Volatility · Pricing a trading path

Observation

Option-implied volatility may differ from subsequent realized volatility, but subtracting two annualized numbers is not a trading return. Maturity, strike, surface shape, hedge frequency, and the path all affect actual PnL.

Mechanism

Buyers pay for tail protection and convexity; sellers bear jump and liquidity risks. Supply/demand imbalances may also produce premia. Long-term premium collection may include a few enormous losses. Implied volatility above realized volatility does not guarantee profitable volatility selling.

Hypothesis

Fix a class of maturities and moneyness, compare advance implied volatility with realized-volatility forecasts using past information only, and apply systematic Delta hedging. Define net-return and tail constraints before selecting a model. Future realized volatility cannot be an entry indicator.

Data

Obtain two-sided quotes, multipliers, expiry/settlement rules, executable underlying quotes, rates/financing assumptions, and the Greeks model version. Trades or midquotes alone cannot prove executability. Reject and record missing/crossed quotes and unstable near-expiry estimates.

Signal

Map the forecast difference into bounded risk notional while limiting Delta, Gamma, Vega, and maturity concentration. Delta neutrality removes only local first-order direction sensitivity. Delta changes after jumps; neutrality is not risklessness across a path. Naked short risk cannot be measured by premium size alone.

Backtest

Revalue options and hedge legs step by step, explicitly accounting for bid/ask spreads, rehedging costs, and financing. Without validated pricing/fill models, submit a research design and externally reproducible data experiment rather than inventing net model returns. Compare fixed and adaptive hedge frequency on costs and tail losses together.

Falsification

Add gaps, rising implied volatility, surface-skew changes, and hedge-venue failures. Check tails against available capital. If profits depend on midquote fills or omitted jumps, keep the candidate in Testing. A sample without crises does not establish low seller risk.

Exercise and project acceptance

Without real money, draw two underlying paths with identical endpoints but different trajectories. Explain how rehedging frequency changes trade counts and funding needs. Add a jump scenario and list numerical claims not yet supported by models. Submit specifications, paths, cost definitions, Greek exposures, and a falsifiable protocol. Explicitly rejecting model gaps is acceptable; inventing PnL from a volatility difference is not.

See Advanced D for risk limits and Advanced F for promotion gates.