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bazzat
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Joined: May 6th, 2011, 3:14 pm

Time value of interest rate collar

June 1st, 2011, 12:55 pm

Hi all,I am currently evaluating EURIBOR zero-cost collars for hedging purposes. I noticed that while the total NPV of such a strategy is 0, the intrinsic and time values are non-zero (but with opposite sign). Intuitively I would expect a zero-cost strategy to have zero time value. In particular, if I short a collar (i.e. a short cap and long floor) the time value is negative and the cash flows as implied by the forward rates have a positive value. So my question is, where exactly does this negative time value come from? I see a couple of possible candidates to explain this, but I am unsure:1) The risk premium of the strategy i.e. expected spot rates under the real world measure are higher than current forward rates. 2) The convexity of ZCB prices with respect to rates i.e. expected spot rates under the risk-neutral measure are higher than current forward rates. Can anyone help clear this up for me?Thanks,B.
 
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DocToc
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Joined: January 20th, 2010, 9:32 am

Time value of interest rate collar

June 1st, 2011, 5:47 pm

my 2 cents: by collar i assume you mean a risk reversal. you can make this zero cost by buying an atm floor and selling otm caps (assuming your skew sloped up from atm to otm on the cap side).therefore at initiation assuming this is zero cost the forwards are roughly near the atm floor therefore giving you a -ve time value. as the forward moves say market sells off massively then your otm cap now becomes a short atm cap therefore => you get a +ve time value.theoretically if there were no skew then i dont think you should have a time value as you would buy the x-10bps floor and sell x+10 bps cap to get a zero pv (in a normal model) and you MUST also have equal and opposite theta's. maybe its more to do with lognormality and introduction of a skew.But I am sure there are much more experienced people who can guide you.
 
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bazzat
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Time value of interest rate collar

June 2nd, 2011, 7:23 am

Thanks for your reply DocToc.By short collar I mean short cap and long floor. Both are OTM. Copy and paste the Bloomberg data below into Excel and you will see that the values in the Time PV column sum to a negative number and the values in the Intrinsic PV sum to a positive number. I don't think the reason is due to lognormality as the data is from market quotes and is model independent. (Apologies, I cannot attach a file directly).Expiry,Pay Date,Days,Notional,Cap Strike,Cap Vols,Floor Strike,Floor Vols,Reset Rate,Hedge Ratio,Payment,Discount,Intrinsic PV,Time PV,PV09/02/2011,12/06/2011,91,"-10,000,000.00",2.5,86,1.68269,84,0.45634,-1,"31,000.77",0.99858,30954.92,1.83,"30,956.75"12/02/2011,06/06/2012,183,"-10,000,000.00",2.5,88.59,1.68269,86.65,0.52353,-0.97,"59,148.90",0.996445,58714.7,223.95,"58,938.65"05/31/2012,12/06/2012,183,"-10,000,000.00",2.5,73.78,1.68269,77.26,0.77156,-0.86,"48,608.84",0.993021,45992.45,2277.16,"48,269.62"12/04/2012,06/06/2013,182,"-10,000,000.00",2.5,70.32,1.68269,74.2,1.17454,-0.82,"32,569.46",0.987582,25370.96,6794.04,"32,165.00"06/04/2013,12/06/2013,183,"-10,000,000.00",2.5,57.54,1.68269,62.4,1.69337,-0.8,"12,294.09",0.979911,0,12047.11,"12,047.11"12/04/2013,06/06/2014,182,"-10,000,000.00",2.5,55.21,1.68269,59.91,2.18568,-0.83,"-8,332.69",0.969946,0,-8082.26,"-8,082.26"06/04/2014,12/08/2014,185,"-10,000,000.00",2.5,43.42,1.68269,47.95,2.48431,-0.82,"-19,786.79",0.957543,0,-18946.7,"-18,946.70"12/04/2014,06/08/2015,182,"-10,000,000.00",2.5,42.14,1.68269,46.93,2.89422,-0.84,"-37,205.59",0.94358,-18805.47,-16300.98,"-35,106.44"06/04/2015,12/07/2015,182,"-10,000,000.00",2.5,36.1,1.68269,40.92,3.37848,-0.83,"-57,213.58",0.928024,-41215.23,-11880.33,"-53,095.55"12/03/2015,06/06/2016,182,"-10,000,000.00",2.5,34.94,1.68269,40.3,3.74543,-0.83,"-73,699.97",0.911072,-57364.21,-9781.74,"-67,145.95"
 
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bazzat
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Joined: May 6th, 2011, 3:14 pm

Time value of interest rate collar

June 2nd, 2011, 7:30 am

Or perhaps the reason is as simple as the fact that even though the cost is 0, overall, I am taking on risk - the risk of a short call being open-ended. Therefore, the overall position is short and analgous to a short cap or call option where the option writer receives money but gives away time value. What is puzzling me is the fact that with this strategy the option writer receives no money, but is still short time value.