An option is a derivative contract that grants the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a stated expiration date, in exchange for a premium paid to the seller (writer) of the option.
Option terminology
- Underlying: The asset on which the option is written (e.g., stock, index, currency, commodity, rate).
- Strike (exercise) price: The fixed price at which the underlying can be bought (call) or sold (put) if exercised.
- Expiration: The last date on which the option can be exercised; American options allow exercise any time up to expiry, European only at expiry.
- Premium: The price paid by the buyer to acquire the option; equals intrinsic value plus time value at purchase.
- In/at/out of the money: Describes moneyness; for calls, spot above/equal/below strike; for puts, spot below/equal/above strike.
- Holder vs writer: Buyer owns the right with limited loss to premium; writer assumes obligation with potentially large losses depending on position.
Call option
A call option gives the holder the right to buy the underlying at the strike by expiry; the payoff at maturity is max(S_T − K, 0), and the profit nets the paid premium. Calls are used to express bullish views with limited downside, or to create covered-call income when written against owned stock, trading upside for received premium.
Put option
A put option gives the holder the right to sell the underlying at the strike by expiry; the payoff at maturity is max(K − S_T, 0), and the profit nets the premium. Puts are commonly used for portfolio insurance (protective puts) to cap downside, while put writing can generate income in exchange for the obligation to buy the asset if it declines.
Pricing of options
- Intrinsic value and time value: Premium equals intrinsic value plus time value, with time value reflecting uncertainty and time remaining to expiration.
- Key drivers (the “Greeks” intuition):
- Underlying price: Higher spot raises call values and lowers puts, all else equal.
- Strike and time: Lower strikes and more time increase call values; more time increases both call and put time value.
- Volatility: Higher expected volatility raises option premiums by increasing the probability of finishing in the money.
- Rates and income: Higher interest rates tend to increase calls and decrease puts on non-dividend assets; dividends or yields generally decrease calls and increase puts.
- No-arbitrage relationships: Put–call parity for European options on non-dividend assets states C − P = S_0 − K·e^{−rT}, with adjustments for dividends/yields as applicable.
Interest rate options
Interest rate options provide convex exposure to movements in interest rates and fixed-income prices, often cash-settled to a rate or index.
- Caps and floors: A cap is a series of call options on an interest rate (caplets) that pays when the reference rate exceeds the strike; a floor is a series of put options on a rate (floorlets) that pays when the rate falls below the strike.
- Swaptions: Options on interest rate swaps; a payer swaption confers the right to enter a swap paying fixed and receiving floating (beneficial if rates rise), while a receiver swaption confers the right to receive fixed and pay floating (beneficial if rates fall).
- Uses:
- Hedging: Borrowers cap floating-rate costs with caps; investors protect bond portfolios with payer swaptions; issuers hedge callable risk with receiver swaptions.
- Structuring: Banks and treasuries tailor callable/putable bonds, collars (cap + short floor), and contingent protection for specific rate scenarios.
Practical illustrations
- Bullish equity view: Buying a call at-the-money limits downside to the premium while participating in upside above the strike; writing a covered call against existing shares adds income but caps upside beyond the strike.
- Downside protection: A protective put under an equity or index portfolio establishes a floor on losses for a known cost (the premium), effectively insuring the portfolio during volatility.
- Borrower hedge: A firm with floating-rate debt purchases a cap so that payments above the strike are offset by cap payouts, bounding interest expense in rising-rate environments.
Risk notes and governance
Options embed leverage and convexity; while buyers face limited loss to the premium, writers can face large or theoretically unlimited losses in uncovered positions, requiring robust margining and risk controls. Suitability assessment, clear strategy objectives (hedging, income, speculation), and disciplined position sizing are essential before trading options.
CAIIB exam Risk Management related articles in model “F” (elective paper)
