Options Markets Class Outline

  1. Payoffs and replications: call, put, covered call, risk reversal, straddles, strangles, collar, log profile, variance swap, put-call parity, the idea of static hedging.Hull 8,9,10
  2. Options market: stock options, stock indices options, currency options, eurodollar futures options, caps/floors, swaptions.
  3. Where to get data.
  4. Dimensions that need to pay attention to: strike, expiry, spot, interest rates, dividend yields (discrete dividends), American premium.
  5. Trading activities, trading volume, open interest: Who are trading options, who are using them at different markets?
  6. Black-Scholes model
  7. Binominal method (Hull 11, code up, useful later for American options)
  8. Original model assumptions (Diffusion)
  9. BS formula
  10. Greeks
  11. The (extended) applicability of BS formula (risk premiums, predictability, local vols, st vol with terminal value of known terminal quadratic variation)
  12. PDE
  13. Probability density function.
  14. Characteristic function, cumulant-generating function, moment-generating function (Kendall: Chapter 4).
  15. Compute moments from them
  16. Inversion formula
  17. Quadrature method for cumulative distribution function.
  18. FFT for density inversion. Coding BS model: invert to get density from characteristic function. Quadrature method to get distribution. Leave density as a free input.
  19. Generalized Fourier transforms and option pricing.
  20. Two methods, theory and derivation.
  21. Modify the quadrature/fft code for option pricing, try it on BS.
  22. Levy models: BS, Merton, DPL.
  23. Derive Levy-Khintchine formula for different models
  24. Convexity adjustment for return dynamics.
  25. Coding:
  26. Code up P-characteristic function for density computation.
  27. Code up Q-Fourier transform for option pricing.
  28. Calibrate the Q-dynamics to option prices (one day)
  29. Calibrate the P-dynamics to time series returns (interest rates, exchange rates, stocks, stock indices; divide and conquer)
  30. Summarize the evidence, check the code.
  31. Time changetheory.
  32. Use Heston (93) as an example to illustrate the link to traditional specifications (memorize).
  33. General classes for multi-dimensional time changes.
  34. Affine class: Derive the Laplace transform from the PDE.Derive the Heston model solution independently and in closed book.
  35. The effect of jumps on the PDE and derivation.
  36. Quadratic class.
  37. Model design (Derive the Fourier transform of the asset return):
  38. Stocks, stock indices, and CAPM
  39. International CAPM
  40. Stock dynamics in the presence of corporate default
  41. Exchange rates
  42. Pricing kernel
  43. From Q to P, market prices of risks and expectation hypotheses
  44. Estimate Q-dynamics that involve time changes (stochastic volatilities)
  45. Estimate P- and Q-dynamics jointly.
  46. Other adventures
  47. CEV-type Levy models with time change
  48. Pricing interest-rate options
  49. 3/2 model and its extensions (numerical issues)