Commodities what's different?

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Commodities what's different?

  1. 1. What are commodities?Commodities Derivatives Risk Management Models Commodities - An Alternative Asset Seminar Cycle on Quantitative Finance - CRM-UAB Madimon Consulting Ramon Prat 20 December 2012 Madimon Consulting Commodities - An Alternative Asset
  2. 2. What are commodities? Commodities Derivatives Risk Management Modelsa different asset class Stocks and Bonds can be valued on the basis of the net present value of expected cash flows n CFi i=1 PV = (1 + ri )i Commodities do not provide a claim on a ongoing stream of revenue and cannot be valued on the basis of PV. Consume : ie corn as feedstock or food stock Transform : ie crude oil into diesel or gasoline Madimon Consulting Commodities - An Alternative Asset
  3. 3. What are commodities?Commodities Derivatives Risk Management Models Madimon Consulting Commodities - An Alternative Asset
  4. 4. What are commodities? Commodities Derivatives Risk Management ModelsExposure to commodities Purchase the underlying Invest in Natural Resource Companies: Debt & Equity Commodity Futures and Options Contracts Commodity Swaps and Forwards Commodity Linked Notes, ETFs and other instruments Madimon Consulting Commodities - An Alternative Asset
  5. 5. What are commodities?Commodities Derivatives Risk Management Models Madimon Consulting Commodities - An Alternative Asset
  6. 6. What are commodities? Commodities Derivatives Risk Management ModelsCommodities Risks every commodity is traded in a spot market made of originators, marketers, manufacturers which face four types of risk: Price : commodity, currency derivatives Logistics : freight derivatives Delivery : clearing houses Credit : clearing houses Madimon Consulting Commodities - An Alternative Asset
  7. 7. What are commodities?Commodities Derivatives Risk Management Models Madimon Consulting Commodities - An Alternative Asset
  8. 8. What are commodities? Commodities Derivatives Risk Management ModelsNew Risks Associated with Hedging Basis Risk: Cash prices and futures price might not be perfectly correlated Roll Yield (Backwardation)/Cost(Contango) Collateral Yield Madimon Consulting Commodities - An Alternative Asset
  9. 9. What are commodities? Commodities Derivatives Risk Management ModelsEquilibrium Relationship Between Spot Prices and ForwardPrices F0,T = S0 e (r −δt )t ; r=risk free rate; δ=convenience yield if r > δ ⇒ contango if r < δ ⇒ backwardation Madimon Consulting Commodities - An Alternative Asset
  10. 10. What are commodities? Commodities Derivatives Risk Management ModelsMain Categories: Markow Process vs Non-Markow Models Neutral Probabilities versus Real Probabilities Stochastic vs Deterministic One stochastic variable or more than one stochastic variable Complete Markets vs Incomplete Markets Modeling the Underlying or the Derivative Drift / No-drift / mean-reversion Discrete versus Continuous Models Madimon Consulting Commodities - An Alternative Asset
  11. 11. What are commodities? Commodities Derivatives Risk Management ModelsMarkow Process vs Models with Memory Markow Processes: P(Xm ∈ B/Xn , . . . , X0 ) = P(Xm ∈ B/Xn ) Cox-Ross-Rubinstein: Binomial model (discrete): tree Brownian Motion (continuous): Xt+1 = Xt + Wt+1 Black Scholes ... Non Markow Processes: multivariate statistics ARMA Processes (discrete):Xt+1 = aXt + t+1 Volatility Clustering Processes (continuous - Heston) GARCH Processes: σt = σ 2 + aσt−1 + bZt−1 2 2 2 ... Efficient Market Hipotesis implies stocks are Markowian. But commodities usually exhibit seasonality . . . Madimon Consulting Commodities - An Alternative Asset
  12. 12. What are commodities? Commodities Derivatives Risk Management ModelsNeutral Probabilities versus Real Probabilities Neutral Probabilities: Martingales Cox-Ross-Rubinstein: Binomial model (discrete): tree Brownian Motion (continuous): Xt+1 = Xt + Wt+1 Black Scholes ... Real Probabilities: Multivariate Statistics Neutral Probabilities: Sell side ⇒ sell to the market Real Probabilities: Buy side, ⇒ usually the buyer is not risk neutral !!! Madimon Consulting Commodities - An Alternative Asset
  13. 13. What are commodities? Commodities Derivatives Risk Management ModelsStochastic vs Deterministic Stochastic ⇒ Interested in the path t → T dSt St = (r − δ)dt + σdWt Deterministic ⇒ Interested only in the value at T dSt St = (r − δ)dt if the purpose of the trade is the physical delivery will not be interested in the path . . . if the purpose is hedging a portfolio the path is crucial . . . Madimon Consulting Commodities - An Alternative Asset
  14. 14. What are commodities? Commodities Derivatives Risk Management ModelsOne stochastic variable or more than one stochasticvariable Geometric Brownian motion: dFt = Ft (r − δ)dt + σdWtF Heston Model, stochastic return & stochastic volatility: dFt = Vt Ft dWtF dVt = av (bv − Vt )dt + cv Vt dWtV (W F , W V )t = ρFV t Modified Heston Model, stochastic return & stochastic inventory: dFt = It Ft dWtF dIt = ai (bi − It )dt + cI It dWtI (W F , W I )t = ρFI t Madimon Consulting Commodities - An Alternative Asset
  15. 15. What are commodities? Commodities Derivatives Risk Management ModelsComplete Markets vs Incomplete Markets Complete ⇒ can be hedged Plain Vanilla Options on Equities Futures of Soybeanmeal ... Incomplete ⇒ can not be hedged Credit Default Swaps of sovereign debt ? Weather derivatives ... If the market is incomplete, who is hedging? If there is no way to hedge someone has to sell insurance cross-hedging Madimon Consulting Commodities - An Alternative Asset
  16. 16. What are commodities? Commodities Derivatives Risk Management ModelsModeling the Underlying or the Derivative Underlying Aritmetic Brownian motion Prices: X (t + dt) = Xt + αdt + σdWt Geometric Browniam Motion of Underlying Returns: dSt St = (r − y )dt + σdWt ... Derivative dFt Futures Return with no drift: Ft = σdWt ... Both: Underlying & Derivative Cox-Ross-Rubinstein: Binomial model Madimon Consulting Commodities - An Alternative Asset
  17. 17. What are commodities? Commodities Derivatives Risk Management ModelsDrift / No-Drift / Mean-Reversion Drift No-Drift Mean-reversion Some commodities such as crude oil seems inescapably destined to have a positive drift Other commodities such as some industrial products seems that can not increase in price, because when the marginal income is higher than the marginal cost, producers increase production and prices decline and visceversa. Some commodities such as electricity have clear seasonality (intraday) with reversion to the mean Madimon Consulting Commodities - An Alternative Asset
  18. 18. What are commodities? Commodities Derivatives Risk Management ModelsDiscrete vs Continuous Time Models Discrete time processes mostly used for risk - portfolio management: Ft1,t2 (x1, x2, . . .) ≡ P{Xt1 ≤ x1 , Xt2 ≤ x2 . . .} where P is the real probability 1 Continuous time models mostly used to price derivatives: ˜ ˜ Pt = E {Pt+τ , τ ≥ 0} where the pricing process is a martingale which uses a Q risk neutral probability 1 The Cox-Ross-Rubinstein is a complete discrete model which uses risk neutral probability Madimon Consulting Commodities - An Alternative Asset
  19. 19. What are commodities? Commodities Derivatives Risk Management ModelsSome points to think about: Choose the model based on the specific needs 1. Dont fear the risk of falling behind 2. Use real risk indicators 3. Fit models to data, not data to models 4. Listen to alternative stories 5. Conduct behavioural self-assessments Madimon Consulting Commodities - An Alternative Asset
  20. 20. What are commodities?Commodities Derivatives Risk Management Models PDF #1 Persian & Ptolemaic canal Roman & Arab canal Route in common Suez canal (1869-present) passage through Bitter Lakes Madimon Consulting Persian & Ptolemaic canal Commodities -canal Alternative Asset An Roman & Arab

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