www.levelupbootcamps.com 4/4/21 Derivatives Option Strategies 4/4/21 LevelUp, LLC©2021 All rights reserved 1 1 Derivatives & Currency Management Option Strategies 4/4/21 LevelUp, LLC©2021 All rights reserved 2 2 Level Up, LLC©2021 All rights reserved 1 www.levelupbootcamps.com 4/4/21 Risk Management with Options Synthetic Positions • Synthetic Long & Short Forward Option Strategies • Synthetic Puts & Calls Multiple Option Strategies Single Option + Underlying Single Option Directionless Volatility Long U/L Risk Reduction Writing Puts • Long Straddle = LC + LP Covered Call = U/L + SC • Lower purchase cost • Short Straddle = SC + SP • Income enhancement • Fiduciary put = SP + Money Spreads • Reduce at favorable price cash to cover (ftn 13) “Small Moves Up or Down” • Target price realization The Greeks • Bull & Bear Call Spreads • Manza Case 1. Delta + & - • Bear & Bull Put Spreads Protective Put = U/L + LP 2. Gamma + • Insurance Calendar Spreads 3. Theta (time) - Collar = U/L + LP + SC Short “Its all about Theta” 4. Vega (Implied Vol) + • Risk Reversal • Long Calendar Spread Portfolio Mgt • Short Calendar Spread Short U/L Risk Reduction 1. Strategies using • Short U/L + Long Call volatility & market view • Short U/L + Short Put 2. Adjusting risk exposure 4/4/21 LevelUp, LLC©2021 All rights reserved 3 3 Single Option Strategies Refresher . just in case + + X S Long Call – LC S Short Call – SC - - X “writing” Want U/L up – bullish Want U/L down – bearish Right to buy at strike price X Obligated to sell at strike price X Max gain = ∞ when S > X Max gain = premium received Max loss = premium paid Max loss = –∞ (unlimited) B/E = strike (X) + premium paid B/E = X + premium received Payoff = Max (0, S – X) Payoff = Min (0, X – S) or –Max (0, S – X) Profit = Payoff – premium paid Profit = Payoff + premium received + + Long Put – LP Short Put – SP X S “writing” S - X - Want U/L down – bearish Want U/L up – bullish Right to sell at strike price X Obligated to buy at strike price X Max gain = X – premium paid Max gain = premium received Max loss = premium paid Max loss = –X + premium received B/E = X – premium paid B/E = X – premium received Payoff = Max (0, X – S) Payoff = Min (0, S – X) or –Max (0, X – S) Profit = Payoff – premium paid Profit = Payoff + premium received 4/4/21 LevelUp, LLC©2021 All rights reserved 4 4 Level Up, LLC©2021 All rights reserved 2 www.levelupbootcamps.com 4/4/21 Synthetic Forward Positions Bullish bet: Buy underlying Direction Synthetic Long Fwd = LC + SP, same strike & expiry trades Synthetic Short Fwd = SC + LP, same strike & expiry Bearish bet: T Sell underlying Should be zero-cost if X = S0(1 + rf) Motivation: possible arbitrage opportunity & customizable Profit Profit Synthetic Long Forward Synthetic Short Forward = LC + SP = SC + LP LC – upside J LP - downside X SP – downside L X SC - downside Same payoff as Same payoff as SC long underlying short underlying Replicates long stock Loss Replicates short stock Loss Exploit arbitrage opportunity Ex 1 Eliminate future price risk Ex 2 BBox 1 4/4/21 LevelUp, LLC©2021 All rights reserved 5 5 Position Equivalencies Synthetic Long Forward = LC + SP = Long Stock Stock @ expiry 40 50 60 Put-Call-Forward Parity Long 50 Call payoff OTM = 0 ATM = 0 ITM = 10 F (T)/(1+r)T = LC + SP + X/(1+r)T Short 50 Put payoff ITM = -10 ATM = 0 OTM = 0 0 Portfolio Value -10 0 +10 Long stock @ 50 -10 0 +10 Long Fwd/Futures @ 50 -10 0 +10 Ex 1 & 2 Synthetic Short Forward = SC + LP = Short Stock Stock @ expiry 40 50 60 Short 50 Call payoff OTM = 0 ATM = 0 ITM = -10 Long 50 Put payoff ITM = 10 ATM = 0 OTM = 0 Portfolio Value 10 0 -10 Short stock @ 50 10 0 -10 Ex 3 Short Fwd/Futures @ 50 10 0 -10 4/4/21 LevelUp, LLC© 2021 All rights reserved 6 6 Level Up, LLC©2021 All rights reserved 3 www.levelupbootcamps.com 4/4/21 “Synthetic” Long Forward vs. Long Forward Market maker sold - short 3-mo forward on VOD No dividends until maturity Counterparty can buy 10,000shrs VOD @ 200.35pence Annualized interest rate = 0.70% Current VOD price S0 = 200 pence Put premium = Call premium How can I hedge my Alternatively short forward position? Hedge the Short Forward w/ Borrowing Synth. Long Forward w/ Options (LC & SP) • Borrow (10,000shrs VOD x 200 • Create synthetic long forward with options pence)/100 = £20,000 • Buy calls @ strike 200.35p Synthetic • Then buy 10,000 VOD shrs at 200 pence • Sell puts @ strike 200.35p long forward = (£20,000) to cover short • Same strike & same expiration • No upfront cost since 100% financed Forward Contract @ Expiration Synthetic Long Forward Contract @ Expiration • Market maker delivers 10,000 • If VOD > 200.35p, then market maker exercises shrs VOD to the counterparty ITM call, pays £20,035 & receives 10,000shrs VOD • MM receives = 10,000 x 200.35p • MM delivers 10,000 VOD to CP & receives £20,035 = £20,035 • If VOD < 200.35p, then LP owner exercises & MM • Repay loan = 10,000 shrs x 200p (short put holder) receives 10,000 shrs for £20,035 [1+0.70% x 90/360] = (£20,035) & delivers shares to CP & receives £20,035 BBox 1 4/4/21 LevelUp, LLC© 2021 All rights reserved 7 7 Synthetic Puts & Calls Synthetic Long Call = LP + Long Underlying* Think: put-call parity Synthetic Long Put = LC + Short Underlying* Bearish bets Bullish bets without the bond Synthetic Short Call = SP + Short Underlying* S + p = C + x/(1+r)T 0 0 0 Synthetic Short Put = SC + Long Underlying* *Underlying can be replaced with futures, forward Profit Synthetic Long Put Profit Synthetic Short Call = LC + Short U/L = SP + Short U/L Long Same payoff Call as short call SP X X Same payoff as long put Short Short Underlying Underlying Short Loss Loss Put BBox 2 Ex 4 4/4/21 LevelUp, LLC©2021 All rights reserved 8 8 Level Up, LLC©2021 All rights reserved 4 www.levelupbootcamps.com 4/4/21 Synthetic Put & Call Synthetic Long Put = LC + Short Stock = Short Forward/Futures Stock @ expiry 40 50 60 Short stock @ 50 +10 0 - 10 Long 50 Call payoff OTM = 0 ATM = 0 ITM = +10 Same Payoffs Portfolio Value +10 0 0 Long 50 Put +10 0 0 Short Fwd/Futures +10 0 0 Ex 4 Synthetic Long Call = Long Stock + Long Put = Long Fwd/Futures Eliminates downside risk* Stock @ expiry 40* 50 60 Long stock @ 50 - 10 0 +10 Same Payoffs Long 50 Put payoff ITM = +10 ATM = 0 OTM = 0 Portfolio Value 0 0 +10 Long 50 Call 0 0 +10 Long Fwd/Futures 0 0 +10 Ex 5 4/4/21 LevelUp, LLC©2021 All rights reserved 9 9 Position Equivalence Summary Long Call Short Put Synthetic + = long forward Short Call Long Put Synthetic + = short forward Short Stock Long Call Synthetic + = long put Long Stock Long Put Synthetic + = long call 4/4/21 LevelUp, LLC© 2021 All rights reserved 10 10 Level Up, LLC©2021 All rights reserved 5 www.levelupbootcamps.com 4/4/21 Synthetic Long Put Example Synthetic Long Put = Long Call + Short Forward/Futures HF mgr. short 1-mo forward to deliver 50,000 shrs G No dividends until maturity Long forward position can buy 50,000 shrs @ £18 Company may exceed Current stock price ST = £16 expectations next month HF mgr. has • But HF mgr. remains bearish bearish outlook • Desires to hedge risk (price up) wants insurance • Wants to benefit prices below £16 Short Forward • Avoid losses above £16 from short Profit if price falls & loss if price rises Synthetic Long Put (LC + Short U/L) = 50,000 shrs x (£18 – ST) • Buy/long 50,000 £16 Calls @ 50 pence If £18 < ST , HF mgr losses on short, price up • HF mgr. shorted 50,000 of Generali If ST < £18, HF mgr gains, price fell below 18 Synthetic Long Put @ Expiration • Long call payoff = 50,000 shrs x [Max (0, ST – £16)] – £0.50 premium Combined • If ST <16,- then call expires OTM & worthless Portfolio • Short forward payoff = 50,000 shrs x (£18 – ST), below £18 short fwd profits Position • If ST <16, then short forward profits = 50,000 x (£18 – ST – £0.50) = £75,000 • If ST >16, then call is exercised = 50,000 x (£18 – £16 – £0.50) = £75,000 4/4/21 LevelUp, LLC© 2021 All rights reserved EOC 1 BBox 2 11 11 The Greeks Delta D Gamma G • Change in option price (premium) • Change in delta for a change in the given a small change in U/L price U/L price – faster gain or loss • Approximates how much an option’s • Measures curvature in option price price will change given a small change relationship with U/L price in U/L – option sensitivity • Long call & long puts are ALWAYS • Long call delta is POSITIVE POSITIVE • Long put delta is NEGATIVE • Gamma = DDelta/DU/L value • Long call delta 0 to +1, put delta -1 to 0 • Greater gamma near the money EOC 16 Vega n Implied Volatility Theta Q Time • Change in option price (premium) for a • Decrease in option premium given change in U/L volatility of returns the passage of time • Value of unobservable volatility • Daily change in option price • Solved within BSM • Time decay value • Long call & long put vega is POSITIVE • Long calls & long puts theta is • Vega rises & falls when U/L volatility NEGATIVE expectations change 4/4/21 LevelUp, LLC© 2021 All rights reserved 12 12 Level Up, LLC©2021 All rights reserved 6 www.levelupbootcamps.com 4/4/21 Delta (Δ) The amount the option price/premium changes for a $1.00 move in the underlying Portfolio Deltas are “additive” asset Δ = Slope of Price Curve Combine the deltas of each position Basics Δ Example Portfolio Δ Long Underlying Δ = +1 Long Call 0.45 (given) Short Underlying Δ = −1 Long Put −0.55 (given) Long Call + D 0 < Δ < 1 Covered Call = LS + SC +1 − 0.45 = 0.55 Short Call - D −1 < Δ < 0 Protective Put = LS + LP +1 + (−0.55) = 0.45 Long Put - D −1 < Δ < 0 Syn Long Fwd = LC + SP 0.45 − (−0.55) = 1.0 Short Put + D 0 < Δ