# ATM Delta-Hedged Option Strategy on QQQ + Alternative Strategy Comparison

## Thesis Statement

This strategy captures relative mispricing between implied and realized volatility by trading QQQ ATM call options and dynamically delta hedging the underlying. If implied volatility (IV) exceeds realized (historical) volatility, the option is likely overpriced, and the strategy shorts the option and delta-hedges using QQQ shares. If IV is underpriced, we go long. The strategy profits from volatility mean-reversion and uses delta hedging to neutralize directional risk.

## Strategy Design

- Underlying Asset: QQQ (NASDAQ-100 ETF)
- Instrument: ATM listed call option expiring Dec 17, 2021
- Capital: $2 million
- Start Time: 10:00 AM on Dec 1, 2021
- Decision Rule:
- If IV > HV → short the call (expecting mean reversion)
- If IV < HV → long the call (expecting volatility breakout)
- Hedging Frequency: Hourly (on the hour)
- PnL Goal: Maximize returns without crossing margin constraints

## Assumptions

- QQQ has liquid options and low spreads (allowing frequent rebalancing).
- Historical volatility (HV) is a fair proxy for realized volatility
- Implied volatility (IV) reflects current market pricing expectations
- Delta from the option chain is reliable for hedging

## Strategy

1. Calculate historical volatility from the last 25 daily closes of QQQ
2. At 10 AM, select the ATM call option with the closest strike above QQQ price and expiry on 12/17/2021
3. Compare implied volatility of the option to historical volatility:
- IV > HV: Sell the call (expect overpricing and decay)
- IV < HV: Buy the call (expect volatility spike)
4. Use delta hedging every hour to remain market-neutral

## Trade Execution Logic

- Determine option position size based on capital and margin constraints
- Place buy/sell order on our selected ATM call
- Calculate delta from the option greeks
- Hedge by buying/selling QQQ shares to offset delta
- Re-hedge hourly or if position drifts significantly

## Risk Management

- Limit capital used for options to 5% of cash
- Limit margin usage to 70%, with 30% reserved buffer
- Reduce option size by 1/3 if margin buffer is breached
- Use `PerformDeltaHedge()` to size hedges carefully within available margin
- Monitor total margin used vs available throughout the day

## Rebalancing & Scheduling

- Recalculate historical volatility each morning
- Log daily and total PnL at market close
- Re-hedge every hour
- Monitor margin and adjust size if thresholds are approached
- Close all positions at expiry

## Backtest Result

### [Quantconnect Backtest Link](https://www.quantconnect.com/terminal/processCache/?request=embedded_backtest_de555322f10e387cac3994658cff7290.html)


Our strategy produced a net profit of $61,012.52 (+5.52%) over a 2.5-week holding period without triggering any margin calls.

Key Metrics:
- Sharpe Ratio: 3.04 — excellent risk-adjusted performance
- Max Drawdown: just 2.9% — strong downside control
- Win Rate: 76% (with an average win of 0.09% vs. loss of only -0.02%)
- Profit-Loss Ratio: 5.53 — trades were highly asymmetric in favor of gains
- Portfolio Turnover: 26.76% — moderately active but not overly frequent
- Annualized Return (extrapolated): 216.9% — high strategy momentum

Our strategy successfully captured mispricings between implied and realized volatility through smart option positioning and timely delta hedging — producing high alpha and minimal risk exposure during a short-term window.

## Alternative Strategy Comparison

### [QuantConnect Backtest Link](https://www.quantconnect.com/terminal/processCache/?request=embedded_backtest_d52a7825dac5c34e387cc6a6769fff38.html)

We explore variations of the base delta-hedging strategy by changing the option strike, type, and expiration, and identify the variant with the highest return. Each variation still uses the same core delta-hedging and IV/HV comparison logic.

| No. | Option Type | Strike | Expiration | Net PnL ($) | Outcome |
|-----|-------------|--------|------------|------------------|---------------|
| 1 | Call | OTM | 12/17/2021 | 18,027.53 | **Highest return** |
| 2 | Put | ATM | 12/17/2021 | 13,921.25 | 2nd best |
| 3 | Put | ITM | 12/17/2021 | 0.00 | No trades |
| 4 | Put | OTM | 12/17/2021 | 0.00 | No trades |
| 5 | Call | ATM | 12/10/2021 | -2,116.00 | Earlier expiry underperformed |
| 6 | Call | ATM | 12/17/2021 | -8,256.28 | Base strategy |
| 7 | Call | ITM | 12/17/2021 | -88,188.01 | Largest loss |

## Intuition

- OTM Calls have:
- Lower premiums → lower capital risk
- High gamma → more responsive to sharp moves
- Higher vega → more sensitive to volatility spikes (which were captured well by IV > HV signals)
- Short-dated ATM calls (Exp 12/10) underperformed due to insufficient time for delta adjustments to compound effectively
- ITM Calls exposed our strategy to large directional risk and were punished due to misaligned delta moves and high premiums