Section 2 - R8 - Option Strategies

Question 1

Synthetic Forward (Formula)

Answer 1

Long Fwd = Long Call + Short Put

Question 2

Call Payoff (Formulas)

Answer 2

Long Call = Max [(S-X), 0] - C0
Short Call = Min [(S-X), 0] + C0

Question 3

Put Payoff (Formulas)

Answer 3

Long Put = Max [(X-S), 0] - P0
Short Put = Min [(S-X), 0] + P0

Question 4

Δ Delta (Formula)

Answer 4

Δ = Δ Option / Δ Price
(+) Call
(-) Put

Question 5

Gamma (Formula)

Answer 5

Gamma = Δ Delta / Δ Price

(+) Long Option
(-) Short Option

Question 6

Vega (Formula)

Answer 6

Vega = Δ Option / Δ Vol

(+) Long Option
(-) Short Option

Question 7

Theta (Formula)

Answer 7

Theta = Δ Option / Δ Time

(-) for short option

Question 8

Covered Call (Formula)

Answer 8

Covered Call = Long Asset + Short Call

Payoff:
1) OTM: Gain = Limited to Premium
2) ITM: Loss will occur

Motivation:
- Yield enhancement if OTM
- Reduce LONG ASSET position
- Get P&L @ expiration

Question 9

Portfolio Covered Call Value (Formula)

Answer 9

Long Covered Call Perspective:

Portfolio Value = (St - Value of Call)
Value of Call = Max [(S-X), 0]

Question 10

Covered Call P&L (Formula and Rationale)

Answer 10

ITM Gain P&L = [(X-S0) + C0]

OTM Gain P&L = [Δ Asset Value + C0]

Rationale:

Always gain C0 as sold call
Gains ΔSt if OTM due to long asset
Gains (X-S0) because I locked sell @ X

Question 11

Protective Put & Portfolio Value (Formula)

Answer 11

Protective Put = Long Stock + Buy Put

Long Protective Put Value = St + Value Put
Value Put = Max [(X-St), 0]

Rationale: Limit losses

Question 12

Protective Put Payoff (Formula)

Answer 12

Payoff = Max [(S-X), 0] = ΔSt - P0 + Max [(X-St), 0]

Question 13

Δ Delta Range for Calls & Puts (Interval)

Answer 13

Δ Call: [0,1], acts like stock @ 1
Δ Put: [-1,0], acts like stock @ 0

Question 14

Δ Delta Call Behavior (Example)

Answer 14

ITM Call ~Δ = 1
OTM Call ~Δ = 0

Question 15

Δ Delta Put Behavior (Example)

Answer 15

ITM Put ~Δ = (-1)
OTM Call ~Δ = 0

Question 16

Bull Spread (Concept)

Answer 16

Position Gain: ↑ Asset Prices

Position:
1) Sell Call @ High = Cheap
2) Buy Call @ Low = Expensive

Question 17

Bull Spread Payoff (Formula)

Answer 17

Long Bull Maximum Payoff = (X High - X low) + (C High - C Low)

Question 18

Bear Spread (Concept)

Answer 18

Position Gain: ↓ Asset Prices = ↑ Gains

1) Buy Put @ High = Expensive
2) Sell Put @ Low = Cheap

Question 19

Bear Spread Payoff (Formula)

Answer 19

Long Bear Spread Payoff = (X High - X Low) - (P High + P Low)

Question 20

Straddle (Concept, Example & Payoff)

Answer 20

1) Long Straddle = Buy Call + Buy Put @ X = Long Vol
2) Format: V-shape

Example:
Xc = 2.29 = Long Call @ S + 2.29
Xp = 2.28 = Long Put @ S - 2.28
Σ = 4.57
∴ V-Shape is formed @ (Xc + Xp)

Payoff:
If St > (Xc + Xp) = CALL ITM = (S1-X) - C0 - P0
If St < (Xc + Xp): PUT ITM = (X-S1) - C0 - P0

Question 21

Collar (3 Formulas)

Answer 21

1. Collar = Long Stock + Short Call @ X High + Long Put @ X Low
2. Collar = Covered Call + Long Put
3. Collar = Protective Put + Short Call

Question 22

Collar (Concept & Format)

Answer 22

Concept: Sacrifices upside potential to lock losses

Format: Escadinha tradicional c/ minimum profit

Question 23

Zero Cost Collar (Concept)

Answer 23

Payoff from (+C0) premium and (-P0) premiums cancel each other

Question 24

Collar Gain

Answer 24

a. If St > XH = Short Call ITM
a. Gain A = [(XH-S0) +C0 -P0]
a. Reason: Locked sell @X High

b. If XH > St > XL = Nothing ITM
b. Gain B = [(St-S0) +C0 - P0]
b. Reason: Get Δ Prices

c. If St < XL = Buy Call ITM
c. Gain C = [(XL-S0) + C0 - P0]

Question 25

Calendar Spreads (Long and Short)

Answer 25

Long Cal Spread = Sell Near + Buy Long
Short Cal Spread = Buy Near + Sell Long

Question 26

Calendar Spreads (Concept)

Answer 26

Theta Play. Possible to get Theta Positive.

Question 27

Volatilty Types (List)

Answer 27

Historical: Observable
Implicit: Derived from Option Pricing Model and Derivatives traded in the market

Question 28

Volatility Skew (Concept)

Answer 28

Volatility is more steeper for Puts @ Low Strikes

Rationale: Pessimists buy more downside protection than optimists = ↑ Put Prices = ↑ Vol Puts OTM

Tip: ↑ Steeper = Bull Market

Question 29

Volatility Smile (Concept)

Answer 29

U-Shaped. OTM Calls and OTM Puts are more volatile because they are overpriced.

Question 30

Risk Reversal Strategy (Description)

Answer 30

Long Risk Reversal = Asset Price will ↑

Buy OTM Call @ X High = Underpriced
Sell OTM Put @ X Low = Overpriced