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london


Total Posts: 307
Joined: Apr 2005
 
Posted: 2018-04-18 17:36
A bank has offered to buy out a friends restricted stock units and replace with theirs. This bank - being Phrench - has some interesting wrinkles in their incentive scheme and he has asked for help understanding.

Here are the details:

The payout each June is either:
1. the arithmetic average of 25 days of VWAP from Feb to March
or
2. underlying shares in the bank


Presumably:
if price in June GREATER than 25 day VWAP in Feb to Mar
then they cash settle based on VWAP earlier in the year.

If price in June LESS than 25 day VWAP in Feb to Mar
then they deliver physical shares.


He is giving away the option to deliver either cash or shares in June.

Question: How does he value this option?
(ie what is this optionality worth to them)

He wants a simple explanation or example that he can use in negotiation with their HR ....

Unfortunately, the best i could say was that it depends on:
1. how many days in the year,
2. the volatility of the the stock,
3. the length of the VWAP window and
4. the time delay betweeen the VWAP window & the decision to deliver stock or cash.

Can one of you explain this in simple terms?
Let me know if any more detials would be helpful.
He wants to go back to them within 48 hours.

thanks!




Patrik
Founding Member

Total Posts: 1354
Joined: Mar 2004
 
Posted: 2018-04-19 03:04
From the banks perspective, if I get it correctly, their economics is:
max(S-vwap,0) - S for some number of years. They're all the same so we just look at a single case.

So when S greater than vwap their outcome is = S-vwap -S = -vwap
And when S smaller than vwap their outcome is = 0 - S = -S

(let's ignore the cash vs share delivery - assume things are liquid enough we could sell shares to get same outcome as cash settlement to simplify)

So hence we can look at it like them being short the forward and long an average strike call.

As a first step forget about the vwap part and think of the similar forward strike call (fixing on say the last day of the vwap). That one you can look up some closed for solutions for as an approx starting point (e.g. http://www.globalriskguard.com/resources/deriv/fwd_4.pdf from a quick google).

How the vwap then influences the pricing isn't super obvious to me at this late hour. My first thought was that if we use a very long averaging window and a high vol, then the distribution of that average relative to the last day of the window should become wider (the mean wouldn't move much, just a slight vol carry effect), so if I were to run a bunch of MC paths on that the winning scenarios (where we have a low vwap) are positively impacted while the losing paths still has a zero payoff. So from that it'd be worth more to the bank the longer the averaging period is - compared to the simple forward strike call.

Hope that helps.

Capital Structure Demolition LLC Radiation

TakeItAndRun


Total Posts: 96
Joined: Apr 2010
 
Posted: 2018-04-19 09:49
In other terms, your friend is:
Long stock, short Asian call(strike = VWAP, dt = 3 months)

For a quick approximation:
Long stock, short 3-month ATM call

By 3 months I mean: End of June - End of March

ronin


Total Posts: 317
Joined: May 2006
 
Posted: 2018-04-19 20:55
If you are trying to kill this situation, ask the company to provide daily mark to market for the cliquet.

And the auditor has to confirm their mark every quarter.


"There is a SIX am?" -- Arthur

london


Total Posts: 307
Joined: Apr 2005
 
Posted: 2018-04-20 18:48
Thank you one, thank you all.

The penny is slowly droping for me

This is effectively short a forward strike call (per Patrik)

In march every year, he will find himself long stock and short a call (per takeitandrun)
where strike = VWAP feb-mar , dt = 3 months.

So, back of the envelope (& lots of hand waving): he can look at the current premium of ATM 3m call as an estimate of the minimum value he is giving away.

thank you, thank you,.
NP still rocks!


TonyC
Nuclear Energy Trader

Total Posts: 1269
Joined: May 2004
 
Posted: 2018-05-01 06:59
>thank you, thank you,
>NP still rocks!

I was unaware there was a time when we had stopped rockin'

flaneur/boulevardier/remittance man/energy trader

london


Total Posts: 307
Joined: Apr 2005
 
Posted: 2018-05-01 16:51
@Tony C: you, of all people, will always rock

That was mostly a reflection on my involvment in recent years.
Alas, I havent made drinks on either side of Atlantic in far, far too long.


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