Derivatives
Options and asymmetric payoffs
An option gives the right but not the obligation; the premium buys asymmetry and moves the break-even away from the strike.
Definition
An option is a contract that gives the holder the right, but not the obligation, to buy or sell an asset at a fixed strike price before or at expiry. The seller receives a premium for taking the obligation on.
The payoff is asymmetric: losses are capped at the premium while the upside stays open. That asymmetry is what the premium pays for.
Intuition
Buying an option is like buying insurance with no deductible and no ceiling. You know the most you can lose, and you keep the benefit of a favourable move.
When to use it
- Insuring a position while keeping the upside.
- Expressing a view with a known maximum loss.
- Shaping the payoff of a hedge with a cap, a floor, or a collar.
When not to use it
- When the premium is a cost the budget cannot absorb.
- Selling options without understanding that the loss can exceed the premium received.
- For very short-dated speculation where time decay dominates.
Formula
Call payoff at expiry
Payoff = max(S − K, 0)
The value of the right to buy at the strike.
- S
- Price of the underlying at expiry
- K
- Strike price
Formula
Call profit
Profit = max(S − K, 0) − Premium
Payoff after the cost of the option.
Formula
Call break-even
Break-even = K + Premium
The underlying price at which the position neither gains nor loses.
Worked example
A call finishes in the money
A call has a strike of ৳600 and costs a premium of ৳25. The underlying finishes at ৳680.
- 1
Payoff
max(680 − 600, 0) = ৳80.
- 2
Profit
80 − 25 = ৳55 per unit.
- 3
Break-even
600 + 25 = ৳625; below that the option loses money.
The option finishes valuable but the break-even is above the strike, because the premium has to be earned back first.
Common mistakes
- Confusing payoff with profit; the premium is part of the result.
- Assuming an in-the-money option is a winning trade.
- Ignoring time decay, which erodes an option even when the underlying is flat.
How it connects
is an advanced form of
The source extends the target once the basics are secure.
- Forwards, futures, and hedging: Options add asymmetry that a forward cannot provide.
relates to
Useful to study together, in either order.