Two foundational options trading texts studied side by side via semantic query: Sheldon Natenberg’s Option Volatility and Pricing and Pierino Ploeg’s How to Calculate Options Prices and Their Greeks. What follows are the convergent patterns and the four ideas most worth carrying forward.
The 5 Core Patterns Both Books Converge On#
1 — Volatility Is the Real Asset#
You are not trading calls and puts. You are trading volatility. The direction of the underlying is secondary. Both books spend more time on volatility than on any other topic.
2 — The Gamma-Theta Tension Is the Engine of Everything#
Every options position is a bet on one side of this tradeoff:
| Long Gamma | Short Gamma | |
|---|---|---|
| You want | Large moves | Underlying to stay still |
| You collect | Gamma scalp profits | Daily theta |
| You pay | Daily theta | Exposure to large moves |
Every strategy — straddles, strangles, spreads, ratio writes — is a variation of this tension.
3 — Delta-Neutral Is the Baseline, Not the Strategy#
Delta-hedging is table stakes — the prerequisite to isolating a volatility bet from directional noise. Neutralize direction, then trade what remains.
4 — BSM Is the Map, Not the Territory#
Both books teach Black-Scholes thoroughly, then spend equal time on its failures. The central violated assumption: volatility is not constant. BSM is a necessary scaffold — not a truth.
5 — The Vol Surface Is Where the Real Edge Lives#
Once you know BSM and the greeks, your edge comes from reading the volatility surface better than the next trader:
- Skew — implied vol varies by strike
- Term structure — implied vol varies by expiration
- Smile — U-shaped IV curve across strikes in some markets
Implied Volatility — The Market’s Forward-Looking Signal#
BSM has 5 inputs: price, strike, time, interest rate, volatility. All observable except future volatility. Implied volatility (IV) inverts this — take the market option price and solve backwards for the volatility that would produce it.
IV = the market’s consensus forecast of future realized volatility
The Vol Risk Premium#
Implied vol almost always runs above realized vol. That gap is the volatility risk premium — the market systematically overpays for insurance. Natenberg documents this with S&P 500 data over a decade. The premium is persistent.
The spread is a signal:
| IV − RV | Market State | Regime Signal |
|---|---|---|
| Large positive | Market is fearful | Bear regime — crisis incoming |
| Near zero | Market is calibrated | Bull or Choppy |
| Negative (RV > IV) | Market is complacent | Regime shift risk |
The Leverage Effect#
When the underlying drops, at-the-money implied vol rises. Falling prices increase financial risk, so vol spikes. This is why vol skew is almost always negatively sloped — lower strikes carry higher IV. A sudden IV spike on a down move is a regime transition signal, not noise.
Short Volatility — Why You Cannot Just Always Sell#
The vol risk premium is real. Selling options generates steady theta income most of the time. But the failure mode is catastrophic and convex.
Natenberg, on a short straddle after a gap move:
“The trader will find himself naked short deeply in-the-money calls, each acting like short underlying contracts.”
How to Calculate Greeks, on gamma convexity:
“A move of $4 will cost 16 times as much as a $1 move. A trader who is short gamma will need to expect and anticipate them.”
Loss scales with the square of the move. You collect nickels for months, then lose the account in a single session.
The professional answer is conditional selling — not always. The kurtosis of the market determines the right position:
| Market | Distribution | Position |
|---|---|---|
| Platykurtic | Thin tails, bounded moves | Short gamma — collect theta |
| Leptokurtic | Fat tails, rare catastrophic moves | Long gamma or flat |
Crypto is persistently leptokurtic. The fat tail is structural.
Four Key Ideas — Two From Each Book#
Natenberg Idea 1 — Rehedging Frequency Is a Gamma Capture Policy#
“By rehedging the position each week, we were able to capture a series of profits resulting from the mismatch between the option’s changing delta and the fixed delta of the underlying contract.”
Gamma profit doesn’t sit passively — you must actively rehedge to realize it. Each delta rebalance locks in a gain from the price move. The optimal rehedging frequency is regime-dependent: aggressive in volatile regimes, infrequent in calm ones.
For a regime-conditioned RL agent, this translates directly — the “trade / don’t trade” decision is a dynamic rehedging policy. Gamma captured per unit of transaction cost paid is a natural reward signal.
Natenberg Idea 2 — Volatility Contracts: Trade Vol Without Touching Options#
“Traders have sought a less complicated method — this has led to the development of volatility contracts.”
Realized variance contracts and VIX futures let you take a position on volatility directly — no options greeks to manage. The VIX can double or triple in short periods.
Crypto equivalent: Deribit DVOL futures. When your regime detector says Bear, go long DVOL — pure vol exposure with the regime posterior as the entry trigger. Cleaner execution than constructing a delta-hedged options book.
Greeks Book Idea 1 — Kurtosis as an Explicit Position Selection Rule#
“One would prefer being short gamma when being in a platykurtic environment and being long gamma when being in a leptokurtic environment.”
The book identifies the transition between distribution regimes as the key event. Your position type should flip when the market’s distribution character flips — not on a fixed schedule.
Crypto is persistently leptokurtic. The default position should be long gamma. Only flip short gamma in explicitly identified low-kurtosis windows — the Choppy regime in an HMM framework. Bull and Bear are both leptokurtic — stay long gamma in both.
Greeks Book Idea 2 — Vomma: Convexity on Your Convexity#
“The change in vega for options is called vomma. The vega of out-of-the-money options changes when volatility changes.”
When vol spikes from 20% to 30%, ATM options barely change their vega — but OTM puts increased their vega by 66%. That acceleration is vomma — the second derivative of option price with respect to vol.
Buying OTM options before a regime shift generates a double-convexity payoff:
- Vol rises → vega profit (first order)
- Vega itself grows as vol rises → vomma profit (second order)
When a Bear regime posterior begins climbing, OTM puts are the highest-leverage instrument — not because of delta, not just vega, but because vomma compounds as the regime deepens. The regime detector is the timing signal; vomma tells you which option to buy once you’ve timed it.
The Connection to Regime Detection#
The options vol framework maps precisely onto HMM regime states:
| Regime | Vol Character | Distribution | Position |
|---|---|---|---|
| Bull | RV stable, IV slightly elevated | Platykurtic | Sell vol — collect theta |
| Choppy | RV low, IV compressed | Platykurtic | Sell vol — tightest edge |
| Bear | RV spikes, IV spikes more | Leptokurtic | Long gamma / long DVOL / OTM puts |
The γ_k(i) regime posteriors from a Hidden Markov Model are already a probabilistic vol-regime classifier — which is exactly what an options vol surface trader reads manually. Most retail traders who blow up on short vol have no such classifier. They sell into the Bear regime because the premium looks juicy right before the crash.
A regime detector is the risk management layer that systematic short vol strategies are missing.
Sources: Sheldon Natenberg, Option Volatility and Pricing (2nd Ed.) · Pierino Ploeg, How to Calculate Options Prices and Their Greeks