11.4 Options Markets

Options Markets

FMP–12 is the market-structure and payoff foundation for options. Later readings (properties, strategies, exotics, Greeks, BSM) build on this vocabulary. Here the job is to know what options are, how they pay, how exchanges clear them, and how warrants/convertibles/ESOs differ from vanilla listed options.

Option Types, Uses, and Moneyness

A call option gives the holder the right, not the obligation, to buy the underlying at strike K. A put gives the right to sell at K. The writer (seller) has the obligation if the holder exercises.

Uses: hedging (protective puts, covered calls), speculation (directional or volatility views), and income (writing options). Risk management cares that long options are long volatility/convexity with capped loss (premium), while short naked options have large or unlimited downside.

Moneyness (for a call; reverse inequalities for puts):

Intrinsic value = max(S − K, 0) for calls; max(K − S, 0) for puts. Time value = option premium − intrinsic. Prior to expiry, OTM options can still trade at positive prices due to time value.

Payoff Versus Profit & Loss

Payoff at expiry usually means the option’s intrinsic value (what exercise delivers), not subtracting premium. P&L / profit subtracts the premium paid (or adds premium received for writers).

Long call payoff = max(S_T − K, 0) Long call profit ≈ max(S_T − K, 0) − premium (ignore rates for the sketch; precisely, compare to FV of premium)

Long put payoff = max(K − S_T, 0) Long put profit ≈ max(K − S_T, 0) − premium

Short positions flip the signs: short call profit ≈ premium − max(S_T − K, 0), with unlimited downside as S_T → ∞.

Worked payoff example

Stock at expiry could be 90, 100, or 120. Strike-100 call premium paid was $6.

Breakeven for the long call ≈ K + premium = 106 (ignoring timing of premium).

Protective put sketch

Own stock bought at $100; buy one-year put K = 95 for $4. Floor on effective sale ≈ 95; net floor versus purchase ≈ 95 − 4 = 91 if you mark premium against the hedge (accounting presentation varies). Upside remains open minus the put cost—insurance with a deductible-like gap below the purchase price.

Dividends, Splits, and Corporate Actions

Cash dividends: Higher expected dividends (all else equal) decrease call values and increase put values, because dividends pull down expected forward/stock paths under the risk-neutral carry view. Deep ITM American calls may be exercised just before a large dividend; European calls cannot, so they may be worth less than intrinsic in theory around dividends (no early exercise).

Stock splits and stock dividends: Exchanges adjust listed option strikes and contract multipliers so the economic claim is preserved. Example: 2-for-1 split → strike halves, number of shares per contract doubles (standard adjustment pattern). Without adjustment, optionality would be distorted.

M&A / special dividends: Can trigger unusual contract adjustments or make early exercise/assignment dynamics important; read exchange notices in practice—exam focuses on direction of dividend effects and split mechanics.

Exchange Trading: Commissions, Margin, Exercise

Exchange-traded equity options are standardized by strike, expiry, and underlying. The clearinghouse becomes central counterparty: buyers and sellers post margin; winners/losers settle through the CCP.

Closing a position (buy back a short, sell a long) is usually preferred to exercise when time value remains—exercising throws away time value.

Worked margin intuition

Writing a naked call on a $100 stock with K = 105 may require margin on the order of a fraction of underlying plus mark-to-market—not the full stock price, but enough that a spike in S hurts the writer’s account quickly via variation. A covered call substitutes share ownership for much of that margin requirement.

Warrants, Convertibles, and Employee Stock Options

These are option-like but not identical to exchange-traded puts/calls.

Dilution: When warrants or ESOs are exercised, the firm issues new shares (typically), increasing share count. Valuation for the firm/shareholders must account for that transfer. Listed exchange calls are claims on existing shares between investors—no issuer dilution.

Convertibles: Parity ≈ conversion ratio × stock price. If parity >> bond “straight” value, the convertible trades like equity; if stock collapses, the bond floor (credit-risky) matters. Call provisions let issuers force conversion when stock is high.

ESOs: Employees often cannot hedge or sell options; they may exercise early for diversification/liquidity. Standard BSM overstates value to the employee relative to a tradable option; firms still expense fair value under accounting rules using option models with expected life adjustments.

Worked warrant dilution sketch

Firm has 10 million shares outstanding, stock $20. Issues 1 million warrants with strike $25. If exercised when stock is $30, warrant intrinsic = $5 each, but the firm receives $25 × 1m = $25m cash and issues 1m new shares. Post-exercise equity value and per-share claims depend on enterprise value including the cash injected—dilution is real but partially offset by strike proceeds.

Synthesis

Map every FRM options vignette to rights vs obligations, payoff vs P&L, and who issues the claim. Use moneyness and intrinsic/time value for quick checks. Treat dividends as bearish for calls/bullish for puts, and treat warrants/ESOs/convertibles as diluted or constrained cousins of vanilla options—not interchangeable with OCC-listed calls.