Doubt on exotics

[Chintan]

Hi David...

I have few doubts on exotics....

1) Barrier Options - In study notes, it is mentioned tht for down and in and up and in options,
the barrier "MAY BE ABOVE OR BELOW current stock price".

FOR DOWN AND IN OPTION:- Does this not mean tht if the stock price goes down and touches a barrier
then it will come into existence...and hence the barrier has to be below the current stock price....??

FOR UP AND IN OPTION:- Does this not mean tht if stock price goes up and hits the barrier level then it will come
into existence and hence the barrier has to be above the current stock price...??

2) Lookback options:- In diagram given in study notes, you will find tht you have mentioned "K1 is minimum duirng life"..Here....its the minimum stock price over the life of option....so....i guess instead of K1 it shud be
Stock price (Since K stands for Strike).....the strike does not change....and hence minimum stike
will not come in picture....Do i understand in rite way ?

3) Shout Option:- How come 2 strikes are involved....Shout option allow the holder to shout once during
the life of option.....and the max of intrinsic value as on shout date and exercise date will be the payout...
I dont understand why will there be 2 strikes.....I'm confused...

Please help me clear my understandings.....

 

[David Harper CFA FRM]

Hi Chintan,

1) Yes, my mistake. For down and in, *initial* stock price > barrier. For up and in, *initial* stock price < barrier. You are absolutely correct, I will fix.

2) That's just notation. Technically the lookback has a *floating* strike. So, all i mean there is: strike (k) = min(stock/asset price during life).

3) When the holder shouts, that creates a (floating) strike price (K1). Then later, at expiration, that "shouted" intrinsic value (based on the first self-selected strike) is compared to a "more typical" intrinsic value at expiration, based on K2. Or, put another way, an inception there is a strike (K2) like a plain vanilla option. Just like regular. Then just add the feature that allows user to set another (fluid) strike during the life. And MAX() between them...

David

 

[Chintan]

Hi David,

Thanks for yr prompt response.

Will it be right on my part to think of Lookback Option as the option which gives a payoff between
minimum stock price and the fixed stike price (Minimum for a put and Maximum for call) ?

And Shout Option as the one whose pay-off is maximum (intrinsic value on shout date ; instrinsic value on normal
expiry date ) ?

Talking about greeks - Is there any relation between VEGA and GAMMA ? I have read that Vega is highest for long term ATM option. This will mean that Gamma will also be very high for long term ATM option. However, i've also read that short term ATM option has large gamma.

Can you please throw some light on this ?

Chintan

 

[David Harper CFA FRM]

Hi Chintan,

Regarding the LOOKBACK, no. Keep in mind, as an option, you have the right, in the case of a Eurpoean CALL option, to buy the asset (the stock). The lookback is not different this way, at expire, you have option to buy the stock. The only difference is that *instead* of a fixed strike price, your strike price is floating (unknown at inception) and will equal the minimum stock price during the life. So (if call) payoff = MAX[Stock price (at exercise) - MIN (stock price during life), 0]. Only the fixed strike is replaced by floating strike; i.e., K = MIN (S)

Regarding the shout, yes, exactly CORRECT! Hull forumulates the shout as the following, which is the same exact thing:

shout = max (0, Stock final - Stock at shout) + (stock at shout - strike). Note this is equivalent to:

shout = max(0 + stock at shout - strike, Stock final - Stock at shout + stock at shout - strike)
shout = max(stock at shout - strike, Stock final - strike) =
shout = max(intrinsic @ shout, intrinsic @ final)

Regarding relationship btwn vega & gamma, yes a very direct relationship but it is not reviewed (in Hull) or tested for FRM:
vega = gamma*vol*stock^2*Time; i.e., high gamma implies high vega.

IMO, gamma is tough to intuit. Best way is to know the shape of the Delta charts and, knowing them, as gamma is rate of change of delta, you will be able infer gamma by imagining the slope of the delta line.
(see http://forum.bionicturtle.com/viewreply/659/)

This practice is more natural for gamma vs. strike price: for deeply in the money and deeply out of money, delta is getting stable at, respectively, 1.0 and 0. As delta is stable (decelerating) gamma is approaching zero in these cases. Ergo, gamma is higher for long term ATM, just as you say.

for long-term/short term, it is frankly harder to intuit, but if you look at Hull's chart that plot ATM versus time, you'll see that slope of line to delta is sharper for shorter time to maturity.

David

 

[Chintan]

Hi David,

Thanks for the explanation on greeks as well as exotics.

I'm really sorry to bother you like this with lookback option....but i cannot be at peace if something is puzzling my
mind.....

For lookback option, I understand tht thr are 2 types of lookback options - One with fixed strike and the other with variable strike.

What you are referring to is the one with variable strike. While what i'm referring to is the one with fixed strike.

For Fixed strike 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.

For fixed strike put - the option can be exercised at the asset's lowest price....

In the absence of any information in exam....can i consider lookback option as the one with fixed strike ?

 

[David Harper CFA FRM]

Hi Chintan,

(please don't be sorry, it's what the site is for!)

Yes, you are absolutely correct, there are two types (fixed strike and floating strike).

But, no on your assumption: for FRM exam purposes, and to my above point, I am speaking from the assigned John Hull (Ch 22). Hull only refers to floating strike lookback option: for a call, at expire, payoff = current stock - MIN(stock price).

So, yes you are correct in broad truth, but for practical (FRM exam purposes) consider the lookback to be the lookback with floating strike.

David

 

[Chintan]

Thanks David.

Point Noted.