrier and knocking out the option. The reverse is true of the reverse knockin option. It will still be cheaper than the plain vanilla option but not by very much. The higher the implied volatility, the less of a difference there will be in price between the reverse knockin option and the corresponding plain vanilla option. If we own a reverse knock-out option and a reverse knock-in option with the same maturity, strike and trigger, holding the combined position is equivalent to owning the corresponding plain vanilla option.
Managing reverse barrier options can be a difficult proposition, especially if as it gets close to maturity spot trades near the barrier. A double barrier option is like a more complicated version of a reverse barrier option. Asian options contrary to what one might think on the face of it, the term Asian option refers to options whose payoff is contingent upon the path that spot takes over the lifetime of the option. With our previous examples of cash positions and plain vanilla positions, the payoff of these structures followed a "ramp-style" payoff. That is to say, their payoff was determined by the location of spot at expiry with respect to the strike. If the option is in-the-money, take the difference and multiply it by the notional amount to determine its final value. Here, the payoff depends on the path that spot took over the life of the option.
The payoff of average rate options is calculated by taking the difference between the average for a pre-set index over the life of the option and the strike price and then multiplying this difference by the notional amount. Because an average of a spot price is less volatile than a spot price, average rate options are naturally cheaper than the corresponding plain vanilla options. The payoff of lookback options depends on the best rate that spot traded over the life of the option.
A lookback call gives the owner the right to buy the underlying at expiry at a strike price equal to the lowest price that spot traded over the life of the option. A lookback put gives the owner the right to sell the underlying at expiry at a strike price equal to the highest price that spot traded over the life of the option.
Lookbacks are expensive. Anything that gives you the right to pick the top or the bottom is going to be costly. As a general rule of thumb, some people like to think that lookback prices are in the ballpark if they are roughly twice the price of an at-the-money straddle.
Compound Options
A compound option is an option-on-an-option. It could be a call-on-a-call giving the owner the right to buy in 1 month's time a 6 month 1.55 US dollar call/Canadian dollar put expiring 7 months from today (or 6 months from the expiry of the compound). The strike price on the compound is the premium that we would pay in 1 month's time if we exercised the compound for the option expiring 6 months from that point in time. It could be a put-on-a-call giving the owner the right to sell in 1 month's time a 6 month 1.55 US dollar call/Canadian dollar put expiring 7 months from today.
These types of products are often used by corporations to hedge the foreign exchange risk involved with overseas acquisitions when the success of the acquisition itself is uncertain. Why buy a vanilla hedge or enter into a forward contract until you are sure that you will be buying the foreign company? Sophisticated speculators use compound options to speculate on the volatility of volatility. We will discuss that in a subsequent article.
Article by Chand Sooran, Principal, Victory Risk Management Consulting Inc.
an introduction to exotic options
This article will provide a brief overview of exotic options. We have already talked about so-called "plain vanilla options", the simple puts and calls that are priced in the exchange-traded markets and the over-the-counter markets for equities, fixed income, foreign exchange and commodities. Exotic options are either variations on the payoff profiles of the plain vanilla options or they are wholly different kinds of products with optionality embedded in them. The exotic options market is most developed in the foreign exchange market so we will restrict ourselves here to using foreign exchange examples, although we could easily talk about any of the other asset classes.
Barrier Options
A barrier option is like a plain vanilla option but with one exception: the presence of one or two trigger prices. If the trigger price is touched at any time before maturity, it causes an option with pre-determined characteristics to come into existence (in the case of a knock-in option) or it will cause an existing option to cease to exist (in the case of a knock-out option).
There are single barrier options and double barrier options. A double barrier option has barriers on either side of the strike (i.e. one trigger price is greater than the strike and the other trigger price is less than the strike). A single barrier option has one barrier that may be either greater than or less than the strike price. Why would we ever buy an option with a barrier on it? Because it is cheaper than buying the plain vanilla option and we have a specific view about the path that spot will take over the lifetime of the structure.
Intuitively, barrier options should be cheaper than their plain vanilla counterparts because they risk either not being knocked in or being knocked out. A double knockout option is cheaper than a single knockout option because the double knockout has two trigger prices either of which could knock the option out of existence. How much cheaper a barrier option is compared to the plain vanilla option depends on the location of the trigger.
First, let us think of the case where the barrier is out-of-the-money with respect to the strike. Consider the example of a plain vanilla 1.55 US dollar Call/Canadian dollar put that gives the holder the right to buy USD against Canadian dollars at a rate of 1.55 for 1 month's maturity. Spot is currently trading at 1.54. Consider now the 1.55 US dollar call/Canadian dollar put expiring in 1 month that has a knockout trigger at 1.50. The knockout option will be cheaper than the plain vanilla option because it might get knocked out and the holder of the option should be compensated for this risk with a lower up front premium. However, it is not very likely that 1.50 will trade, so the difference in price is not that great. If we move the trigger to 1.53, the knockout option becomes considerably cheaper than the plain vanilla option because 1.53 is much more likely to trade in the next month.
Note that for a given trigger, we would expect the difference in price between the plain vanilla price and the knockout price to increase with moves higher in implied volatility. A higher implied volatility means that spot is more likely to trade at the trigger than if spot were less volatile. A greater likelihood of trading at the trigger means a greater likelihood of getting knocked out.
The reverse logic applies to knock-in options. The knock-in 1 month 1.55 US dollar call with a trigger of 1.53 will be more expensive than the 1 month 1.55 US dollar call with a knock-in trigger of 1.50 because 1.53 is more likely to trade. If we own the 1 month 1.55 US dollar call/Canadian dollar put that knocks out at 1.53 and we also own the 1 month 1.55 US dollar call/Canadian dollar put that knocks in at 1.53, the combined position is equivalent to owning the plain vanilla 1 month 1.55 US dollar call.
Now, turn to the case where the barrier is in-the-money with respect to the strike. Imagine that the spot US dollar/Canadian dollar exchange rate is trading at 1.54. Consider the price of a 1 month 1.50 US dollar call/Canadian dollar put. This option has quite a bit of intrinsic value to it, already. Its premium will be at least 0.04 Canadian dollar cents/US dollar notional. The price of a 1 month 1.50 US dollar call/Canadian dollar put that knocks out at 1.56 is much cheaper than the plain vanilla 1 month 1.50 US dollar call because of the likelihood of spot trading as high as 1.56. In the blink of an eye, 0.06 Canadian dollar cents/US dollar notional worth of intrinsic value could be knocked out if spot were to trade at 1.56. A knock out option in which the barrier is in-the-money with respect to the strike is called a reverse knockout option. A knock-in option in which the barrier is in-the-money with respect to the strike is called a reverse knockin option.
How do we make money with this position? We buy the cheaper 1 month 1.50 US dollar call/Canadian dollar put that knocks out at 1.56 if we believe that spot will be contained within a narrow range around the current spot. Ideally, spot drifts higher very slowly, ending up just under 1.56 at expiry (say at 1.5580) without ever trading that level. We exercise the option, buying our US dollars against Canadian dollars at 1.50 and sell them simultaneously in the spot market, locking in 0.5580 Canadian dollar cents/US dollar notional. The higher the implied volatility at the time the option is priced, the cheaper the knock out option with the in-the-money trigger will be, compared to the similar plain vanilla option.
Higher implied volatilities suggest a greater probability of triggering the barrier and knocking out the option. The reverse is true of the reverse knockin option. It will still be cheaper than the plain vanilla option but not by very much. The higher the implied volatility, the less of a difference there will be in price between the reverse knockin option and the corresponding plain vanilla option. If we own a reverse knock-out option and a reverse knock-in option with the same maturity, strike and trigger, holding the combined position is equivalent to owning the corresponding plain vanilla option.
Managing reverse barrier options can be a difficult proposition, especially if as it gets close to maturity spot trades near the barrier. A double barrier option is like a more complicated version of a reverse barrier option. Asian options contrary to what one might think on the face of it, the term Asian option refers to options whose payoff is contingent upon the path that spot takes over the lifetime of the option. With our previous examples of cash positions and plain vanilla positions, the payoff of these structures followed a "ramp-style" payoff. That is to say, their payoff was determined by the location of spot at expiry with respect to the strike. If the option is in-the-money, take the difference and multiply it by the notional amount to determine its final value. Here, the payoff depends on the path that spot took over the life of the option.
The payoff of average rate options is calculated by taking the difference between the average for a pre-set index over the life of the option and the strike price and then multiplying this difference by the notional amount. Because an average of a spot price is less volatile than a spot price, average rate options are naturally cheaper than the corresponding plain vanilla options. The payoff of lookback options depends on the best rate that spot traded over the life of the option.
A lookback call gives the owner the right to buy the underlying at expiry at a strike price equal to the lowest price that spot traded over the life of the option. A lookback put gives the owner the right to sell the underlying at expiry at a strike price equal to the highest price that spot traded over the life of the option.
Lookbacks are expensive. Anything that gives you the right to pick the top or the bottom is going to be costly. As a general rule of thumb, some people like to think that lookback prices are in the ballpark if they are roughly twice the price of an at-the-money straddle.
Compound Options
A compound option is an option-on-an-option. It could be a call-on-a-call giving the owner the right to buy in 1 month's time a 6 month 1.55 US dollar call/Canadian dollar put expiring 7 months from today (or 6 months from the expiry of the compound). The strike price on the compound is the premium that we would pay in 1 month's time if we exercised the compound for the option expiring 6 months from that point in time. It could be a put-on-a-call giving the owner the right to sell in 1 month's time a 6 month 1.55 US dollar call/Canadian dollar put expiring 7 months from today.
These types of products are often used by corporations to hedge the foreign exchange risk involved with overseas acquisitions when the success of the acquisition itself is uncertain. Why buy a vanilla hedge or enter into a forward contract until you are sure that you will be buying the foreign company? Sophisticated speculators use compound options to speculate on the volatility of volatility. We will discuss that in a subsequent article.
Article by Chand Sooran, Principal, Victory Risk Management Consulting Inc.
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