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

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Room 1: A Barn on Fire 3

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) JanFeb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Purchase at End of Month No Coverage Insurance Contract Period Farmer must decide: Monthly target milk marketings (M t+i ) expected feed usage (C t+i, SBM t+i ) Gross Margin Deductible (D)

How is LGM-Dairy priced? JanFeb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Purchase at End of Month No Coverage Insurance Contract Period 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).

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

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

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

Class III Milk Futures: Open Interest

Home-feed profile: Insuring 8-10 th month

Why using deferred contracts works the best

Room 2: Mind your Tail

How is LGM-Dairy priced? JanFeb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Purchase at End of Month No Coverage Insurance Contract Period 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).

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

Lower tail dependence

Upper tail dependence

Copulas: Tool for dealing with nonlinear dependencies GaussianClaytonGumbel

Comparing Copula Families

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 Home-FeedMarket-Feed Deductible$0.00$1.10$0.00$1.10 Official RMA Method $14,569$7,380$20,350$13,308 Rank Correlations $14,998$7,719$16,439$9,504 Empirical Copula $15,286$8,219$15,478$8,246 Unlike most situations in financial sector, in livestock margin insurance tail dependence decreases portfolio risk.

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

How is LGM-Dairy priced? JanFeb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Purchase at End of Month No Coverage Insurance Contract Period 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).

Are Futures Prices Unbiased?

Testing for bias in futures prices

Test Design

Essential assumption: Lognormality Bootstrap procedure

Testing for Futures Price Bias

Testing for Implied Volatility Bias

Effect of biases on LGM premiums Home-FeedMarket-Feed Deductible$0.00$1.10$0.00$1.10 Official RMA Method 9,7435,19113,3168,873 Biased Soymeal Futures 9,74413,438 5,1928,992 Biased Milk Volatility 10,9726,28714,2359,686

Room 4: A reason to smile. 39

How is LGM-Dairy priced? JanFeb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Purchase at End of Month No Coverage Insurance Contract Period 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? In the current RMA ratings method, only at-the-money puts and calls are used to estimate variance of the terminal prices. Date: Jun 26, 2006 Contract: Corn, Dec ’06 Futures Price: $2.49

42 Volatility smiles induced by high kurtosis

43 Volatility skews induced by high skewness

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

Scenario 1: Corn as the only source of risk Corn skewness boosted 60%

Scenario 2: Corn as the only source of risk Corn kurtosis boosted 60%

Scenario 3: Corn as the only source of risk Both skewness and kurtosis boosted

Scenario 4: Two sources of risk – milk and corn Effect 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 (612) Department of Applied Economics University of Minnesota-Twin Cities 317c Ruttan Hall 1994 Buford Avenue St Paul, MN