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E. Options Strategies (E.19--E.22)

Harvest the volatility risk premium and exploit skew/term-structure dislocations in gold and silver options. These strategies generate income from the structural overpricing of implied volatility while maintaining tail-risk awareness.

E.19 Volatility Risk Premium

Module: qgtm_strategies/vol_risk_premium_pm.py Class: VolRiskPremiumPMStrategy ID: vol_risk_premium_pm

Economic Rationale

Implied volatility of options on GLD and SLV systematically exceeds realized volatility -- the volatility risk premium (VRP). This premium compensates option sellers for bearing jump/gap risk. The strategy harvests the VRP by selling straddles or strangles when IV is rich relative to recent RV, with a tail-hedge overlay triggered by VIX term structure inversion.

Signal Formula

Step 1 -- Realized vol (close-to-close):

\[ \text{RV}_{21d} = \sqrt{\frac{252}{21} \sum_{i=0}^{20} \bigl(\ln P_{t-i} - \ln P_{t-i-1}\bigr)^2} \]

Step 2 -- VRP computation:

\[ \text{VRP}_t = \text{IV}_{\text{ATM},t} - \text{RV}_{21d,t} \]

Step 3 -- Rolling percentile:

\[ \text{pctile}_t = \text{percentile\_rank}\!\bigl(\text{VRP}_t,\; \text{VRP}_{[t-252, t]}\bigr) \]

Entry rules:

Condition Action
\(\text{pctile}_t \geq 0.75\) Sell premium (short straddle/strangle)
VIX front > VIX back (inversion) Buy OTM puts (tail hedge overlay)
\(\text{pctile}_t < 0.25\) Close short vol

Position sizing:

\[ \text{notional} = \text{base\_size} \times \frac{\text{VRP}_t}{\bar{\text{VRP}}_{252}} \times \frac{1}{\text{IV}_t / 0.15} \]

Scale down as IV rises (vol-of-vol risk).

Factor Exposures

Factor Loading
Volatility -0.7
Metals +0.2
Carry +0.5

Capacity & Decay

  • Max capacity: $15M notional (options liquidity constrained)
  • Alpha half-life: 30 days
  • Kill condition: Strategy loses > 3 monthly premiums in a single event
  • Expected Sharpe: 0.6--1.0

References

  • Carr & Wu (2009) "Variance Risk Premiums"
  • Bollen & Whaley (2004) "Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?"
  • Israelov & Nielsen (2015) "Covered Calls Uncovered"

E.20 Skew

Status: Planned

Economic Rationale

The options skew (put IV vs call IV) for GLD embeds the market's tail-risk pricing. When the put-call skew is extreme (puts very expensive relative to calls), the market is overpricing downside protection. Selling the skew (risk reversal: sell OTM puts, buy OTM calls) harvests this overpricing. Conversely, when skew is flat or inverted, tail risk is underpriced.

Signal Formula (Proposed)

\[ \text{skew}_t = \text{IV}_{25\Delta\text{P}} - \text{IV}_{25\Delta\text{C}} \]
\[ z_{\text{skew}} = \text{zscore}\!\bigl(\text{skew}_t,\; 252\bigr) \]
Condition Trade
\(z_{\text{skew}} > 2\) Sell put skew (sell 25d put, buy 25d call)
\(z_{\text{skew}} < -1\) Buy put protection (skew too cheap)
Otherwise Flat

Expected Properties

  • Max capacity: $10M
  • Expected Sharpe: 0.4--0.8

E.21 Gamma Scalp

Status: Planned

Economic Rationale

Long straddle + delta-hedge at high frequency. Profits when realized vol exceeds implied (the opposite of E.19). Deployed when IV is historically cheap (bottom quartile) and an event catalyst is approaching (FOMC, NFP, CPI). The gamma gain from large moves exceeds the theta decay paid.

Signal Formula (Proposed)

Entry condition:

\[ \text{IV\_pctile}_t < 0.25 \quad \wedge \quad \text{event\_days} \leq 5 \]

Delta-hedge frequency: Re-hedge when delta moves by \(\pm 0.05\) or every 2 hours, whichever comes first.

P&L decomposition:

\[ \text{PnL} = \underbrace{\frac{1}{2}\Gamma S^2 (\Delta r)^2}_{\text{gamma gain}} - \underbrace{\Theta \cdot \Delta t}_{\text{theta cost}} + \underbrace{\text{vega} \cdot \Delta\text{IV}}_{\text{vol move}} \]

The strategy is profitable when gamma gain > theta cost.

Expected Properties

  • Max capacity: $8M
  • Expected Sharpe: 0.5--0.9
  • Key risk: Event does not materialize; theta bleeds out the position

E.22 Vol Term Structure

Status: Planned

Economic Rationale

The volatility term structure for gold options (1M IV vs 3M IV vs 6M IV) embeds expectations of future vol regimes. When the term structure is in steep contango (long-dated IV >> short-dated), sell the back and buy the front (calendar spread). When inverted, do the opposite.

Signal Formula (Proposed)

\[ \text{slope}_t = \frac{\text{IV}_{3M} - \text{IV}_{1M}}{\text{IV}_{1M}} \]
\[ z_{\text{slope}} = \text{zscore}\!\bigl(\text{slope}_t,\; 252\bigr) \]
Condition Trade
\(z_{\text{slope}} > 2\) Sell back-month, buy front-month (calendar spread)
\(z_{\text{slope}} < -1.5\) Sell front-month, buy back-month
Otherwise Flat

Expected Properties

  • Max capacity: $12M
  • Expected Sharpe: 0.5--0.8

References (all E strategies)

  • Mixon (2011) "What Does Implied Volatility Skew Measure?"
  • Bakshi, Kapadia, Madan (2003) "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options"
  • Broadie, Chernov, Johannes (2009) "Understanding Index Option Returns"