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MaxwellSheffield
Topic Author
Posts: 70
Joined: December 17th, 2013, 11:08 pm

### Option on futures

Hi all,Option on Eurodollar futures with an up front premium are quoted , maturity= start date of the underlying future . No margin for the option . Those instruments does not seem to be collateralized. How do we price them ? In particular, how do we discount the payoff? It would be theoretically wrong to use the MM related to the collateral rate , as there is no collateral to finance the upfront ...Should I really consider the funding cost?

BenjG
Posts: 28
Joined: November 25th, 2013, 3:17 pm

### Option on futures

I don't think there is any reason why you should use the collateral rate to discount the option.Indeed, following classical Black Scholes arguments, the dynamic hedging strategy will be to buy/sell the futures by borrowing/lending at a risk free rate. In your case, this risk free rate has nothing to do with the collateral rate of the futures. It is linked to your debt-equity structure (EURIBOR + spread for a bank).However, if the option is collateralized with a different collateral rate (let's say EONIA), then posting the margin calls will be equivalent to (see Bianchetti) borrowing/lending at EONIA.The key point (and I don't know the market practice) is: will you model the futures price with GBM or the underlying of the futures ? Because your risks will not be the same !

Martinghoul
Posts: 3255
Joined: July 18th, 2006, 5:49 am

### Option on futures

I think you shouldn't be discounting the premium... If my recollection is correct (and I think I posted on this very subject a long time ago), that's the right way to do it.

MaxwellSheffield
Topic Author
Posts: 70
Joined: December 17th, 2013, 11:08 pm

### Option on futures

I found this paper ' http://developers.opengamma.com/quantit ... amma.pdfit seems that the author discounts with the "risk free rate".BenjG : I agree that uncollateralized transaction should be discounted at the funding rate. As for the future price, it is modelled with a short rate model.Martinghoul : I m curious to see that, I could not find your topic.

BramJ
Posts: 372
Joined: January 10th, 2006, 2:01 pm

### Option on futures

MaxwellSheffield
Topic Author
Posts: 70
Joined: December 17th, 2013, 11:08 pm

### Option on futures

your link is about american options, unless you talk about the fact that they do not discount . Well , it is not my problem actually. In the link, they want to price a future option where there is a margin process for the option as well.In my case, Eurodollar future option (CME), there is no margin process.

BenjG
Posts: 28
Joined: November 25th, 2013, 3:17 pm

### Option on futures

Sorry, but I don't understand where is your problem.If I remember well, the futures is martingale under the RN measure (not the forward measure, that is why you need a convexity adjustment to retrieve the price from the quoted forward). Hence, you can use a Black Scholes formula. Is it the fact that you have to consider the risk free rate constant that is incorrect for you ?I didn't go through the details of Henrard's paper but I don't think it is robust to use a 2 factors model. Indeed, when you'll have your nice formula how will you callibrate the parameters ? Vol and correl ? It's the same problem when considering quanto options. You can get nice closed form solution with smile but the incertitude on the correlation makes it difficult to use in practice... And you finaly end up with the classic log-normal quanto adjustment because it is robust !

BramJ
Posts: 372
Joined: January 10th, 2006, 2:01 pm

### Option on futures

QuoteOriginally posted by: MaxwellSheffieldyour link is about american options, unless you talk about the fact that they do not discount . Well , it is not my problem actually. In the link, they want to price a future option where there is a margin process for the option as well.In my case, Eurodollar future option (CME), there is no margin process.Take the time to read through the tread. From that thread:QuoteTo translate symbolically from the BS DE to the fully margined futures options DE (see Haug section 1.1.4 - but it has a typo - or my notes chapter SAFEX, the SA futures exchange) you set q=r=0 and S=F.

cemil
Posts: 221
Joined: September 16th, 2005, 7:44 am

### Option on futures

Hello guys,Are anybody have clues about american option on interest future pricing under normal volatility?
Last edited by cemil on February 5th, 2014, 11:00 pm, edited 1 time in total.

Cuchulainn
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Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Option on futures

I see OpenGamma has something to say http://developers.opengamma.com/quantit ... mma.pdfNot sure if that is what you are looking for.
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MaxwellSheffield
Topic Author
Posts: 70
Joined: December 17th, 2013, 11:08 pm

### Option on futures

I think I was not clear. First of all, thank you for your contribution. BenjG :Hence, you can use a Black Scholes formula. Is it the fact that you have to consider the risk free rate constant that is incorrect for you ?BramJ : To translate symbolically from the BS DE to the fully margined futures options DE (see Haug section 1.1.4 - but it has a typo - or my notes chapter SAFEX, the SA futures exchange) you set q=r=0 and S=F. For sure , we have to discount since there is no magining , as said in my first post , as said in the thread in nuclear finance, as said by BenjG. Furthermore, Marc Henrard in his paper uses the MM account as numeraire. At the time those papers were written, there was one single curve( except Henrard 's)Now ' Ok let assume a BS model, r constant or not , itis not the problem , but its nature ....what is r in practice ? What should I use to discount ? My OIS curve ? It seems wrong since there is no collateral. That is my problem.In other words : Why should I use OIS discounting in an uncollateralized derivative?If OIS discounting is wrong, How should I discount ? Am I nitpicking cuz I want to include FVA?For BenjG, the final purpose of that is to construct curves considering convexity adjustments. I want to build a 3m libor curve to price derivatives under CSA. You must know that the most liquid instruments must be priced considering the OIS curve and do not have standard cash flow. So the simplest way to get this adjustments is by using a short rate model, so I m doing the inverse of what you talked about. I wanna calibrate my model to Options onfutures to adjust my OIS and Libor curves.
Last edited by MaxwellSheffield on February 5th, 2014, 11:00 pm, edited 1 time in total.

BenjG
Posts: 28
Joined: November 25th, 2013, 3:17 pm

### Option on futures

OK now I understand ! You want to get the parameters that you will use in your bootstrap. Hence what you are looking for is an instrument that contains the OIS volatility and correlation information.So let's say you use a 2 factors model (Henrard's or the other proposed below), you will still have 1 equation and 2 unknowns (correlation and OIS vol giving your Libor vol already calibrated). Have you any idea about another liquid derivative that could close the problem ?By the way, I think you should have a look at this paper (also on wilmott magazine march 2013). We derived a convexity adjustment using a slightly different approach. While Pitterbarg ("Funding beyound discounting" that was used by Henrad I think) used a 2 factors model on the Libor and basis Libor-OIS, we used it on the Libor and OIS...In practice you consider a constant basis, hence no convexity adjustment. Moreover, if the trade is not collateralized then you use the Libor curve to discount +CVA+DVA+FVA (in theory).

MaxwellSheffield
Topic Author
Posts: 70
Joined: December 17th, 2013, 11:08 pm

### Option on futures

Thx BenjG for your paper , I ll have a look.I keep the model simple ,no stochastic spread and one factor.

BenjG
Posts: 28
Joined: November 25th, 2013, 3:17 pm

### Option on futures

If you have only one factor then how could you derive the convexity adjustment ? You'll need at some point the joint distribution OIS-Libor. One convenient choice is a 2 factors HW model, that allows to change of measure simply.

MaxwellSheffield
Topic Author
Posts: 70
Joined: December 17th, 2013, 11:08 pm

### Option on futures

the spread is constant