How do settlement rules affect the price of options?

Paul · May 20th, 2003, 9:20 pm

This one from chris33. "For example if I have an option on a stock that settles at T+3, how should this be incorporated into the BS model?"And (from me), how can you incorporate the complicated SP500 expiration fixing rules into an option price?P

FDAXHunter · May 23rd, 2003, 8:48 am

The Settlement delay does not affect the price of the option, at least not in the B/S model (constant interest rate). They could settle T+365 for all you care.What do you mean complicated expiration fixing rules? They are pretty straight forward... just calculate the so called SET (first transaction of each component stock). But you are going to be hedging with futures, so it's more of a problem of having the SET in line with your traded futures, which can be a problem. Not much you can do... Sometimes it'll work for you and sometimes against you.

volat · June 13th, 2003, 11:10 am

Hi,I disagree -this is the 1st time!- with FDAX. Of course the price is slightly modified. All good pricers incorporates sucha feature.... It has just to do with discounting the payoff....Regards.

FDAXHunter · June 15th, 2003, 1:27 pm

Disagree all you want, volat:The question was: "For example if I have an option on a stock that settles at T+3, how should this be incorporated into the BS model?"B/S has constant interest rates, hence it does not matter if I discount with the Spot rate say 3 months or with the 12x15 FRA rate, they will be the same But you are right that any realistic price incorporates this... but of course any realistic pricer does not utilize B/S... all stock options are American Regards.

granchio · July 21st, 2003, 7:53 pm

IMHO, volat is right, even at constant rates you have to correct. B.S. price is E(payoff) at expiry discounted the payoff with the discount factor z(T).if you settle the payoff 3 days later you should discount with z(T+3) hence the price in a constant rates will be different(i.e. BS * z(T+3)/z(T) ).Of course if you include the settlement on the option payoff you should also remember that the premium payment settles later, not to mention the effects on the forward of the settlement rules for the underlying... it is all doable (and done), if a touch tedious.

JDVEGA · August 7th, 2003, 5:44 am

USING FINANCIAL ARBITRAGEOUS ARGUMENTS, ITS EQUIVALENT GIVING THE PAYOFF TODAY OR GIVING IT 3 DAYS / MONTHS... LATER. WHAT YOU HAVE TO DO IS TO APPLY THE IMPLY DISCOUNT FACTOR TO THE PAYOFF AS IT OCCURS IN TIME "T".

kaihenry · August 30th, 2003, 3:07 pm

So how exactly does it work then? Let's say S = $100, X= $100, r=5%, T=1year, v=30%. That makes a call worth $14.23. Now if I settle 3 months later, how does that affect my call price? Alternatively, by how much is it affected if X would be very close to zero?

derivababy · January 15th, 2004, 10:31 am

Hi Kainhenryfeed your data into the Granchio's recipe: BS * z(T+3)/z(T) (just a discount factor adjustment...)Hope this helps.