FX OPTIONS MARGIN MODEL SEPTEMBER 2015, SAXO BANK

Transcription

1 F PTINS MRGIN MDEL SEPTEMER 2015, S NK

2 F Expiry Margin Description (1/2) Calculation For a given currency pair the F Expiry Margin model calculates a potential maximum future loss in a given F option strategy (if there is a maximum loss it will always occur at a strike) given the current market prices. If there is a potential unlimited loss either downwards (spot price limited to 0) or upwards, we look at the potential exposure at expiry in these intervals and apply spot margin requirement on the notional amount. If the strategy has both a potential loss at a strike and a potential unlimited loss downwards and/or upwards, the margin requirement will be the maximum of the three calculations. The calculations are done per expiry and summed up. In any case, however, evaluating the potential outcome of all options in the portfolio, the total margin requirement will be capped to the highest potential exposure multiplied by spot margin requirement. This will ensure that we always have a margin requirement smaller than or equal to the margin requirement of an equivalent spot position. The model allows for netting with spot and forwards if they are in the same currency cross as the options. Spot and forwards are treated the same. The model allocates any available spot and forward amount to the option strategy (per expiry and nearest expiry have priority), such that the highest potential exposure at expiry on the options is minimized. ny amount of spot and forwards that is not allocated to an expiry will be margined as a spot position.

3 F Expiry Margin Description (2/2) Collateral For each expiry and currency pair, we consider the net value of an option strategy. If the net value of an option strategy for one expiry is positive, the model will deduct this value from the client collateral. This means that it is not possible to use the value of the options for margin trading. If the net value of an option strategy for one expiry is negative, there is no collateral deduction. Example EURUSD spot is trading at 1.09, and we are entering a 1 million EURUSD short call spread at strike 1.10 and at strike 1.11 with the two calls having the same expiry. The maximum loss is the difference between the strikes, so 1,000,000 x 0.01 = 10k USD. There is no potential unlimited loss downwards or upwards. The highest potential exposure at expiry is 1 million, since this will be the case if the short leg of the spread expires in-the-money and the long leg of the spread expires out-of-the-money. So the margin requirement will be the minimum of the maximum loss (10k USD) and the margin requirement for a 1 million spot position. Had EURUSD spot been at 1.105, i.e. having an unrealized loss of 5k, the margin requirement would be 5k USD. (maximum future loss)

4 Spot allocation in F Expiry Margin explained (1/2) ssume that we have a short call spread with an amount of 1 of some instrument at strike 10 and 15 at some expiry (see Figure 1). Now you open an amount of 1 at a price of 15 of the underlying. How can this be allocated to this option strategy? It will be allocated such that the maximum potential exposure in the strategy is minimized. Figure 1 Hence, without any allocation of spot the maximum potential exposure is -1 and it happens if they expire when the underlying price is between 10 and 15. elow 10, the exposure is 0. bove 10, the exposure is also

5 Spot allocation in F Expiry Margin explained (2/2) What happens if we allocate 0.5 of the underlying to the strategy? The payoff profile will change (see Figure 2). Now, the maximum potential exposure is 0.5. It will be 0.5 below 10, it will be -0.5 between 10 and 15, and it will be 0.5 above 15. ny other allocation of spot will lead to a maximum potential exposure in the interval (0.5, 1]. Thus, with an allocation of 0.5, we have hit the minimum. The margin calculation will then be based on the above strategy plus the remaining spot of 0.5. This means that it will be the maximum of spot margin times 0.5 (which is the exposure below 10) and the loss at the strike 15, plus the remaining 0.5 of spot times spot margin. If we have another option strategy with a later expiry, the remaining spot will attempt to be allocated to this and the exact same calculation is done again. This reasoning will continue until there is either no option expiries left or any amount of spot left

6 Reduce Margin Requirement in F Expiry Margin (1/3) Reducing with spot In the new model, we have to consider the delta signed notional for each expiry and currency pair. Delta signed notional means: Long call: Positive notional Long put: Negative notional Short call: Negative notional Short put: Positive notional Then the spot amount that gives the largest margin reduction that can be done in an expiry is calculated as the difference between the largest potential long exposure and the largest potential short exposure divided by -2 (on the options in the expiry). I.e. for each expiry: ptimal amount to allocate = (exp long+exp short ) 2 Where exp long is positive or zero, and exp short is negative or zero. Note that above formula is also the formula to find the amount of spot to allocate to each expiry. I.e. the formula to find 0.5 on previous slide.

7 Reduce Margin Requirement in F Expiry Margin (2/3) Reducing with spot Example Instrument Strike Expiry Date L/S mount So we have three strikes. What is the potential exposure? elow the first strike, 1.045: We have two options that are ITM. Short put of 10M and short put of 170M. Hence, the potential exposure is 180M. etween and 1.12: We have one option that is ITM. Short put of 170M. etween 1.12 and 1.145: We have one option that is ITM. Short call of -50M. bove 1.145: We have two options that are ITM. Short call of -50M and short call of -10M. Hence, a total of -60M. So the largest potential long exposure is 180M, and the largest potential short exposure is -60M. The spot amount that gives the largest margin reduction on the first expiry is then (180 + (-60)) / -2 = -60M. This calculation is done per each expiry. Since the spot allocation prioritizes the nearest expiry highest, we will, depending on the sign of spot to trade to get the largest reduction on the first expiry, sum up all negative spot amount or positive spot amounts to get the total amount of spot to trade.

8 Reduce Margin Requirement in F Expiry Margin (3/3) Reducing with spot Example This means that, if we add following position in the example: What is then the potential exposure? elow 1.10: ITM Short put of 150M bove 1.10: Nothing that is ITM So the largest potential long exposure is 150M and the largest potential short exposure is 0M. The spot amount that gives the largest margin reduction will then be ( ) / -2 = -75M. The total amount of spot to trade is then -135M. Had it been a short call, the spot amount that gives the largest margin reduction would have been 75M (positive), and since the nearest expiry has priority we would have disregarded this and traded -60M. However, this should only be done if: 1. The combined delta has the opposite sign of the total spot amount to trade. 2. The combined delta of the options is larger than or equal to the exposure of 135M (in this example). If the combined delta is smaller, then a regular delta hedge should be traded, since we would otherwise potentially increase the risk of the portfolio. 3. In any other situation, the margin can only be reduced with options.

9 F Expiry Margin Impact analysis (1/7) The following follows an impact analysis when changing from the old margin method to the F Expiry Margin method. set of what is considered the most traded strategies has been chosen to show the impact. Naked short call Covered call Protective put Short call spread, two different expiries, ITM-version and TM-version Long call spread, two different expiries, ITM-version and TM-version Short straddle Long straddle Naked short call 1M EURUSD, strike 1.10, expiry May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -36,199 Closing amount -36,661 ccount value 998,428 ccount value 998,357 Net equity for margin 998,428 Net equity for margin 998,357 vailable for margin trading 968,428 vailable for margin trading 975,691 Used for margin requirements 30,000 Used for margin requirements 22,666 Not available as margin collateral 0 Not available as margin collateral 0

10 F Expiry Margin Impact analysis (2/7) Covered call 1M EURUSD spot, 1M EURUSD SC, strike 1.10, expiry May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -36,679 Closing amount -37,100 ccount value 997,902 ccount value 997,889 Net equity for margin 997,902 Net equity for margin 997,889 vailable for margin trading 967,902 vailable for margin trading 979,595 Used for margin requirements 30,000 Used for margin requirements 18,294 Not available as margin collateral 0 Not available as margin collateral 0 Protective put 1M EURUSD spot, 1M EURUSD P, strike 1.08, expiry May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount 25,649 Closing amount 25,880 ccount value 998,618 ccount value 998,444 Net equity for margin 972,969 Net equity for margin 998,444 vailable for margin trading 951,620 vailable for margin trading 973,667 Used for margin requirements 21,349 Used for margin requirements 24,778 Not available as margin collateral 25,649 Not available as margin collateral 0

11 F Expiry Margin Impact analysis (3/7) ITM Short call spread 1M EURUSD SC, strike 1.09, 1M EURUSD C, strike 1.11, expiries May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -10,919 Closing amount -10,837 ccount value 997,703 ccount value 997,905 Net equity for margin 997,703 Net equity for margin 997,905 vailable for margin trading 989,255 vailable for margin trading 995,135 Used for margin requirements 8,447 Used for margin requirements 2,771 Not available as margin collateral 0 Not available as margin collateral 0 ITM Short call spread 1M EURUSD SC, strike 1.09, 1M EURUSD C, strike 1.11, expiries ug 2015: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -8,973 Closing amount -8,836 ccount value 998,578 ccount value 998,907 Net equity for margin 998,578 Net equity for margin 998,907 vailable for margin trading 988,570 vailable for margin trading 984,507 Used for margin requirements 10,008 Used for margin requirements 14,400 Not available as margin collateral 0 Not available as margin collateral 0

12 F Expiry Margin Impact analysis (4/7) TM Short call spread 1M EURUSD SC, strike 1.11, 1M EURUSD C, strike 1.12, expiries May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -5,404 Closing amount -5,285 ccount value 997,694 ccount value 998,086 Net equity for margin 997,694 Net equity for margin 998,086 vailable for margin trading 992,840 vailable for margin trading 996,623 Used for margin requirements 4,854 Used for margin requirements 1,463 Not available as margin collateral 0 Not available as margin collateral 0 TM Short call spread 1M EURUSD SC, strike 1.11, 1M EURUSD C, strike 1.12, expiries ug 2015: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -2,031 Closing amount -1,913 ccount value 998,597 ccount value 998,816 Net equity for margin 998,597 Net equity for margin 998,816 vailable for margin trading 990,815 vailable for margin trading 993,680 Used for margin requirements 7,782 Used for margin requirements 5,135 Not available as margin collateral 0 Not available as margin collateral 0

13 F Expiry Margin Impact analysis (5/7) ITM Long call spread 1M EURUSD C, strike 1.09, 1M EURUSD SC, strike 1.11, expiries May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount 8,632 Closing amount 8,752 ccount value 997,775 ccount value 997,994 Net equity for margin 989,143 Net equity for margin 997,994 vailable for margin trading 989,143 vailable for margin trading 995,217 Used for margin requirements 0 Used for margin requirements 2,777 Not available as margin collateral 8,632 Not available as margin collateral 0 ITM Long call spread 1M EURUSD C, strike 1.09, 1M EURUSD SC, strike 1.11, expiries ug 2015: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount 6,301 Closing amount 6,574 ccount value 998,657 ccount value 999,178 Net equity for margin 992,356 Net equity for margin 999,178 vailable for margin trading 992,356 vailable for margin trading 984,358 Used for margin requirements 0 Used for margin requirements 14,820 Not available as margin collateral 6,301 Not available as margin collateral 0

14 F Expiry Margin Impact analysis (6/7) TM Long call spread 1M EURUSD C, strike 1.11, 1M EURUSD SC, strike 1.12, expiries May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount 3,015 Closing amount 3,106 ccount value 997,688 ccount value 997,898 Net equity for margin 994,673 Net equity for margin 997,898 vailable for margin trading 994,673 vailable for margin trading 996,403 Used for margin requirements 0 Used for margin requirements 1,496 Not available as margin collateral 3,015 Not available as margin collateral 0 TM Long call spread 1M EURUSD C, strike 1.11, 1M EURUSD SC, strike 1.12, expiries ug 2015: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount 292 Closing amount 366 ccount value 998,648 ccount value 998,903 Net equity for margin 998,356 Net equity for margin 998,903 vailable for margin trading 998,356 vailable for margin trading 994,742 Used for margin requirements 0 Used for margin requirements 4,162 Not available as margin collateral 292 Not available as margin collateral 0

15 F Expiry Margin Impact analysis (7/7) Short straddle 1M EURUSD SP, 1M EURUSD SC, strikes 1.095, expiries May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount -70,495 Closing amount -71,399 ccount value 997,456 ccount value 997,807 Net equity for margin 997,456 Net equity for margin 997,807 vailable for margin trading 967,456 vailable for margin trading 981,381 Used for margin requirements 30,000 Used for margin requirements 16,426 Not available as margin collateral 0 Not available as margin collateral 0 Long straddle 1M EURUSD P, 1M EURUSD C, strikes 1.095, expiries May 2016: EURUSD spot: F Expiry Margin EUR ld Margin EUR Closing amount 68,196 Closing amount 69,414 ccount value 997,766 ccount value 997,989 Net equity for margin 929,570 Net equity for margin 997,989 vailable for margin trading 929,570 vailable for margin trading 981,665 Used for margin requirements 0 Used for margin requirements 0 Not available as margin collateral 68,196 Not available as margin collateral 16,324

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