Option Strategies. Probability distributions. Performance 1.1 Market scenario undecided. Volatility undecided 1.1.1 Complete hedge using options The payoff of the underlying asset (long share) can be completely hedged by selling a call, buying a put option and selling a riskless bond. This combination would behave like selling the underlying security. 1.1.2 Box Spread Table 1. Box Spread. The Value Matrix S<E1 E1<S<E2 S>E2 Call -C1 -C1 + S - E1 -C1 + S - E1 - Call +C2 +C2 +C2 -( S - E2) Put -P2 + E2 - S -P2 + E2 - S - P2 - Put +P1 - (E1 - S) + P1 + P1 Total payoff -C + E2 - E1 -C + E2 - E1 -C + E2 - E1 Profit /Loss E2-E1 E2-E1-C1+C2+P1-P2 E1 E2 Spot Price (S) Figure 1. Box Spread Derivatives Market 231231-0345 1.2 Market scenario undecided. Volatility rising 1.2.1 Long Straddle Table 2. Long Straddle. The Value Matrix S<E S>E Call -C0 -C0 + S - E Put -P0 + E - S - P0 Total payoff + E - S - C0 - P0 + S - E -C0 - P0 Profit Break-even Point S=E-(P0+C0) /Loss -(P0+C0) Break-even Point S=E+P0+C0 E Spot Price (S) CF=-(P0+C0) Premiums Figure 2. Long Straddle 2 Derivatives Market 231231-0345 1.2.2 Long Strangle Table 3. Long Strangle. The Value Matrix S<E1 E1<S<E2 S>E2 Put (E1) -P1 + E1 - S -P1 - P1 Call (E2) -C2 - C2 - C2 + S - E2 Total payoff -P1 -C2 + E1 - S - P1 - C2 - P1- C2+ S - E2 Profit Break-even Point S=E1- (P1+C2) /Loss E1 E1-(P1+C2) Break-even Point S=E2+P1+C3 -(P1+C2) E1 E2 Spot Price (S) Figure 3. Long Strangle 3 Derivatives Market 231231-0345 1.2.3 Short Butterfly Spread Table 4. Short Butterfly Spread. The Value Matrix S<E1 E1<S<E2 E2<S<E3 S>E3 - Call (E1) C1 C1 - S + E1 C1 - S + E1 C1 - S + E1 - Call (E3) C3 C3 C3 C3 - S + E3 Call (E2) -2C2 -2C2 -2C2 + 2(S - E2) -2C2 + 2(S - E2) Total payoff -S + E1 S - 2E2 + E1 -2E2 + E1 + E3 -2C2 + C1 + C3 - 2C2 + C1 + C3 - 2C2 + C1 + C3 - 2C2 + C1 + C3 Profit Break-even Point S=E1+(C1+C3-2C2) /Loss Break-even Point S=E3-(C1+C3-2C2) -2C2+C1+C3 E1 E2 E3 Spot Price (S) E1-E2+C1+C3-2C2 Figure 4. Short Butterfly Spread 4 Derivatives Market 231231-0345 1.2.4 Short Condor Table 5. Short Condor. The Value Matrix S<E1 E1<S<E2 E2<S<E3 E3<S<E4 S>E4 - Call (E1) +C1 C1 - (S - E1) C1 - (S - E1) C1 - (S - E1) C1 - (S - E1) Call (E2) -C2 -C2 -C2 + S - E2 -C2 + S - E2 -C2 + S - E2 Call (E3) -C3 -C3 -C3 -C3 + S - E3 -C3 + S - E3 - Call (E4) C4 C4 C4 C4 C4 - (S - E4) Total payoff C -S + E1 + C -E2 + E1 + C -E3 -E2 +E1 +S -E3 -E2 +E1 +E4 +C +C Profit Break-even Point S=E2-C1-C4+C2+C3 /Loss Break-even Point S=E3+C1+C4-C2-C3 E2-E1 E2-E1+C1+C4-C2-C3 E1 E2 E3 E4 Spot Price (S) +C1+C4-C2-C3 Figure 5. Short Condor 5 Derivatives Market 231231-0345 1.3 Market scenario undecided. Volatility falling 1.3.1 Short Straddle Table 6. Short Straddle. The Value Matrix S<E S>E - Call +C0 +C0 - (S - E) - Put +P0 - (E - S) + P0 Total payoff S -E +C0 + P0 E - S +C0 + P0 Profit Break-even Point S=E-(P0+C0) /Loss Break-even Point S=E+P0+C0 (P0+C0) E Spot Price (S) (P0+C0) -E Figure 6. Short Straddle 6 Derivatives Market 231231-0345 1.3.2 Short Strangle Table 7. Short Strangle. The Value Matrix S<E1 E1<S<E2 S>E2 - Put (E1) P1 - E1 + S P1 P1 - Call (E2) C2 C2 C2 - S + E2 Total payoff P1 + C2 - E1 +S P1 + C2 P1 + C2 - S + E2 Profit Break-even Point S=E1- (P1+C2) /Loss Break-even Point P1+C2 S=E2+P1+C3 E1 E2 Spot Price (S) Figure 7. Short Strangle 7 Derivatives Market 231231-0345 1.3.3 Long Butterfly Spread Table 8. Long Butterfly Spread. The Value Matrix S<E1 E1<S<E2 E2<S<E3 S>E3 Call (E1) -C1 -C1 + S - E1 -C1 + S - E1 -C1 + S - E1 Call (E3) -C3 -C3 -C3 -C3 + S - E3 - Call (E2) +2C2 +2C2 +2C2 - 2(S - E2) +2C2 - 2(S - E2) Total payoff 2C2 -C1-C3 S - E1 -S + 2E2 - E1 2E2 - E1 - E3 +2C2 -C1-C3 +2C2 -C1-C3 +2C2 -C1-C3 Profit Break-even Point S=E1+(C1+C3-2C2) /Loss Break-even Point S=E3-(C1+C3-2C2) E2-E1-C1-C3+2C2 E1 E2 E3 Spot Price (S) 2C2-C1-C3 Figure 8. Long Butterfly Spread 8 Derivatives Market 231231-0345 1.3.4 Long Condor Table 9. Long Condor. The Value Matrix S<E1 E1<S<E2 E2<S<E3 E3<S<E4 S>E4 Call (E1) -C1 -C1 + S - E1 -C1 + S - E1 -C1 + S - E1 -C1 + S - E1 - Call (E2) +C2 +C2 +C2 - S + E2 +C2 - S + E2 +C2 - S + E2 - Call (E3) +C3 +C3 +C3 +C3 - S + E3 +C3 - S + E3 Call (E4) -C4 -C4 -C4 -C4 -C4 + S - E4 Total payoff -C S - E1 - C E2 - E1 - C E3 + E2 - E1 - S E3 + E2 - E1 - - C E4 - C Profit Break-even Point S=E1+C1+C4-C2-C3 /Loss E2-E1 Break-even Point S=E4-(C1+C4-C2-C3) E2-E1-C1-C4+C2+C3 E1 E2 E3 E4 Spot Price (S) -C1-C4+C2+C3 Figure 9. Long Condor 9 Derivatives Market 231231-0345 1.4 Market scenario bulish. Volatility undecided 1.4.1 Long Call + Short Put Long call and short put replicates long share. 1.4.2 Bull Spread Table 10. Bull Call Spread. The Value Matrix S<E1 E1<S<E2 S>E2 Call (E1) -C1 -C1 + S - E1 -C1 + S - E1 - Call (E2) +C2 +C2 +C2 - S + E2 Total payoff C2 -C1 + S - E1+C2 -C1 E2 - E1 +C2 -C1 Profit /Loss Break-even Point S=E1+C1-C2 E2-E1 C2-C1 E1 E2 Spot Price (S) Figure 10. Bull Call Spread 10 Derivatives Market 231231-0345 1.4.3 Rotated Vertical Bull Spread Table 11. Rotated Vertical Bull Spread. The Value Matrix S<E S>E Call -C0 -C0 + S - E - Put +P0 - (E - S) + P0 Total payoff S - E - C0 + P0 + S - E - C0 + P0 Profit /Loss Break-even Point S=E-P0+C0 CF=P0-C0 E Spot Price (S) Premium Figure 11. Rotated Vertical Bull Spread 11 Derivatives Market 231231-0345 1.5 Market scenario bulish. Volatility rising 1.5.1 Long Call Long call is the simplest strategy for an investor expecting rise in prices and rise in volatility. 1.5.2 Protective Put Table 12. Protective Put. The Value Matrix S<E S>E Long share S S Put -P0 + E - S - P0 Total payoff E -P0 S - P0 Long share Profit /Loss E CF=P0 Break-even Point Premium S=E-P0 E Spot Price (S) Figure 12. Protective Put 12 Derivatives Market 231231-0345 1.5.3 Call Ratio Back Spread Table 13. Call Ratio Back Spread. The Value Matrix S<E1 E1<S<E2 S>E2 - Call (E1) +C1 +C1 - S + E1 +C1 - S + E1 Two calls (E2) -2C2 -2C2 -2C2 + 2 (S - E2) Total payoff +C1 - 2C2 - S + E1 + C1 - 2C2 S + E1 - 2E2 +C1 - 2C2 Profit /Loss Break-even Point S=2E2-E1+2C2-C1 C1-2C2 E1 E2 Spot Price (S) E1-E2+C1-2C2 E1-E2 Figure 13. Call Ratio Back Spread 13 Derivatives Market 231231-0345 1.6 Market scenario bulish. Volatility falling 1.6.1 Short Put Short put is the simplest strategy for an investor expecting fall in prices and fall in volatility. 1.6.2 Covered Call Table 14. Covered Call. The Value Matrix S<E S>E Long share S S - Call +C0 +C0 - (S - E) Total payoff S + C0 E + C0 Long share Profit /Loss E Break-even Point S=E+C0 CF=C0 Premium E Spot Price (S) Figure 14. Covered Call 14 Derivatives Market 231231-0345 1.6.3 Ratio Call Spread Table 15. Ratio Call Spread. The Value Matrix S<E1 E1<S<E2 S>E2 Call (E1) -C1 -C1 + S - E1 -C1 + S - E1 Two short Puts (E2) +2C2 +2C2 +2C2 - 2( S - E2) Total payoff -C1 + 2C2 + S - E1 - C1 + 2C2 -S - E1 + 2E2 -C1 + 2C2 Profit /Loss E2-E1+2C2-C1 Break-even Point S=2E2-E1+2C2-C1 E2-E1 2C2-C1 E1 E2 Spot Price (S) (2C2<C1) Figure 15. Ratio Call Spread 15 Derivatives Market 231231-0345 1.7 Market scenario bearish. Volatility undecided 1.7.1 Short Call + Long Put Short call and long put replicates short share or short futures. 1.7.2 Bear Spread Table 16. Bear Put Spread. The Value Matrix S<E1 E1<S<E2 S>E2 Put (E2) -P2 + E2 - S -P2 + E2 - S - P2 - Put (E1) +P1 - (E1 - S) + P1 + P1 Total payoff +P1 - P2 + E2 - E1 + P1 - P2 + E2 - S + P1- P2 Profit /Loss Break-even Point S=E2+P1-P2 E2-E1 E2-E1+P1-P2 P1-P2 E1 E2 Spot Price (S) Figure 16. Bear Put Spread 16 Derivatives Market 231231-0345 1.7.3 Rotated Vertical Bear Spread Table 17. Rotated Vertical Bear Spread.