Portfolio Margin

Dederi uses portfolio margin for strategy-level risk control. To accurately evaluate the maximum potential loss under portfolio margin, two key factors are considered: ±15% fluctuations in future prices and the maximum changes in option implied volatility. Additionally, we introduce future contingency and option contingency to address risks arising from liquidity shocks.

Future Simulated PnL and Contingency

Future Simulated PnL

Consider futures contract $i$ with expiration date $T_i$ , mark price $F^{T_i}$ , and current position $Q_i$ . The FutureSimPnL with price shock factor $\Delta_k$ , where $\Delta_k \in \text{PriceShockRange}$ , is calculated as follows:

FutureSimPnL = \sum_{i}[Q_i(F^{T_i}(1+\Delta_k)) - Q_iF^{T_i}] = \Delta_k \sum_{i}Q_iF^{T_i}

Future Contingency

Future contingency accounts for the negative impact of transactions on liquidity, particularly for large position traders. By incorporating future contingency into margin calculations, liquidity risks caused by transactions can be mitigated effectively. Given the current index price $I_0$ , the future contingency is calculated as follows:

FutureContingency = FutureContingencyFactor \cdot I_0 \cdot \sum_{i=1}^{N} |Q_i|

Example

Alice holds 10 long positions in ETH-10JAN24 futures, with a current price of

I_0 = 2243.3

and an annualized basis rate

ABR = 0.08

F_0 = 2243.3 \cdot e^{0.08 \cdot (20 / 365)} = 2253.2

FutureContingency = 0.006 \cdot 2243.3 \cdot 10 = 134.6

Future Simulated PnL Table:

Price Shock	-15%	-12%	-9%	-6%	-3%	0%	3%	6%	9%	12%	15%
PnL	-3380	-2704	-2028	-1352	-676	0	676	1352	2028	2704	3380

Option Simulated PnL and Contingency

Option Simulated PnL

Assume the current time is $t$ , option $i$ has a strike price $K$ and expiration $T_i$ , with the underlying futures price for the same expiration $F^{T_i}$ . Futures price under ±15% fluctuation can be expressed as:

F_k^{T_i} = (1 + \Delta_k) F^{T_i}

For implied volatility, we consider three scenarios: up, same, and down, based on $\text{MaxIVChange}$ :

MaxIVChange_{up} = \left(\frac{30}{T_{\text{days}}}\right)^{VPower} \cdot UpFactor

MaxIVChange_{down} = \left(\frac{30}{T_{\text{days}}}\right)^{VPower} \cdot DownFactor

Where $T_{\text{days}}$ is the remaining days to expiration. For $T_{\text{days}} > 30$ , $\text{VPower}$ is set to $\text{LongTermVPower}$ ; otherwise, it is $\text{ShortTermVPower}$ . The adjusted implied volatilities are calculated as:

\sigma_i^{down} = \sigma_i(1 - MaxIVChange_{down}), \sigma_i^{same} = \sigma_i, \sigma_i^{up} = \sigma_i(1 + MaxIVChange_{up})

By inputting the initial parameters $F^{T_i}, \sigma_i, T_i, t, K, r$ into the Black model , we can obtain the initial prices of options with different types (Call/Put) and strike prices under current market conditions. Subsequently, we input different futures prices and volatilities into the Black model, generating 33 option prices (11 $\Delta k$ × 3 scenarios). Finally, we calculate the OptionSimPnL by comparing these prices with the initial option prices of the same type and strike price. The algorithm is as follows:

OptionSimPnL_k^{up} = \sum_{i=1}^{N} \left[Q_i \left(V(F_k^{T_i},\sigma_i^{up},T_i,t,K,r)-V(F^{T_i},\sigma_i,T_i,t,K,r)\right)\right]

OptionSimPnL_k^{same} = \sum_{i=1}^{N} \left[Q_i \left(V(F_k^{T_i},\sigma_i^{same},T_i,t,K,r)-V(F^{T_i},\sigma_i,T_i,t,K,r)\right)\right]

OptionSimPnL_k^{down} = \sum_{i=1}^{N} \left[Q_i \left(V(F_k^{T_i},\sigma_i^{down},T_i,t,K,r)-V(F^{T_i},\sigma_i,T_i,t,K,r)\right)\right]

Example

Continuing from the previous example, Alice not only holds 10 long ETH-10JAN24 futures contracts but also owns 10 long ETH-10JAN24-2300-C call options. The current underlying futures price is

F_0=2253.2

, with remaining 20 days to expiration and implied volatility given as

\sigma_i=0.2

MaxIVChange_{\text{up}} = \left(\frac{30}{20}\right)^{0.3} \cdot 0.45 = 0.5082

MaxIVChange_{\text{down}} = \left(\frac{30}{20}\right)^{0.3} \cdot 0.3 = 0.3388

\sigma_i^{up} = 0.2 \cdot (1 + 0.5082) = 0.3016

\sigma_i^{down} = 0.2 \cdot (1 - 0.3388) = 0.1322

Option Simulated PnL Table:

Price Shock	Futures Price	up	same	down
-15%	1915.2	-229.2	-231.4	-231.4
-12%	1982.8	-221.7	-231.2	-231.4
-9%	2050.4	-198.0	-229.0	-231.4
-6%	2118.0	-138.0	-215.1	-230.6
-3%	2185.6	-13.9	-158.0	-217.0
0%	2253.2	202.6	0.00	-124.5
3%	2320.8	528.4	311.8	169.7
6%	2388.4	962.5	782.9	691.4
9%	2456.0	1487.8	1368.8	1332.7
12%	2523.6	2079.3	2014.2	2004.4
15%	2591.2	2712.5	2682.0	2680.1

Option Contingency

Option contingency, similar to futures contingency, addresses the liquidity impact of options trading. Including this in margin calculations effectively mitigates potential risks arising from trading-induced liquidity changes. For a given expiration date $T$ , the corresponding futures price and strike prices of the options are $F^T$ and $K^T$ , respectively. For each expiration date, options are arranged by their respective strike prices (i.e., $K_1, K_2, ..., K_n$ ), and, based on this ordering, the option positions at strike $j$ are calculated as follows:

StrikePosition(K_j^T) = CallPosition(K_j^T) + PutPosition(K_j^T)

Calculate $\text{AdjustedStrikePosition}$ ：

AdjustedStrikePosition(K_j^T) = \begin{cases} StrikePosition \cdot \frac{ \left| \frac{K_j^T - F^T}{F^T} \right|}{ATMRange}, &if \left| \frac{K_j^T - F^T}{F^T} \right| < ATMRange \\[8pt] StrikePosition, &else \end{cases}

Calculate $\text{NetPosition}$ ：

Strike prices are partitioned into two groups based on their relation to $F^T$ (above and below). Within each group, the $\text{NetPosition}$ is set equal to the $\text{AdjustedStrikePosition}$ for the strike price closest to $\text{ATMRange}$ .

Starting from the two nearest strike prices in each group, the calculation extends outward to all strike prices. Specifically, it proceeds sequentially from the higher strike near $\text{ATMRange}$ toward the maximum strike, and from the lower strike near $\text{ATMRange}$ toward the minimum strike.

If the $\text{NetPosition}$ of the previous strike price is positive, the $\text{NetPosition}$ of the current strike price equals the $\text{AdjustedStrikePosition}$ of the current strike price plus the $\text{NetPosition}$ of the previous strike price. If the $\text{NetPosition}$ of the previous strike price is zero or negative, the $\text{NetPosition}$ of the current strike price equals the $\text{AdjustedStrikePosition}$ of the current strike price.

Example

Assuming the current BTC futures price is 43219.77, the calculation of the net positions for options proceeds as follows:

Call Position	Strike	Put Position	Strike Position	$\frac{K_T - F^T}{F^T}$	Adjusted Strike Position	Net Position
	43200
10	43300	-20	-10	0.19% < 10%	-0.19	-0.19
50	43600	-30	20	0.88% < 10%	1.76	1.76
-30	44000	-40	-70	1.81% < 10%	-12.64	-10.69
80	45000	60	140	4.12% < 10%	57.67	57.67
-15	50000	25	10	15.69% > 10%	10.00	67.67

ContingencyFactorPosition(T) = -((-0.19) + (-10.69)) = 10.88

Calculate $\text{OptionContingency}$ ：

ContingencyFactorPosition(T) = -\sum_{j=1}^{n} \min(NetPosition(K_j^T), 0)

OptionContingency(T) = OptionContingencyFactor \cdot ContingencyFactorPosition(T) \cdot F^T

OptionContingency = \sum_{T} OptionContingency(T)