Standard Portfolio Analysis of Risk(SPAN)は、Chicago Mercantile Exchange(CME)の開発による証拠金の計算方法です。この方法は、世界中の多くのクリアリングハウスと取引所によって、クリアリングハウスがキャリングFCMから、またFCMが顧客から収集する、先物と先物オプションのパフォーマンスボンド(証拠金)の計算のために使用されています。
SPANは、先物とオプションコントラクトの原資産価格の変動、またをオプションの場合には時間による減衰やインプライドボラティリティの変化も反映する16の仮想の市場シナリオを使用して、ポートフォリオが一定の時間内(通常は1日)に耐えうる最悪の場合の損失を割り出すことによって証拠金を設定します。
SPANによる証拠金計算の最初のステップは、最終的な原資産が同じポジションを、複合商品と呼ばれるグループに分けるところから始まります。 次に、SPANは、シナリオごとに最大の仮想損失を発生させた状態をスキャンリスクとし、複合商品内の各ポジションのリスクを計算してまとめます。16のシナリオは、複合商品の価格スキャン範囲(一定の時間内に起こり得る原資産価格の最大の変動)およびボラティリティスキャン範囲(オプションに起こり得るインプライドボラティリティの最大の変動)に基づいて決定します。
原資産価格が$1,000、乗数が100、価格スキャン範囲が6%の株式指数ABCのロング先物とロングプットをひとつずつ保有するポートフォリオを想定します。 このポートフォリオのスキャンリスクは、シナリオ14の$1,125になります。
# |
1 ロング先物 |
1 ロングプット |
合計 |
シナリオ詳細 |
1 |
$0 |
$20 |
$20 |
価格に変動なし。スキャン範囲でボラティリティが上がる |
2 |
$0 |
($18) |
($18) |
価格に変動なし。スキャン範囲でボラティリティが下がる |
3 |
$2,000 |
($1,290) |
$710 |
価格スキャン範囲で価格が1/3上がる、スキャン範囲でボラティリティが上がる |
4 |
$2,000 |
($1,155) |
$845 |
価格スキャン範囲で価格が1/3上がる、スキャン範囲でボラティリティが下がる |
5 |
($2,000) |
$1,600 |
($400) |
価格スキャン範囲で価格が 1/3下がる、スキャン範囲でボラティリティが上がる |
6 |
($2,000) |
$1,375 |
($625) |
価格スキャン範囲で価格が1/3下がる、スキャン範囲でボラティリティが下がる |
7 |
$4,000 |
($2,100) |
$1,900 |
価格スキャン範囲で価格が2/3上がる、スキャン範囲でボラティリティが上がる |
8 |
$4,000 |
($2,330) |
$1,670 |
価格スキャン範囲で価格が2/3上がる、スキャン範囲でボラティリティが下がる |
9 |
($4,000) |
$3,350 |
($650) |
価格スキャン範囲で価格が2/3下がる、スキャン範囲でボラティリティが上がる |
10 |
($4,000) |
$3,100 |
($900) |
価格スキャン範囲で 価格が 2/3下がる、スキャン範囲でボラティリティが下がる |
11 |
$6,000 |
($3,100) |
$2,900 |
価格スキャン範囲で価格が3/3上がる、スキャン範囲でボラティリティが上がる |
12 |
$6,000 |
($3,375) |
$2,625 |
価格スキャン範囲で価格が3/3上がる、スキャン範囲でボラティリティが下がる |
13 |
($6,000) |
$5,150 |
($850) |
価格スキャン範囲で価格が 3/3下がる、スキャン範囲でボラティリティが上がる |
14 |
($6,000) |
$4,875 |
($1,125) |
価格スキャン範囲で価格が 3/3下がる、スキャン範囲でボラティリティが下がる |
15 |
$5,760 |
($3,680) |
$2,080 |
価格が劇的に上がる(価格スキャン範囲の3倍) * 32% |
16 |
($5,760) |
$5,400 |
($360) |
価格が劇的に下がる(価格スキャン範囲の3倍) * 32% |
この後、スキャンリスクチャージがコモディティ内スプレッドチャージ(先物カレンダー・スプレッドのベーシス・リスクを考慮した金額)とスポットチャージ(満期が引渡し可能な銘柄のポジションのリスク上昇をカバーするチャージ)に加算され、商品間スプレッドクレジット(相関する商品間のオフセットポジションに対するマージンクレジット)によるオフセット分減額されます。 この合計額は、ショート・オプションの必要最低額(ディープアウトオブザマネー・オプションを含むポートフォリオの最低必要証拠金を確実に徴収するため)と比較され、いずれか大きい方が複合商品の残額となります。これらの計算は、すべての複合商品に対して行われ、ポートフォリオの必要証拠金合計は、すべての複合商品のリスクの合計から、異なる複合商品間で発生するリスク相殺のためのクレジットを差し引いたものに等しくなります。
PC-SPANとして知られるSPAN必要証拠金の計算に使用されるソフトウェアは、CMEのウェブサイトより利用可能です。
イントロダクション
詳細の参照先
先物オプションは、先物証拠金と同様に、SPANマージンと呼ばれる計算アルゴリズムで取引所によって管理されています。 SPANに関する詳細および機能は、CME Groupのウェブサイト、www.cmegroup.comをご参照下さい。 ウェブサイト内でSPANを検索すると、これに関する情報と機能が沢山見つかります。 SPAN(Standard Portfolio Analysis of Risk)のシステムは、 高度に洗練された手法で、事実上あらゆる市場シナリオを分析し、パフォーマンスボンドの必要額を算出します。
一般的にSPANは以下のように機能します:
SPANは、デリバティブと現物銘柄のポートフォリオが一定の期間(通常は、1取引日)に合理的に発生させ得る最悪の損失を計算し、ポートフォリオ全体のリスクを査定します。これは様々な市場状況でポートフォリオに発生する利益と損失を計算して行われます。 この手法の中核となるのがSPANのリスク配列であり、様々な条件の下で特定のコントラクトがどのように価値を得る、または失うかを示す数値の組み合わせです。条件はそれぞれリスクシナリオと呼ばれます。各リスクシナリオの数値は、価格変動(または原資産価格)、ボラティリティ変動、満期までの時間短縮の特定の組み合わせにおいて、あるコントラクトに発生する利益または損失を表します。
SPANマージンのファイルは取引所によって一定の間隔で1日中 IBKRに送信され、SPANマージン計算機能に接続されます。 先物オプションはすべて、満期になるか口座から決済されるまでリスクがあるものとして計算され続けます。 アウトオブザマネーになる可能性は関係ありません。 すべてのシナリオは、市場のボラティリティが極端になった場合に起こり得ることを考慮する必要があり、そのため、これら先物オプションの証拠金の影響は、オプションのポジションが存在しなくなるまで考慮される必要があります。 SPANの必要証拠金は、あらかじめ設定された極端な場合の市場変動シナリオと比較され、いずれか大きい方が必要証拠金として使用されます。
Introduction
Where to Learn More
Tools provided to monitor and manage margin
How to determine if you are borrowing funds from IBKR
Why does IBKR calculate and report a margin requirement when I am not borrowing funds?
The Standard Portfolio Analysis of Risk (SPAN) is a methodology developed by the CME and used by many clearinghouses and exchanges around the world to calculate the Performance Bond (i.e., margin requirement) on futures and options on futures which the clearinghouse collects from the carrying FCM and the FCM, in turn, from the client.
SPAN establishes margin by determining what the potential worst-case loss a portfolio will sustain over a given time frame (typically set to one day), using a set of 16 hypothetical market scenarios which reflect changes to the underlying price of the future or option contract and, in the case of options, time decay and a change in implied volatility.
The first step in calculating the SPAN requirement is to organize all positions which share the same ultimate underlying into grouping referred to as a Combined Commodity group. Next, SPAN calculates and aggregates, by like scenario, the risk of each position within a Combined Commodity, with that scenario generating the maximum theoretical loss being the Scan Risk. The 16 scenarios are determined based upon that Combined Commodity’s Price Scan Range (the maximum underlying price movement likely to occur for the given timeframe) and Volatility Scan Range (the maximum implied volatility change likely to occur for options).
Assume a hypothetical portfolio having one long future and a one long put on stock index ABC having an underlying price of $1,000, a multiplier of 100 and a Price Scan Range of 6%. For this given portfolio, the Scan Risk would be $1,125 scenario 14.
# |
1 Long Future |
1 Long Put |
Sum |
Scenario Description |
1 |
$0 |
$20 |
$20 |
Price unchanged; Volatility up the Scan Range |
2 |
$0 |
($18) |
($18) |
Price unchanged; Volatility down the Scan Range |
3 |
$2,000 |
($1,290) |
$710 |
Price up 1/3 Price Scan Range; Volatility up the Scan Range |
4 |
$2,000 |
($1,155) |
$845 |
Price up 1/3 Price Scan Range; Volatility down the Scan Range |
5 |
($2,000) |
$1,600 |
($400) |
Price down 1/3 Price Scan Range; Volatility up the Scan Range |
6 |
($2,000) |
$1,375 |
($625) |
Price down 1/3 Price Scan Range; Volatility down the Scan Range |
7 |
$4,000 |
($2,100) |
$1,900 |
Price up 2/3 Price Scan Range; Volatility up the Scan Range |
8 |
$4,000 |
($2,330) |
$1,670 |
Price up 2/3 Price Scan Range; Volatility down the Scan Range |
9 |
($4,000) |
$3,350 |
($650) |
Price down 2/3 Price Scan Range; Volatility up the Scan Range |
10 |
($4,000) |
$3,100 |
($900) |
Price down 2/3 Price Scan Range; Volatility down the Scan Range |
11 |
$6,000 |
($3,100) |
$2,900 |
Price up 3/3 Price Scan Range; Volatility up the Scan Range |
12 |
$6,000 |
($3,375) |
$2,625 |
Price up 3/3 Price Scan Range; Volatility down the Scan Range |
13 |
($6,000) |
$5,150 |
($850) |
Price down 3/3 Price Scan Range; Volatility up the Scan Range |
14 |
($6,000) |
$4,875 |
($1,125) |
Price down 3/3 Price Scan Range; Volatility down the Scan Range |
15 |
$5,760 |
($3,680) |
$2,080 |
Price up extreme (3 times the Price Scan Range) * 32% |
16 |
($5,760) |
$5,400 |
($360) |
Price down extreme (3 times the Price Scan Range) * 32% |
The Scan Risk charge is then added to any Intra-Commodity Spread Charges (an amount that accounts for the basis risk of futures calendar spreads) and Spot Charges (A charge that covers the increased risk of positions in deliverable instruments near expiration) and is reduced by any offset from an Inter-Commodity Spread Credit (a margin credit for offsetting positions between correlated products). This sum is then compared to the Short Option Minimum Requirement (ensures that a minimum margin is collected for portfolios containing deep-out-of-the-money options) with the greater of the two being the risk of the Combined Commodity. These calculations are performed for all Combined Commodities with the Total Margin Requirement for a portfolio equal to the sum of the risk of all Combined Commodities less any credit for risk offsets provided between the different Combined Commodities.
The software for computing SPAN margin requirements, known as PC-SPAN is made available by the CME via its website.
Futures options, as well as futures margins, are governed by the exchange through a calculation algorithm known as SPAN margining. For information on SPAN and how it works, please research the exchange web site for the CME Group, www.cmegroup.com. From their web site you can run a search for SPAN, which will take you to a wealth of information on the subject and how it works. The Standard Portfolio Analysis of Risk system is a highly sophisticated methodology that calculates performance bond requirements by analyzing the “what-ifs” of virtually any market scenario.
In general, this is how SPAN works:
SPAN evaluates overall portfolio risk by calculating the worst possible loss that a portfolio of derivative and physical instruments might reasonably incur over a specified time period (typically one trading day.) This is done by computing the gains and losses that the portfolio would incur under different market conditions. At the core of the methodology is the SPAN risk array, a set of numeric values that indicate how a particular contract will gain or lose value under various conditions. Each condition is called a risk scenario. The numeric value for each risk scenario represents the gain or loss that that particular contract will experience for a particular combination of price (or underlying price) change, volatility change, and decrease in time to expiration.
The SPAN margin files are sent to IBKR at specific intervals throughout the day by the exchange and are plugged into a SPAN margin calculator. All futures options will continue to be calculated as having risk until they are expired out of the account or are closed. The fact that they might be out-of-the-money does not matter. All scenarios must take into account what could happen in extreme market volatility, and as such the margin impact of these futures options will be considered until the option position ceases to exist. The SPAN margin requirements are compared against IBKR's pre-defined extreme market move scenarios and the greater of the two are utilized as margin requirement.
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