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Anatoliy Swishchuk Math & Comp Finance Lab Dept of Math & Stat, U of C “Lunch at the Lab” Talk

Paper Review: “On the Pricing and Hedging of Volatility Derivatives” by S. Howison, A. Rafailidis and H. Rasmussen (Applied Mathematical Finance J., 2004). Anatoliy Swishchuk Math & Comp Finance Lab Dept of Math & Stat, U of C “Lunch at the Lab” Talk February 10, 2006. Variance Swap.

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Anatoliy Swishchuk Math & Comp Finance Lab Dept of Math & Stat, U of C “Lunch at the Lab” Talk

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  1. Paper Review:“On the Pricing and Hedging of Volatility Derivatives”by S. Howison, A. Rafailidis and H. Rasmussen (Applied Mathematical Finance J., 2004) Anatoliy Swishchuk Math & Comp Finance Lab Dept of Math & Stat, U of C “Lunch at the Lab” Talk February 10, 2006

  2. Variance Swap

  3. Realized Variance in Continuous Time

  4. Payoff Function for Variance Swap

  5. Realized Volatility (Discrete Time)

  6. Realized Volatility (Continuous Time)

  7. Payoff Function for Volatility Swap

  8. Payoff Function for Volatility-Average Swap

  9. Payoff Function for Implied Volatility Swap

  10. Payoff for Variance Swaptions

  11. Payoff Functions for Volatility Swaptions

  12. Payoff Function for Volatility and Asset Swaption

  13. Risk-Neutral Pricing Technique

  14. Three Approaches to the Risk-Neutral Pricing • Pricing Independently of the Volatility Model • Pricing by Expectations in a SV Framework • Pricing via Partial Differential Equations

  15. 1st Approach: Pricing Independently of the Volatility Model

  16. 1st Approach: Pricing Independently of the Volatility Model (cntd)

  17. 1st Approach: Pricing Independently of the Volatility Model (cntd)

  18. 2nd Approach: Pricing by Expectations in a SV Framework

  19. 2nd Approach: Pricing by Expectations in a SV Framework (cntd)

  20. 2nd Pricing Approach: Pricing by Expectations in a SV Framework (cntd)

  21. 2nd Pricing Approach: Pricing by Expectations in a SV Framework (cntd)

  22. 3d Approach: Pricing via PDE

  23. 3d Approach: Pricing via PDE (Model)

  24. 3d Approach: Pricing via PDE (Payoffs)

  25. 3d Approach: Pricing via PDE (Payoffs)

  26. 3d Approach: Pricing via PDE (PDE Itself for the Value V of Derivative)

  27. 3d Approach: Pricing via PDE (Mean-Reverting Model)

  28. General Stochastic Volatility Models

  29. Derivation of Certain Expectations

  30. Derivation of Certain Expectations.I.

  31. Derivation of Certain Expectations.II.

  32. Derivation of Certain Expectations.III.

  33. Derivation of Certain Expectations.IV.

  34. Derivation of Certain Expectations.V.

  35. Derivatives Pricing

  36. Mean-Reverting-Like Process

  37. Mean-Reverting-Like Process.I.

  38. Mean-Reverting-Like Process.II.

  39. Popular SV Models. I.

  40. Popular SV Models. II.

  41. Popular SV Models. III.

  42. Popular SV Models. IV.

  43. Popular SV Models. V.

  44. Asymptotical Analysis for Fast Mean-Reversion. I.

  45. Asymptotical Analysis for Fast Mean-Reversion. II.

  46. Asymptotical Analysis for Fast Mean-Reversion. III.

  47. Asymptotical Analysis for Fast Mean-Reversion (Summary).

  48. Examples: 1. The Variance Swap

  49. Examples: 2. The Standard-Deviation Swap

  50. Examples: 3. The Volatility-Average Swap

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