Stochastic Calculus + Option Theory

Stochastic Calculus

36 questions

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  1. Brownian Motion: 2 Definitions
    PREMIUM Not completed
  2. Alternative Definition of Brownian Motion: Lévy’s Characterization
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  3. Brownian Motion: Type of Process
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  4. Calculations for B_t
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  5. Covariance of B_t and B_t^2
    PREMIUM Not completed
  6. Probability, Rotational Symmetry
    PREMIUM Not completed
  7. SSRW vs Brownian Motion: Key Similarities in 1D
    PREMIUM Not completed
  8. Markov Processes
    PREMIUM Not completed
  9. Gaussian Processes
    PREMIUM Not completed
  10. Martingales
    FREE Not completed
  11. Necessary Condition for a Martingale
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  12. How to Prove a Process is a Martingale via Itô
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  13. Simple Examples of Martingales
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  14. 2 Important Martingales from BM
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  15. Optional Stopping Theorem
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  16. Stopped Martingales
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  17. Hitting Times and OST
    PREMIUM Not completed
  18. Itô's Lemma: What Does It Teach Us
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  19. Itô's Lemma: Vanilla Case
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  20. Itô's Lemma: Functions of BM's with Time
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  21. Itô's Lemma: Functions of BM's
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  22. Quadratic Variation
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  23. Extra Term in Itô's Lemma
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  24. Components of Itô's Lemma
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  25. Facts about Stochastic Integrals
    PREMIUM Not completed
  26. Facts about Time Integrals ∫_0^t f(B_s,s) ds
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  27. Facts about Processes of the Form f(B_t,t)
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  28. Stochastic Differential Equations
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  29. Finding Strong Explicit Solutions: 3 examples
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  30. Geometric Brownian Motion
    PREMIUM Not completed
  31. Ornstein–Uhlenbeck Process
    FREE Not completed
  32. 1st Fundamental Theorem of Asset Pricing
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  33. Complete Market
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  34. 2nd Fundamental Theorem of Asset Pricing
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  35. Equivalent Measures
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  36. Girsanov’s Theorem
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