Chapter 12: Trading Strategies Involving Options

4 min read

Principal-Protected Notes

A principal-protected note guarantees the return of the initial investment while providing upside exposure. Structure: invest most of the principal in zero-coupon bonds, use the remainder to buy call options on an index or stock.

Example: $1, 000 t o in v es t f or 5 y e a r s . Z er o - co u p o nb o n d sy i e l d 4$ 1,000 in 5 years = $1,000 × e^{-0.04 × 5} =$ 821. Remaining $179 buys at-the-money calls on the S&P 500.

Positions in an Option and the Underlying Asset

Strategies combining options with the underlying stock:

Strategy	Components	Profit Pattern
Covered call	Long stock + short call	Limited profit, no downside protection
Protective put	Long stock + long put	Downside insurance (stock + put = synthetic call via put-call parity)
Synthetic long forward	Long call + short put (same $K$ , $T$ )	Payoff = $S_T - K$ (like buying stock on margin)
Synthetic short forward	Short call + long put	Payoff = $K - S_T$

Spreads

A spread involves taking a position in two or more options of the same type (both calls or both puts).

Bull Spreads

Buy a call with low strike $K_1$ , sell a call with high strike $K_2$ ( $K_1 < K_2$ ). Also possible with puts.

Maximum profit: $K_2 - K_1 - (c_1 - c_2)$
Maximum loss: Net premium paid $c_1 - c_2$
Used when the investor is moderately bullish

Bear Spreads

Buy a put with high strike $K_2$ , sell a put with low strike $K_1$ ( $K_1 < K_2$ ). Or use calls: buy $K_2$ call, sell $K_1$ call.

Used when moderately bearish

Butterfly Spreads

Combination of a bull spread and a bear spread. Buy one low-strike call at $K_1$ , sell two middle-strike calls at $K_2$ , buy one high-strike call at $K_3$ ( $K_2 = (K_1 + K_3)/2$ ).

Small profit if stock stays near $K_2$
Small loss if stock moves significantly either way
Used when the investor expects low volatility

Calendar (Time) Spreads

Sell a short-dated option, buy a longer-dated option with the same strike. The profit comes from the different rates of time decay.

Combinations

A combination involves both calls and puts on the same underlying.

Straddle

Buy a call and a put with the same strike and maturity:

Profit if: Stock moves significantly in either direction
Loss if: Stock stays near strike
Break-even points: $ST=K±(c+p)S_T = K \pm (c + p)$

Strangle

Buy a call with strike $K_2$ and a put with strike $K_1$ where $K_1 < K_2$ :

Cheaper than a straddle (options are out-of-the-money)
Requires a larger move to be profitable
Break-even: $S_T = K_1 - (p + c)$ and $S_T = K_2 + (p + c)$

Other Payoffs

Strips and Straps

Strip: One call + two puts (betting on large move, especially downward)
Strap: Two calls + one put (betting on large move, especially upward)

Box Spread

A combination of a bull call spread and a bear put spread that should produce a risk-free payoff, equal to $K_2 - K_1$ . In practice, execution costs and exercise risk often make box spreads less than perfectly risk-free.