Exotic options

[Hend Abuenein]

Hi David,

About floating lookback options, would it be correct to say that these options give the owner the opportunity to purchase/sell the stock at its lowest/highest price over the life of the option, given that these prices cannot be determined ex-ante ?

Thanks

 

[David Harper CFA FRM]

Hi Hend,

I hadn't thought of them that way but Hull agrees (nice!):

A floating lookback call is a way that the holder can buy the underlying asset at the lowest price achieved during the life of the option. Similarly, a floating lookback put is a way that the holder can sell the underlying asset at the highest price achieved during the life of the option. - p 562

Also consistent is Peter James (a favorite from my library on exotics; Option Theory), emphasis mine:

The lookback call gives the holder the right to buy stock at maturity at the lowest price achieved by the stock over the life of the option. Similarly, the lookback put allows the holder to sell stock at the highest price achieved. The form of the payoff is unusual in that it does not involve an expression of the form max[0,... ], since ( ST − S min) can never be negative; it has therefore been suggested that this is not really an option at all, although this is largely a matter of semantics. -- Option theory, page 193

now that you mention it, frame it this way, it kind of reminds me of a certain variety of non-qualifed employee stock purchase plan (ESPP) where employees could purchase at the lowest trailing price over a window (and/or 15% discount) but that's in the ESO category i guess, so that's a flawed comparison (I guess you don't hold onto the stock with the lookback, but rather receive the cash payoff).

Interesting! Thanks

 

[Hend Abuenein]

Thank you for the quotes.

 

[LeeBrittain]

Hi David,

I tried to create a new thread for my following question but the site wouldn't allow me to... I click "post new thread", entered my subject title but no box became available to enter a message. Is the system down or am I missing where to post a new topic?

Anyways, my question is on the shape of the volatility smile when there are asset price jumps. In the notes it says that asset price jumps tend to lead to a volatility frown due to the bimodal distribution, but in the practice questions (18.03) it shows an implied smile with jumps in the underlying. Am I missing something here or are those contradictory answers?

Thanks,
Lee

 

[David Harper CFA FRM]

Hi Lee,

I asked our developers to look into the thread issue: we are able to replicate in firefox, so THANK you. I'm confident they can fix.

With respect to Hull's apparent conflict, I totally agree (18.03 is his question). I frankly have not resolved it. From a merely practical matter, I can tell you that question 18.03 is clearly the "correct" and useful view (i.e., jumps are meant to connote a heavy tailed distribution and therefore a smile not a frown).

Contrast with Hull's final section on a single large jump. I think (but am unsure) that the difference is a bimodal distribution with possibility of kurtosis < 3, however, I'm unclear (b/c I also think the mixture of 2 lognormals must be heavier tailed than 1, but have not researched) .

All i can get is that his point seems to be that unusual distributions imply, and here are his words, "an unusual volatility smile." So my best guess is that his example just happens to imply a frown but that we could generate other bimodal/mixtures of lognormals that produced a smile. I apologize I cannot say with any certainty. Thanks again for floating the bug,

 

[Hend Abuenein]

Hi David,
I hope you're doing well.

1- A few questions in GARP's practice exams compare prices of exotic options. The answers I've come across relied on two factors: flexibility given to investor, and European always being cheaper than exotics.
What else is there to consider when comparing for exotic options' values? What makes a barrier option cheaper/more expensive than an Asian or a lookback option, for example?

2- Up/Down and out options are known to have a negative vega, because the higher volatility of the underlying nears its price to the out barrier.
A question in GARP's 2008 practice exam compares a deep ITM to a deep OTM up and out call option asking which has a negative vega (other choices irrelevant).
The answer was that it's the deep ITM up and out call since the higher volatility would risk option exiting barrier or loosing its moneyness.
But why doesn't the same analysis apply to the OTM call?
If the barrier is near K (sensible to a call), and S is much below K (since it's OTM), investor would want S to be increased by high volatility in order to gain moneyness only if it weren't a barrier option. The barrier would make the investor value the option less with the higher volatility.

Am I getting something wrong here?

Thank you

 

[David Harper CFA FRM]

Hi Hend,

Thanks, I hope you are doing well, too!

1. That's interesting, we really should add this perspective to the questions/notes; i.e., key dimensions for evaluating exotics. First, I am not aware that general comparisons can be made among exotics; e.g., I am not aware if we can generalize that a lookback would be less or more valuable than chooser, as both have additional features that make them more valuable than Europeans. We could only do so, to my knowledge, for example, comparing a lookback to a barrier because, in general, lookback > plain vanilla Euro > Barrier, so by syllogism.
(what is the right word to describe the conclusion that a>c, if a>b and c < b??, I must be tired)

I think some noticeable feature dimensions are:

• restrictions/forfeitures: e.g., both barrier and employee/executive options take an option and restrict some of the optionality, which reduces its value
• additional options on the options; e.g., chooser adds an option on top of an option, increases value
• pricing frequencies: if a lookback averages prices, increasing frequency adds value.
  (just my top thoughts, not comprehensive, i think each exotic needs to be considered on its own)

2. Interesting, I had to look this up. See below. With the benefit of this reference, i can see see the intuition if we (per Hull) decompose the up and out call as:
c(up and out) = c (Euro) - call (up and in);

An increase in volatility has two opposing influences:
Higher vol --> Higher value of a vanilla c(Euro), however
Higher vol --> Higher value of the call (up and in)

De Weert is making sense to me in that he's saying that, for an OTM up and out, the first effect dominates, but gives over to the second effect dominating for an ITM (keep in mind, the higher intrinsic value isn't really impacting. Vega is change in volatility, keeping everything else same, so it's really volatility impact on the time value of money). Interesting questions, for sure, I hope that helps b/c I sure learned something here. Back to practice questions for me!

10.8 VEGA EXPOSURE UP-AND-OUT CALL OPTION
A long position in an up-and-out call option is not necessarily long vega. In fact, more often than not a long up-and-out call position results in being short vega. This means that, if the implied volatility of the underlying goes up, the up-and-out call option actually becomes less valuable. The reason being that a higher implied volatility results in a higher probability of the call knocking out and therefore a lower chance of the up-and-out call having a payout at maturity. Naturally, an up-and-out call is not always short vega. Indeed, if it is a very upside barrier the probability of the up-and-out call knocking out is very low anyway and therefore an increase in implied volatility has a much bigger impact on the option part of the up-and-out call than on the fact that there is a higher chance of the option knocking out. Hence an up-and-out call is long vega for very upside barriers and short vega for lower barriers. Source, Chapter 10: http://www.amazon.com/Exotic-Options-Trading-Finance-Series/dp/0470517905