Option Pricing - Greeks

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A basic review of Option Price Sensitivities or Greeks. Delta, Gamma, Vega, Theta and Rho.

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Option Pricing - Greeks

  1. 1. Option Pricing Sensitivity Greeks Advance Risk Models War on Greeks Jawwad Ahmed Farid
  2. 2. Plan Greeks • Delta, Gamma, Vega, Theta • Derivative Portfolio Hedging • Method II, EGS Case • DPD Analysis Credit Risk • PD Models, Barclays BankCapital Adequacy • Capital Adequacy Models & ICAAP • Stress Testing, Solvency IIHow to kill a bank • Integrated Bank Simulation in one day • Liquidity, Capital, Market Risk
  3. 3. ALM • Asset Liability Management Delta Hedging • Derivative Portfolio GreeksBarclays Bank • Libor Crisis, FI Limits, PD Models Value at Risk • Margin Lending & FI Limits Liquidity Stress • Extending Capital Adequacy Testing Enron Gas • Running a risk book Services
  4. 4. Option Greeks Lesson One
  5. 5. Moneyness & value changeDeep Out • Change in value?of Money • VolatilityAt or Near • Change in value? Money • Strike, Spot Deep in • Change in value? • Time Money
  6. 6. The GreeksDelta • Change in value on account of a unit change in the underlyingGamma • Change in Delta on account of a unit change in the underlyingVega • Change in value on account of change in volatilityTheta • Change in value on account of change in time Rho • Change in value on account of change in interest rates
  7. 7. Delta
  8. 8. Gamma
  9. 9. Vega
  10. 10. Theta
  11. 11. Rho
  12. 12. The Greeks against Spot100.0% 2.0% 90.0% 1.5% 80.0% 70.0% 1.0% 60.0% 50.0% 0.5% 40.0% 0.0% 30.0% 20.0% -0.5% 10.0% 0.0% -1.0% 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 Delta Vega Rho Gamma Theta
  13. 13. Delta Call ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑13/19/2013 13
  14. 14. Delta Put ∆𝑃𝑢𝑡 = 1 − 𝑁(𝑑1)3/19/2013 14
  15. 15. Gamma Call ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1 𝑁′(𝑑1) 𝛾𝐶𝑎𝑙𝑙 = 𝑆𝜎 𝑇3/19/2013 15
  16. 16. Gamma Put ?3/19/2013 16
  17. 17. Gamma Put ∆𝑃𝑢𝑡 = 1 − 𝑁 𝑑1 𝑁′(𝑑1) 𝛾𝑃𝑢𝑡 = 𝑆𝜎 𝑇3/19/2013 17
  18. 18. Vega Call ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1 𝑁(𝑑1) 𝛾𝐶𝑎𝑙𝑙 = 𝑆𝛿 𝑇 𝑉𝑒𝑔𝑎 𝐶𝑎𝑙𝑙 = 𝑆𝑁′(𝑑1) 𝑇3/19/2013 18
  19. 19. Vega Put ?3/19/2013 19
  20. 20. Applications?3/19/2013 20
  21. 21. Value of a Call Call = Delta * S - Borrowing3/19/2013 21
  22. 22. Greeks Behaving badlyAt, Near Money Call Options
  23. 23. The Greeks against Time70.0% 20.0% 18.0%60.0% 16.0%50.0% 14.0% 12.0%40.0% 10.0%30.0% 8.0%20.0% 6.0% 4.0%10.0% 2.0% 0.0% 0.0% 0.01 0.03 0.04 0.08 0.10 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.00 Delta Vega Rho Gamma Theta
  24. 24. The Greeks against Vol1.20 0.07 0.061.00 0.05 0.040.80 0.030.60 0.02 0.010.40 - -0.010.20 -0.02 - -0.03 0.01 0.03 0.04 0.08 0.10 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.00 Delta Vega Rho Gamma Theta
  25. 25. The Greeks against Spot100.0% 2.0% 90.0% 1.5% 80.0% 70.0% 1.0% 60.0% 50.0% 0.5% 40.0% 0.0% 30.0% 20.0% -0.5% 10.0% 0.0% -1.0% 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 Delta Vega Rho Gamma Theta
  26. 26. The Greeks against Strike120.0% 2.0%100.0% 1.5% 1.0% 80.0% 0.5% 60.0% 0.0% 40.0% -0.5% 20.0% -1.0% 0.0% -1.5% 75 85 60 65 70 80 90 95 110 120 100 105 115 125 130 Delta Vega Rho Gamma Theta
  27. 27. Vol, N(d1), N(d2), Price1.20 45.00 40.001.00 35.000.80 30.00 25.000.60 20.000.40 15.00 10.000.20 5.00 - - 0.07 0.73 0.85 0.97 0.01 0.13 0.19 0.25 0.31 0.37 0.43 0.49 0.55 0.61 0.67 0.79 0.91 Volatility N(d1) N(d2) Price

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