Analyze trading RFQ competitiveness data

Scenario

You are analyzing a dataset of Request for Quote (RFQ) logs for a specific ticker. Each row in your dataset represents a unique RFQ and contains the following columns: rfq_id, mid_price (the fair market value at the time of the quote), your_quote_price, best_competitor_price, and result (a binary variable where 1 indicates you won the trade, and 0 indicates you lost).

The Task

1. Feature Engineering: Define and calculate a metric representing the "spread deviation" of your quote relative to the market mid-price. How would you normalize this to account for different volatility regimes?
2. Modeling: You suspect that the probability of winning an RFQ follows a logistic relationship with your price competitiveness. Write down the logistic regression equation for the probability of winning P(win=1) given your spread_deviation.
3. Analysis: Suppose you notice that your win rate is significantly higher when the best_competitor_price is close to the mid_price. Propose a way to calculate your 'information edge'—the difference between your pricing model and the competitor's—using only the observed result data.

Constraints & Considerations

• Assume your_quote_price is always on the 'bid' side of the mid-price (i.e., you are buying).
• Your analysis must account for the fact that you only observe the competitor's price when you lose, or via secondary data feeds.
• Consider edge cases where the mid_price is stale or the market is highly illiquid.

Example

If your quote is 99.95, the mid is 100.00, and the competitor quotes 99.98, you lose the trade (result=0). If you quoted 99.99, you might win (result=1). Your goal is to map the sensitivity of the win probability to the gap between your quote and the competitor's best price.