SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
SWilson
Topic Author
Posts: 10
Joined: February 13th, 2018, 5:27 pm

Conditional Strike Option

February 13th, 2018, 8:29 pm

Came across am option that is effectively a collar, where the call/ceiling option let's say is $1.5,  straight up.  The put/floor option lets say is $1.25, fine.  However, if the underlying goes below the put option strike ($1.25), the actual intrinsic settlement uses a 3rd rate called the "conditional" strike which lets say is $1.35 (a value between the floor and ceiling) NOT the $1.25.  Trying to price this is a meaningful but simple way.  It does not have a knockout, barrier, corridor or other exotic type feature.  Any thoughts on breaking this down to use a standard-type valuation for the time value?
 
User avatar
Alan
Posts: 9452
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

Re: Conditional Strike Option

February 14th, 2018, 12:36 am

By "standard-type valuation", I will first assume you mean under a GBM process. All you need is the joint density of (ST,MT):  the terminal value and the minimum of the process over (0,T). 

That density is known in closed form for drifting BM and hence GBM. (Googling shows it's in Mark Joshi's 'Concepts.." book, for example)

Then, the option value is simply the (discounted, double) integral of that density times the payoff function that you gave in your post. (Do the integral numerically and you're done -- if a GBM value is all you really wanted).

Of course, maybe you'll want to go on from there to a more market-consistent model. It would be nice to have the stand-alone ST density agree with the market's RN density which you can infer from Breeden-Litzenberger, for example. Can you infer a model-independent, market-consistent joint (ST,MT) density?  Hard to say --  likely depends on what other types of options are liquid and well-quoted. You may need to calibrate various more complicated models to the vanilla (and other liquid barrier) options, and then do Monte Carlos to price the thing. 
 
User avatar
travisf
Posts: 14
Joined: May 12th, 2015, 8:51 pm

Re: Conditional Strike Option

February 14th, 2018, 12:18 pm

It sounds like this is a two leg option: a 1.5 strike call together with a 1.35 strike put with a knockin barrier at 1.25.  
 
User avatar
Alan
Posts: 9452
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

Re: Conditional Strike Option

February 14th, 2018, 4:03 pm

Good observation -- simpler than mine and a way to use standard formulas (for GBM).
 
SWilson
Topic Author
Posts: 10
Joined: February 13th, 2018, 5:27 pm

Re: Conditional Strike Option

February 14th, 2018, 4:56 pm

Alan, this is helpful.  Yes, using GBM.  So can you elaborate on how I would adjust variables as it relates to N(d1) and N(d2) that you mentioned using a joint density, when we have a put option that has the 2 prices above?  To start I'm going to take some type of average and then go from there.  Also assuming S(t) will be 1.25 since the moneyness is based on that price.  But in reality, intrinsically, the strike is 1.35.
 
SWilson
Topic Author
Posts: 10
Joined: February 13th, 2018, 5:27 pm

Re: Conditional Strike Option

February 14th, 2018, 4:59 pm

Yes, or like travisf says, it operates like a simultaneous knock-in/knock-out.  I was thinking 2 options with a 1.35 strike with a knock-in AND knock-out at 1.25 .
 
User avatar
Alan
Posts: 9452
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

Re: Conditional Strike Option

February 14th, 2018, 5:15 pm

No, I believe travisf is correct. For the put(s) it is entirely (under GBM) a knock-in with a knock-in barrier at 1.25 and strike of 1.35. Under GBM, which is a continuous process (and assuming continuous monitoring), it's impossible for the separate strike of 1.25 to be effective without triggering the knock-in event.

So, just go look up standard formulas for that one. 
Last edited by Alan on February 14th, 2018, 5:19 pm
 
SWilson
Topic Author
Posts: 10
Joined: February 13th, 2018, 5:27 pm

Re: Conditional Strike Option

February 14th, 2018, 5:19 pm

THANKS!
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...