Options#
Week 10 · Nonlinear risk and premium loss#
How can a small retail trading account survive execution friction, drawdowns, leverage, and increasingly complex instruments?
The question this week answers#
How does a payoff that bends around strike and expiry change what “risk” means for a small account?
The point is not to find a “best” trading style or instrument. It is to understand what can make the account fail.
By the end of this lecture#
- distinguish calls and puts as rights, not obligations, to act
- define premium, strike and expiry
- calculate payoff and breakeven at expiry
- explain why bounded loss does not mean low risk
“Maximum loss is capped” can sound safe — losing 100% of the option premium is still a complete loss of the capital committed to that position#
Three ideas that change the risk intuition#
Right, not obligation
The buyer can let the option expire unused, unlike a futures obligation
Premium
Paid upfront; for the buyer it is the maximum possible loss — and can be lost entirely
Nonlinear payoff
The relationship between underlying price and option P/L changes around the strike and expiry
Options change the shape of risk rather than removing it. The size of the premium position still has to fit the account’s survival rules.
A worked example#
A simulated trader buys one call option contract (100 shares) on a stock, strike price $50, premium $2 per share ($200 total). At expiry, the option only has intrinsic value above the strike — the premium must also be recovered before the position is profitable.
The numbers: payoff above the strike#
Stock at $55 at expiry:
(55 − 50) × 100 = $500 intrinsic value − $200 premium
= $300 net profit
Breakeven = strike + premium = 50 + 2 = $52
The numbers: payoff below the strike#
The option expires worthless — the loss is the full $200 premium
The same loss as if the stock had fallen to $30, or to $1
Bounded loss is structurally different from an uncapped short — but the option buyer can still lose every dollar of premium paid.
The payoff bends at the strike#
Bounded loss does not mean small loss: an option buyer can still lose 100% of the premium, while the payoff changes nonlinearly around the strike and expiry.
Try it yourself#
Compare payoffs
A simulated put option has strike $40 and premium $1.50 per share.
Calculate the profit at expiry if the stock is $35, and the breakeven price. Then explain why “bounded loss” is not enough to decide an appropriate position size.
The takeaway#
- Options are rights; futures are obligations.
- The premium is a certain upfront cost and can be lost entirely.
- The payoff is nonlinear, so stock intuition does not transfer cleanly.
- For a small account, the premium still needs a size limit just like any other risk budget.
Next week#
Week 11 — crypto as an extreme case of leverage, liquidation and market-structure risk.