“The invention of marine insurance transformed the risks of trade from fatal uncertainty into manageable cost.”
— Peter Bernstein
As we discussed in Part 1, one of the keys to surviving—and even thriving—in financial markets is hedging. When markets fall, volatility spikes, or systemic crises hit, many investors suffer deep losses. But those who prepared—those who bought “insurance” ahead of time—can preserve capital, or even profit during chaos.
In 2008, Nassim Taleb and the funds that followed his risk philosophy made over 100x returns during the financial crash. That wasn’t luck. It was risk preparation.
In the markets, put options are that insurance.
And here’s the most interesting part: the market doesn’t care if you actually “own a car.”
In other words—you don’t need to hold the underlying stock to buy a put. As long as you pay the premium, the market will pay out if the price drops. In that sense, the financial world is more forgiving than the real one—here, “insurance fraud” is not only legal, it can be a strategy.
The Core Question: Are Puts Cheap or Expensive?
Since a put option is effectively insurance, we should ask the same question we ask with any insurance policy: Is it worth it?
If a put is cheap enough—meaning its price is low compared to the potential payout—then it’s a good buy. Even if you don’t own the stock, the “airdrop insurance” might pay off handsomely in a downturn.
But if the put is expensive, priced far above its average expected payout, then you’re likely overpaying for protection. You might think you’re hedging risk—but in reality, you’re just handing profits to the option seller.
In fact, over long periods of time, option sellers are statistically the side that wins. So how do we avoid being the sucker?
The Fundamental Problem: How Do We Know if a Put is Fairly Priced?
Let’s return to the framework from Part 1.
Just like insurance, a put’s fair price depends on two things:
- How likely is a drop?
(This is the probability distribution.) - If a drop happens, how bad will it be?
(This is the payoff function.)
That’s the basic formula behind a put’s theoretical value:
Put Price = ∫ (Payoff at strike × Probability of landing there)
More precisely:
Put Value = ∫ (K − St) × f(St) dSt
Where:
- K is the strike price
- St is the stock price at expiration
- f(St) is the risk-neutral probability density function at expiration
- We are ignoring the net present value of money in this discussion series for simplicity.
Unlike car insurance, where the damage amount is uncertain, in options, the payoff is crystal clear. If I buy a 550 strike SPX put and the index ends at 5300, I know my payout is 2000 points per contract (or 20,000 dollars in SPX terms). There’s no guesswork.
The only thing we don’t know is the probability that SPX ends up at 5300. Or 5400. Or 5000. That’s where the uncertainty lies.
Enter VIX: A Snapshot of Market Risk
The market doesn’t reveal its true beliefs about probability distributions. Sometimes trading is rational; sometimes it’s full of emotion. But the VIX index, published by the CBOE, is essentially a proxy for the market’s current estimate of future volatility. It’s a way to infer the standard deviation of returns—updated every 15 minutes.
But VIX doesn’t tell you the whole story.
It doesn’t show you the full shape of the distribution—just the average “spread” the market expects. And that brings us to the real game:
Can we do better than the market?
Can You Estimate the Risk Distribution More Accurately Than the Market?
Ultimately, whether a put is “overpriced” or “underpriced” boils down to this:
- Can you estimate the probability of future market drops more accurately than the current market implied distribution?
- Can you do this objectively, and ideally without bias?
- If yes, then you can compare your estimation to the implied distribution behind current VIX levels, and decide whether current put prices are too cheap, fair, or overpriced.
This is the foundation of rational hedging—and even speculative arbitrage.
Final Thought: Risk Pricing Is the Game
Remember, the financial market is not just about picking stocks—it’s about pricing risk. If you can price risk more accurately than the market, even in small edges, that insight can be more powerful than any “hot tip” or macro thesis.
In the next post, we’ll explore how historical data can help us approximate that elusive probability function, and how we might spot situations where puts are underpriced protection—or overpriced fear.