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Marin Bozic - University of Minnesota MFM Seminar, Minneapolis, September 28, 2012

Practical Issues In Pricing (and Using) Asian Basket Options: A Case of Livestock Gross Margin Insurance. Marin Bozic - University of Minnesota MFM Seminar, Minneapolis, September 28, 2012. Room 1: A Barn on Fire. Nature of risk in the dairy sector. Real price risk?

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Marin Bozic - University of Minnesota MFM Seminar, Minneapolis, September 28, 2012

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  1. Practical Issues In Pricing (and Using) Asian Basket Options:A Case of Livestock Gross Margin Insurance Marin Bozic - University of Minnesota MFM Seminar, Minneapolis, September 28, 2012

  2. Room 1: A Barn on Fire

  3. Nature of risk in the dairy sector Real price risk? Prolonged Period of Margins Much Below Average

  4. Livestock Gross Margin Insurance for Dairy Cattle (LGM-Dairy) • Farmer must decide: • Monthly target milk marketings (Mt+i) • expected feed usage (Ct+i,SBMt+i) • Gross Margin Deductible (D)

  5. How is LGM-Dairy priced? • Extract information regarding expected prices and volatilities from futures prices and at-the-money options • Calculate correlations based on historical data • Use Monte Carlo methods to simulate indemnities • Price of the Asian Basket Option set at mark-up over actuarially fair price (e.g. expected indemnity).

  6. A Naïve approach to LGM-Dairy • Identify expected milk marketings, feed amounts • Choose target IOFC margin to protect • Insure equal percentage of each month’s production, e.g. flat coverage for 10 months.

  7. A (bit less) Naïve approach to LGM-Dairy • Identify expected milk marketings, feed amounts • Choose target IOFC margin to protect • Find a least-cost profile that protects the target IOFC.

  8. A (bit less) Naïve approach to LGM-Dairy

  9. Home-feed profile:Insuring 1st-10th month

  10. Home-feed profile:Insuring 1st-3rd month.

  11. Class III Milk Futures: Open Interest

  12. Home-feed profile: Insuring 8-10th month

  13. Why using deferred contracts works the best

  14. Room 2: Mind your Tail

  15. How is LGM-Dairy priced? • Extract information regarding expected prices and volatilities from futures prices and at-the-money options • Calculate correlations based on historical data • Use Monte Carlo methods to simulate indemnities • Price of the Asian Basket Option set at mark-up over actuarially fair price (e.g. expected indemnity).

  16. Is correlation a good way to think about dependence between variables?

  17. Lower tail dependence

  18. Upper tail dependence

  19. Copulas: Tool for dealing with nonlinear dependencies Clayton Gaussian Gumbel

  20. Comparing Copula Families

  21. Empirical Copula • Empirical copula replaces unknown distributions with their empirical counterparts: • Implementation: Bootstrap based on rank-order matrix • Potential shortcomings: Small sample, serial dependency

  22. Effect of non-linear dependence on LGM premiums • Unlike most situations in financial sector, in livestock margin insurance tail dependence decreases portfolio risk.

  23. Room 3: Mr. Black, this drink is flat.

  24. How is LGM-Dairy priced? • Extract information regarding expected prices and volatilities from futures prices and at-the-money options • Calculate correlations based on historical data • Use Monte Carlo methods to simulate indemnities • Price of the Asian Basket Option set at mark-up over actuarially fair price (e.g. expected indemnity).

  25. Are Futures Prices Unbiased?

  26. Testing for bias in futures prices

  27. Test Design

  28. Bootstrap procedure • Essential assumption: Lognormality

  29. Testing for Futures Price Bias

  30. Testing for Futures Price Bias

  31. Testing for Futures Price Bias

  32. Testing for Implied Volatility Bias

  33. Testing for Implied Volatility Bias

  34. Testing for Implied Volatility Bias

  35. Testing for Implied Volatility Bias

  36. Effect of biases on LGM premiums

  37. Room 4: A reason to smile.

  38. How is LGM-Dairy priced? • Extract information regarding expected prices and volatilities from futures prices and at-the-money options • Calculate correlations based on historical data • Use Monte Carlo methods to simulate indemnities • Price of the Asian Basket Option set at mark-up over actuarially fair price (e.g. expected indemnity).

  39. Does it matter if marginal distributions are in fact not lognormal? Date: Jun 26, 2006 Contract: Corn, Dec ’06 Futures Price: $2.49 • In the current RMA ratings method, only at-the-money puts and calls are used to estimate variance of the terminal prices.

  40. Volatility smiles induced by high kurtosis

  41. Volatility skews induced by high skewness

  42. Generalized Lambda Distribution (GLD) allows changing one moment at a time

  43. Scenario 1: Corn as the only source of riskCorn skewness boosted 60%

  44. Scenario 2: Corn as the only source of riskCorn kurtosis boosted 60%

  45. Scenario 3: Corn as the only source of riskBoth skewness and kurtosis boosted

  46. Scenario 4: Two sources of risk – milk and cornEffect nearly disappears

  47. Conclusions • Modeling dependence using correlations may not suffice – tail dependence matters! • Simplistic heuristics and CME settlement rules may have rendered dairy options too cheap. • Volatility smiles may not be important for pricing Asian Basket Options

  48. Practical Issues in Pricing (and Using) Asian Basket Options: A Case of Livestock Gross Margin Insurance MFM Seminar September 28, 2012 Dr. Marin Bozic mbozic@umn.edu (612) 624-4746 Department of Applied Economics University of Minnesota-Twin Cities 317c Ruttan Hall 1994 Buford Avenue St Paul, MN 55108

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