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Introduction to Exotic Options
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Exotic Options
Chooser options
Digital options
Forward starting options
Ladder options
Lookback option
Cliquets
Quanto Options
……..and there are many many more!
Chooser Options
The buyer of a Chooser option has the right, up to a certain date, to decide whether it should be a put or a call.
Example: A two year Chooser option on Google with a choice date of 6 months.
If the strikes of the options within the Chooser are equal it is known as a Simple Chooser, if different a Complex Chooser.
Similar strategy to buyer of a straddle- market going through a volatile period but unsure of direction.
The main difference between the two is that the buyer of a Chooser is confident that the market direction will be revealed within the bounds of the choice date.
Chooser Options
And is therefore willing to choose between a put and a call after the choice date.
This means that, on average, Chooser options are cheaper than straddles (which have both puts and calls up to maturity), but more expensive than the individual puts and calls
A typical structure might have the time to choose equal to half the entire time to expiration of the instrument. The chooser feature becomes increasingly valuable with longer choice periods.
In the limiting case, as the chooser period approaches the entire time to expiration, the instrument becomes equivalent to a straddle.
Whatever the choice date the buyer will always pick the last possible date to choose as there is no benefit to doing so any earlier
Chooser Option Example
A private investor who mainly trades on technical data is convinced that a major movement is about to happen in the FTSE 100 index. On the charts that are available it is clear that the FTSE index is currently trading very close to a major support line at 3000.
The investor believes that the support level will not be broken and that the FTSE will move up strongly. On the other hand a breach of the support level is seen as a major turn in market sentiment and will most likely be followed by a sharp drop in the index.
Chooser Option Example
The investor traditionally would enter into a straddle . However, a potentially better strategy is to enter into a 1 month Chooser Option on a 5 month FTSE option with a strike of 3000. At the end of the month, the investor has the choice of a 5 mth 3000 Put or a 5 mth 3000 Call.
So, a Chooser Option is valid for clients who expect strong volatility in the underlying but who are uncertain about the direction. It is therefore ideal mechanism to take positions on volatility.
Chooser Option Delta
The Delta of a Chooser option can be either positive or negative, depending on whether the put or call is more valuable.
i.e. as the underlying spot rate varies the moneyness of the put and call vary, so theoretically the Delta can vary between -1 and +1
Source: Wolfram
Chooser Option Gamma
As time approaches the choice date the Gamma becomes very large for spot prices close to the two strikes.
This is because at the Choice date , the chooser option will become either a put or call option, which will have roughly opposite deltas at the money. Therefore, the delta of the chooser option will tend to change very quickly around the choice date , and hence Gamma is large.
Chooser Option Gamma
Source: Wolfram
Hedging a Chooser option
Hedging with the underlying is clearly very risky. The trader, who is short the Chooser will be short Gamma, and his hedging losses could therefore be very big.
There is also pin risk attached to trying to create a hedge with the underlying
An effective way if hedging Choosers is with vanilla options
Example:
A trader sells a 2 year Chooser on Google stock with a choice date of 6 months and strikes on the put and call of $400. The short Chooser gives him exposure to a short put and a short call.
Hedging a Chooser option
He believes that in six months the price of the underlying will be higher than it is now based on the way the forwards are trading
He therefore buys a six month put and a two year call with strike $400
1. After six months Google’s share price is above $400. The put expires worthless and his position hedges the short call up until expiry
2 After six months Google’s share price is blow $400. he exercises the put (short shares), keeps the (now) 18 month call. This combination of long call short shares is a long put with a strike of $400, so he is hedged against the short put with the same maturity.
Barrier Options- Digital
Barrier Options are options which have a sudden change of payoff depending on whether or not the underlying asset crosses a pre- specified barrier
One of the simplest examples of this class of exotic option is the Digital Option (also known as Binary Options, All-or-Nothing Options, Fixed Return Options) which gives a fixed payout if the underlying is above or below the digital barrier at expiry and pays nothing in all other cases.
Digital Options
Example:
A client buys a six month European digital on General Dynamics which pays $10 if the stock is above $80 at maturity and 0 otherwise.
The payoff for this option looks like:
Payoff
Underlying
0
$10
$80
Why Digital Options?
One of the many advantages of digital options trading is that the pay-out is determined in advance so the investor is completely aware of what they would earn, or even lose, before the expiration of the option. To reap the benefits of a earning with binary options you only need to be in-the-money by 0.001, whether the underlying asset’s movement was great or small.
Digital Option Greeks
Because the payoff profile of the Digital option is discontinuous at the barrier, the delta will change dramatically around that point, so continuously delta hedging could become very expensive. The Delta function looks like:
Hedging a Digital Option
If Delta hedging with the underlying is expensive then how can a trader hedge a Digital option?
The payoff to a Digital can be replicated with a simple call spread . Consider the following call spread on general Dynamics with strikes $77.5 and $80, compared to the Digital Option on the same stock with a barrier of $80:
Hedging with a Call Spread
Payoff
Stock
$80
$77.5
Call Spread
Digital
Hedging a Digital Option
As the digital option pays $10 if the underlying is above $80, the call spread with $77.5 and $80 strikes will need to be 4 times geared
For example: if GD stock is trading at $85 at maturity, the client gets $10 from the digital, but the trader will get:
{($85-$77.5)-($85-$80)}x 4 = $10, so he is hedged.
What if the underlying is trading at $79 at maturity?: the trader would then get a payout of $1.5 x 4 = $6. So the trader has a cushion at prices >$77.5
Call spreads are in fact the product that a trader books into his risk management system when selling a digital.
Digital Options
So in the GD example above the trader would have booked a short call spread as a proxy for the digital option which he sold to the client.
There are many other kinds of barrier options: down-and-in puts, up-and- out calls, up- and- out puts etc etc
Forward Starting Options
A forward start option is an option that commences at some specified future date with an expiration further in the future. It is essentially a forward on an option, only the premium is paid in advance. Since the asset price at the start of this option is not known a priori, it is common to specify that the strike price will be set in the future so that the option is initially at the money. This would be known as a 100% forward starting option
Why do this?: Forward starting options are usually used to give the trader exposure to forward volatility. In other words, the trader is trading the volatility of volatility.
Forward Starting Options
Example:
A trader buys a delta neutral straddle forward start option with an expiry date of six months and a forward start of three months. In three months time, the strike (which now has 3 months to expiry) is fixed to give a delta neutral straddle. In this case, the buyer of the option is effectively buying volatility for three months starting in three months.
Hedging Forward volatility
Some care needs to be taken when hedging forward start volatility.
Example: a trader is looking to hedge a three year 100% put option starting in 2 years (short) . If he uses the 3 year point on his volatility surface, he will be using a different “skew” to that of the 1 year volatility which is in fact the correct one, as this is effectively a 1 year option.
The Greeks of the forward starting option are similar to the equivalent option with a time to maturity equal to the period between the forward start date and expiration.
But how to hedge?
Hedging Forward Starts
The trader would have to hedge his 100% forward put by buying a 1 year put (long Vega). However as time goes by, the trader would need to role forward this hedge in order to be hedged against his short I year volatility.
Ladder Options
This type of option is particularly popular with retail investors who want to get exposure to the upside of a stock while at the same time locking in the performance of the stock if it ever goes above certain levels.
Consider a retail investor who wants to go long Google stock but wants to make sure that if the stock ever goes above 105% or 110% (of where it is trading now) he is guaranteed at least 5% or 10% respectively.
Buys a 1 year ladder option which guarantees the greater between the performance of Google stock and 5% if the stock ever trades above 105%, and the greater between the performance of Google and 10% if the stock ever goes above 110%
Ladder Options
Mathematically:
= max
Where X =:
0% if Google never >105% during the 1 year term
5% if Google ever >105%……
10% if Google ever >110% ……
These payoffs apply even if the stock falls back below any of the respective “rungs” of the ladder during the life of the option.
The rungs are also knows as reset strikes as that is where the strike will be “reset” once the underlying trades through it.
Ladder Options
Advantages:
Less risky than traditional options as profits locked in as underlying performs
No need to constantly watch the underlying market levels
Disadvantages:
More expensive than a normal option
Lookback Options
A lookback option allows investors to “look back” at the underlying prices occurring over the life of the option and then exercise based on the underlying asset’s optimal value. This type of option reduces uncertainties associated with the timing of market entry.
There are two types of lookback options:
1. Fixed: The option’s strike price is fixed at purchase. However, the option is not exercised at the market price: in the case of a call, the option holder can look back over the life of the option and choose to exercise at the point when the underlying asset was priced at its highest over the life of the option- fixed strike call lookback
Lookback Options
In the case of a put, the option can be exercised at the asset’s lowest price. The option settles at the selected past market price and against the fixed strike- fixed strike put lookback
2. Floating: The option’s strike price is fixed at maturity. For a call, the strike price is fixed at the lowest price reached during the life of the option- floating strike call lookback.
For a put, it is fixed at the highest price. The option settles at market and against the floating strike- floating strike put lookback.
Lookback Options
Mathematically:
Lookback Options
Popular with retail investors- why?
An investor in stocks is always in a dilemma whether to sell and book the current profit, or hold and hopefully earn still higher profits in the future, while risking losing some or all of the unrealized profits. The investor wants to avoid the feeling of REGRET – the regret of holding for too long or the regret of selling too early.
Lookback Options
As it turns out, the lookback options are just the options that act as insurance against regret. For example, with floating strike calls the investor can buy the stock at the minimum price during the life of the lookback option and with floating strike puts the investor can sell at the stock at the maximum price during the life of the lookback option.
Hence these options should be costlier than a European call and as a rule of thumb are usually twice as costly as plain vanilla European calls.
Delta and Vega
The buyer of, for example, a fixed strike call lookback clearly benefits from higher stock prices i.e it is long delta. The payoff also benefits from higher volatility meaning that the option buyer is also long Vega.
The buyer of a fixed strike put lookback would be short Delta and long Vega.
The floating strike call and put lookbacks are long and short Delta respectively, and both are long Vega.
Cliquets
Theses are options where the strike price resets at predetermined points in time. The most common Cliquet option is the Ratchet option.
The ratchet option resets the strike price at predetermined points in time whilst at the same time locking in the performance of the previous period. In other words it is really just a series of forward starting options.
Example:
A 3 year 100% (strike is equal to stock price at reset date) ratchet call option on Apple stock, where the reset period is every year.
Cliquets
Initial stock price $400, end of year 1 $420, end of year 2 $440, end of year 3 $420.
Contribution of year 1 is max [S(1) – S(0), 0] = $20
Contribution of year 2 is max [S(2) – S(1), 0] = $20
Contribution of year 3 is max [S(3) – S(2), 0] = $0.
Theses simple payoff formulas clearly show that the strike resets each year to the prevailing stock price.
Cliquets
The major advantage of the Cliquet, is that the probability of some payout is high. Over the 3 year period, the chance that the market will close lower for three consecutive years, is much lower than the probability that the market will close lower at the END of three years i.e. there is a high probability that even if the market closes lower after three years, that it will have closed higher in at least one of the three years
Cliquets
The Cliquet is suitable for investors with a medium term investment horizon. It is less risky than ordinary medium term options, as there is less specific risk i.e. the reset facility gives the buyer a “second” and “third” chance. This increases the chance of payout, but must be balanced with the higher premium cost. As a series of “pre-purchased” options, the Cliquet is attractive to passive investors as it requires no intermediate management.
They have traditionally been attractive to retail and private investors but traders use Cliquets to take advantage of future assumptions about volatility.
The buyer of a Cliquet is long Vega
Quanto Options
A quanto (or cross-currency derivative) is a cash settled derivative ( futures or options) that has an underlier denominated in one (“foreign”) currency, but settles in another (“domestic”) currency at a fixed exchange rate.
For example, the Chicago Mercantile Exchange (CME) trades futures on Japan’s Nikkei 225 stock index that settles for $5.00 for each JPY.01 of value in the Nikkei index. If you hold a futures contract, and the Nikkei rises JPY 12 (or 12 points), you earn $6000
Or, a call option on Total (quoted in EUR) at strike 147 EUR with pay-off in GBP at FX rate = 1. If Total equity is 150 EUR at maturity of the option, the pay-off will be 3 GBP.
37
Quantos
Quantos are attractive because they shield the purchaser from exchange rate fluctuations. If a US investor were to invest directly in the Japanese stocks that comprise the Nikkei, he would be exposed to both fluctuations in the Nikkei index and fluctuations in the USD/JPY exchange rate. Essentially, a quanto has an embedded currency forward with a variable notional amount
Quantos
Mathematically:
Where is the predetermined FX rate.
Exotics
There is an almost infinite amount of exotic options!
If you are interested in this subject and would like a non-mathematical introduction to exotics the following two books are a good start:
Frans De Weert: Exotic Options Trading
Chia Chiang Tan: Demystifying Exotic Products
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