组合 Greeks 聚合 Delta

问题分析

A portfolio contains the following positions:

• 200 call options with a delta of 0.6
• 150 put options with a delta of -0.4
• A short position of 50 shares of the underlying asset.
  What is the portfolio's aggregate delta?

解法

根据题目要求实现相应功能。核心逻辑需要：

// 核心数据结构和方法——根据题目 API 约定实现
// 1. 确定状态表示——选择支持所需操作的数据结构
// 2. 实现核心算法——确保 O(·) 时间复杂度和正确性
// 3. 处理边界条件——空输入、极值参数、并发访问

验证

用具体输入验证：构造已知输入的测试用例，确认输出匹配预期结果。

复杂度与边界

• 时间复杂度：取决于选用的算法
• 空间复杂度：取决于数据规模
• 关键边界条件：空输入、极值参数、并发场景下的正确性保证

英文解析

Analysis

A portfolio contains: 200 call options with delta 0.6, 150 put options with delta -0.4, and a short position of 50 shares of the underlying asset. The portfolio's aggregate delta is the sum of all position deltas multiplied by their quantities: delta_portfolio = sum(delta_i * quantity_i). Each share has delta = 1, so short 50 shares contributes -50 to aggregate delta.

Solution

struct Position { int quantity; double delta; bool is_share; };
double aggregateDelta(const std::vector<Position>& positions) {
    double total = 0;
    for (const auto& p : positions) {
        double position_delta = p.delta * p.quantity;
        if (p.is_share && p.quantity < 0) position_delta = p.quantity;  // Shares have delta=1
        total += position_delta;
    }
    return total;  // = 200*0.6 + 150*(-0.4) + (-50)*1 = 120 - 60 - 50 = 10
}

Complexity & Edge Cases

• Time complexity: O(N) where N = number of positions
• Space complexity: O(1)
• Edge cases: (1) Short shares contribute negative delta (delta = -1 per share) (2) Delta can exceed +/-1 for options near expiration (3) Portfolio delta of 0 is delta-neutral (market-neutral)

Verification

Compute: 2000.6 + 150(-0.4) + (-50)*1 = 120 - 60 - 50 = 10. Verify positive aggregate delta means portfolio gains when underlying rises. Test delta-neutral scenario (aggregate delta = 0).

Key Considerations

Aggregate delta measures the portfolio's directional exposure to the underlying. Delta = 10 means the portfolio behaves like holding 10 shares long - it gains approximately $10 for each$1 increase in the underlying. Delta hedging involves trading shares oror options to bring aggregate delta to zero, eliminating directional risk while preserving volatility exposure.