The determination methodology for Futures Spread Margins

Transcription

1 The determination methodology for Futures Spread Margins RM Office Version.0

2 Index Introduction... 3 Definition and aim of the Futures Spread Margins Calculation methodology... 4 Page di 6

3 Introduction This document describes the methodology used for the determination of Futures Spread Margins. First of all this kind of margins is defined, describing the aims and the objectives of their existence (point. Then the document describes in detail the calculation methodology applied by the CC&G to determine the amount of the Future Spread Margin (point 3. Definition and aim of the Futures Spread Margins The aim of Futures Spread Margins is to guarantee Futures positions having opposite sign on different maturities (Futures Spread position considering the lower risk level expressed by the interest rate variations: these margins are applied on Futures Spread positions of the same Class. These margins are only computed for Futures positions having opposite sign on different maturities and are equal to the number of Futures Spread positions multiplied for the Future Spread Margin fixed by the CC&G. The Class is the set of contracts of the same kind having the same underlying asset (for example Futures on ENI for the Class of Futures or Options on Fiat shares for the class of options. The number of Futures Spread positions for each Class is equal to Min (Σ long positions; Σ short positions. Page 3 di 6

4 3 Calculation methodology The Futures Spread Margin is determined by the CC&G taking into account that the aim of the Futures Spread Margin is to cover the market risk of two futures position having opposite sign and different maturities. Accordingly the aim is to determine the greatest daily variation, reasonably possible, between the difference of Futures prices F and F (calendar spread having different maturities, and the same difference (calendar spread on the following day. Using the previous notation, the value of a calendar spread on a stock that does not ρ pay dividends is: t ρ t SPR = F F = Se Se, where S is the price of the underlying, ρ e ρ are the interest rates applied on the second and the first maturity and t and t represent the time to maturity. To consider explicitly the case of a calendar spread on a stock that pays dividends between the first and the second maturity, the following notation should be used: SPR = F F = ρdtd ρ ( t ρ t S De e Se expected dividend within the two maturities 3. d, where De ρ dt represents the present value of the Nevertheless this generalization is useless, because the expected dividend affects the level of the calendar spread but it does not have any influence on its variations between two days; so the application of the previous expression can be generalized with a calendar spread without dividends. SPR If the first day A the calendar spread is equal to ρ ( t ρ e e ρt ρt t A = Se Se = S, it can be assumed that the following day B the spread becomes equal to SPR = ( S ± S B e 365 ( ρ ± ρ t ( ρ ± ρ e t 365. So it has been assumed, during a day, a variation of the underlying of ± S, a variation of the interest rates of ± ρ and ± ρ ; moreover a day from the time to maturity has been subtracted. 3 When there are two or more dividends and some of these dividends are distributed before the first maturity and the others between the first and the second maturity we get: STR n ρd itd i ρt = F F = S Die e S i= m i= D e i ρ t d i d i e ρ t Page 4 di 6

5 SPR = SPR Formalizing, the variation of the calendar spread SPR is: B SPR A = ( S ± S e ( ρ ± ρ t ( ρ ± ρ 365 e t 365 S ρ ( t ρ t e e To obtain the largest SPR, some assumptions should be made on ± S, ± ρ and ± ρ. This procedure is repeated for every couple of Futures maturities. The Futures Spread Margin (MFS is assumed to be equal to the highest value of the largest SPR computed for each couple of futures maturities: MFS = Max{ SPR }; i j i, j. The following approach is used to define the hypothesis on ± S, ± ρ and ± ρ : ± S is coherently assumed to be equal to the current Margin Interval, while ρ and ± ρ are fixed equal to the highest daily variations (in absolute value for the appropriate risk free rates. For example, to compute the possible variation of a calendar spread constituted with a Future of first maturity and another Future of third maturity, the largest variations of one month rates and the highest variations of three months rates are considered. The hypothesis about the interest rates variations are appropriately conservative because it is supposed that, between the first and the third maturity of the calendar spread, the yield curve has a torsion equal to ρ + ρ : that is that the two maturities experience simultaneously their largest variation since the introduction of the Euro (January 4 th, 999 and that these variations are of opposite sign. With regards to the signs of the variations to apply, the most protective result can be obtained by assuming an increase in the price of the underlying (+ S equal to the side of the margin interval, a decrease of the interest rate for the first maturity (- ρ and an increase of the interest rate for the second maturity 4 (+ ρ. The calendar spreads that are being considered are based on mid-market prices, while in principle half of the bid-ask spread should be added to the short Futures price and subtracted from the long Futures price, like formalized in the following analytical. 4 This statement can be explained (without using the analytical characteristics of the exponential function in the following way: an interest rate increase for the second maturity raises the Futures price of the second maturity date, a decrease of the rates for the first maturity lowers the Futures price for the first maturity date and the calendar spread (price difference rises. The positive S causes an increase in the price of both the maturities but has a larger effect on the prices of the second maturity (the delta of a Future increases with the time to maturity, raising (slightly the calendar spread. Page 5 di 6

6 expression, where BAS e BAS are the bid-ask spread of the first and second maturities: SPR BA = ( S ± S e t BAS + BAS e + ( ρ ± ρ t ( ρ ± ρ To take into account the bid-ask spread, an additional term (obtained by applying the methodology previously described equal to the highest bid-ask spread given to the market makers for the first maturity of the Future, must be added to the mathematical Futures Spread margin.. Page 6 di 6