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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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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
Nature of risk in the dairy sector Real price risk? Prolonged Period of Margins Much Below Average
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)
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).
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.
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.
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).
Is correlation a good way to think about dependence between variables?
Copulas: Tool for dealing with nonlinear dependencies Clayton Gaussian Gumbel
Empirical Copula • Empirical copula replaces unknown distributions with their empirical counterparts: • Implementation: Bootstrap based on rank-order matrix • Potential shortcomings: Small sample, serial dependency
Effect of non-linear dependence on LGM premiums • Unlike most situations in financial sector, in livestock margin insurance tail dependence decreases portfolio risk.
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).
Bootstrap procedure • Essential assumption: Lognormality
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).
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.
Generalized Lambda Distribution (GLD) allows changing one moment at a time
Scenario 1: Corn as the only source of riskCorn skewness boosted 60%
Scenario 2: Corn as the only source of riskCorn kurtosis boosted 60%
Scenario 3: Corn as the only source of riskBoth skewness and kurtosis boosted
Scenario 4: Two sources of risk – milk and cornEffect nearly disappears
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
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