Barrier Options
advancedPath-dependent options that activate or deactivate when the underlying touches a barrier level. Cheaper than vanilla options due to the additional conditions.
Parameters
Payoff at Expiry
Scenario Analysis
Understanding Barrier Options
What are Barrier Options?
Barrier options are path-dependent options where the payoff depends not only on whether the option is in-the-money at expiry, but also whether the underlying asset has touched a predetermined barrier level during the option's life.
Knock-Out vs Knock-In
The option is deactivated when the barrier is touched. It starts active and becomes worthless if the barrier is breached. The investor loses the premium paid.
The option is activated when the barrier is touched. It starts inactive and only becomes a live option if the barrier is breached. Ideal for speculating on large market moves.
Payoff Formulas
Textbook Example (Table 6.3.1)
| Parameter | Call (Investor A) | Put (Investor B) |
|---|---|---|
| Strike Price | $8.00 | $13.50 |
| Knock-Out Price | $9.00 | $12.00 |
| Current Spot | $7.00 | $15.00 |
| Max Gain | $8.99 - $8.00 = $0.99 | $13.50 - $12.01 = $1.49 |
| If barrier touched | Option is worthless | Option is worthless |
Double Barrier Options
A double barrier option has two barrier levels — one above and one below the strike price. The option is knocked out if either barrier is touched.
Strike: $8.00, Spot: $7.80, Lower Barrier: $7.00, Upper Barrier: $9.00. Max gain: $8.99 - $8.00 = $0.99. Cheaper than a single barrier because it can be knocked out at both ends.
Advantages & Disadvantages
- Cheaper than vanilla options (lower premium)
- Higher returns on capital if barrier conditions met
- Greater selection for diverse market views
- Knock-in ideal for large moves, knock-out for sideways
- High risk of premium loss if barrier conditions breached
- OTC products — counterparty risk
- Less liquid than exchange-traded options
- Premium paid upfront, non-refundable