Week 10: Options

Options are introduced as a right, not an obligation — the distinction Week 9’s futures lecture set up by contrast. A bounded maximum loss sounds like a safer instrument than the short position from Week 8 or the leveraged futures contract from Week 9, and in one narrow sense it is — but this lecture is explicit about where that intuition stops transferring: the premium is a certain cost paid regardless of outcome, a smaller price move than expected can still mean losing all of it, and the payoff bends rather than moving in a straight line.

The question this week answers#

An option’s loss is capped at the premium — so why do small accounts still misjudge how much they can lose trading them? How does trading a right instead of an obligation change the payoff shape and the risk, compared to the futures contract from Week 9?

By the end of this lecture#

• distinguish a call option and a put option as rights, not requirements, to act
• define premium, strike price and expiry
• calculate a call option’s payoff and breakeven price at expiry
• compare an option’s payoff shape to the linear futures payoff from Week 9
• identify where intuition carried over from stocks or futures tends to mislead with options

Key ideas#

A call option gives its buyer the right, but not the obligation, to buy an underlying asset at a set strike price on or before expiry. A put option gives the right to sell instead. This is the core distinction from Week 9: a futures contract obligates both sides; an option’s buyer can simply let it expire unused.

That right isn’t free — it costs a premium, paid upfront, which is also the buyer’s maximum possible loss: if the option expires with no value, the premium is gone, and nothing further is owed. This bounded-loss property is a genuine structural difference from Week 8’s short position, which had no loss ceiling at all — but it comes at the cost of the premium being a real, certain expense regardless of outcome, and a smaller price move than expected can still mean a total loss of that premium.

A worked example#

A simulated trader buys one call option contract (covering 100 shares) on a stock, with a strike price of $50 and a premium of $2 per share ($200 total for the contract).

The numbers#

Payoff if the stock is at $55 at expiry:

(55 − 50) × 100 = $500 intrinsic value, minus the $200 premium paid, for a net profit of $300.

Breakeven price — the price at which the payoff exactly covers the premium:

breakeven = strike + premium = 50 + 2 = $52

Payoff if the stock is at $48 at expiry (below the strike): the option has no value, and the loss is simply the premium paid, $200 — the same loss as if the stock had fallen to $30 or to $1. Unlike Week 8’s short position, the loss doesn’t grow as the price moves further against the position; it’s capped at what was paid upfront.

What a diagram would show#

A payoff diagram: a bent line, flat (at the premium’s negative value) below the strike price and rising at a constant slope above it — plotted next to Week 9’s straight futures payoff line, so the “kink” at the strike is visibly the structural difference between the two instruments.

Try it yourself#

The takeaway#

An option’s bounded loss is a real structural difference from a short stock position, not a reason to treat options as a lower-risk way to always have a position on: the premium is a certain cost, time works against a bought option as expiry approaches, and a right that expires worthless still costs exactly what was paid for it.