What Are Options?
Options are financial derivatives that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a certain date. They come in many varieties and are used for hedging, speculation, and income generation.
| Feature | Options | Futures |
|---|---|---|
| Nature | Asymmetric payoff (right, not obligation) | Symmetric (obligation) |
| Premium | Buyer pays upfront premium | No upfront premium |
| Exercise | Optional (American or European style) | Obligated on expiration |
| Underlying | Equities, ETFs, indices, FX, commodities | Similar, broader scope |
Types of Options
| Type | Description |
|---|---|
| Call Option | Right to buy the underlying asset at strike price. |
| Put Option | Right to sell the underlying asset at strike price. |
| American Option | Can be exercised any time before expiry. |
| European Option | Can only be exercised at expiration. |
| Cash-Settled | Settles to cash value, not delivery of asset. |
| Physically-Settled | Requires delivery of underlying on exercise. |
| Weekly Options | Short-dated options, expiring every week. |
| Daily Options (0DTE) | Same-day expiry, increasingly popular among retail and algorithmic traders. |
Example: Long Call Option
- Underlying: AAPL stock trading at $190
- Strike Price: $200
- Premium: $2.50 per share
- Expiration: 1 month
Payoff at expiry:
Where:
- ( S_T ): Price at expiry
- ( K ): Strike price
- ( P ): Premium paid
If AAPL closes at $210, the payoff is:
Options Pricing
Options are priced using probabilistic models that account for the time value of money and the probability of the option finishing in-the-money. The most common model is Black-Scholes-Merton:
Where:
- ( C ): Call option price
- ( S_0 ): Spot price of underlying
- ( K ): Strike price
- ( T ): Time to maturity
- ( r ): Risk-free interest rate
- ( \sigma ): Volatility of the underlying
- ( N(\cdot) ): Cumulative normal distribution
Other models (e.g., Binomial Tree, Monte Carlo, Heston) are used for path-dependent or exotic options.
Mark-to-Market and Valuation
Options positions are typically marked to market daily based on their theoretical value and observable market prices. This process ensures:
- Real-time profit/loss calculation
- Margin requirements for writers
- Transparency for investors
Options clearinghouses (e.g., OCC in the U.S.) require daily collateral adjustments based on valuation shifts.
Volatility Surfaces and Market Making
Options Market Makers provide liquidity across strikes and expiries by quoting bid/ask prices for many options. To manage risk and remain profitable, they build and update a volatility surface, which maps implied volatility as a function of strike and time:
- Vol Skew: Implied vol varies by strike (e.g., puts trade richer than calls for equities).
- Vol Term Structure: Volatility varies by time to maturity.
By interpolating and extrapolating market data, market makers can:
- Identify mispricings
- Hedge delta, gamma, and vega exposure
- Quote consistently across thousands of strikes
They earn the bid/ask spread and benefit from statistical arbitrage if their models predict future price action better than the market.
Example: Volatility Surface in Equity Options
- Stock: XYZ, trading at $100
- Vol Surface Snapshot:
| Strike \ Time | 1W | 1M | 3M | 6M |
|---|---|---|---|---|
| 90 | 40% | 35% | 30% | 28% |
| 100 | 32% | 30% | 27% | 25% |
| 110 | 34% | 31% | 28% | 26% |
Notice the skew: downside puts (strike 90) have higher implied volatility than at-the-money or upside calls.
Use Cases
- Hedging: Protective puts, covered calls, collars.
- Speculation: Directional bets, volatility plays, earnings trades.
- Yield Enhancement: Selling puts, covered call writing.
- Arbitrage: Box spreads, reverse conversions, dispersion trading.
Summary Comparison: Options vs Swaps
| Feature | Options | Swaps |
|---|---|---|
| Nature | Asymmetric payoff, optionality | Contractual exchange of cash flows |
| Trading Venue | Exchange-traded or OTC | Mostly OTC / SEF |
| Pricing | Volatility-based models (e.g. Black-Scholes) | Discounted cash flow models |
| Mark to Market | Daily via clearinghouse or brokers | Daily or as needed by counterparties |
| Risk Exposure | Delta, gamma, theta, vega | Interest rate, credit, FX exposure |