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. What are commodities?
Commodities Derivatives Risk Management
Models
a 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. What are commodities?
Commodities Derivatives Risk Management
Models
Madimon Consulting Commodities - An Alternative Asset

4. What are commodities?
Commodities Derivatives Risk Management
Models
Exposure 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. What are commodities?
Commodities Derivatives Risk Management
Models
Madimon Consulting Commodities - An Alternative Asset

6. What are commodities?
Commodities Derivatives Risk Management
Models
Commodities 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. What are commodities?
Commodities Derivatives Risk Management
Models
Madimon Consulting Commodities - An Alternative Asset

8. What are commodities?
Commodities Derivatives Risk Management
Models
New 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. What are commodities?
Commodities Derivatives Risk Management
Models
Equilibrium Relationship Between Spot Prices and Forward
Prices
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. What are commodities?
Commodities Derivatives Risk Management
Models
Main 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. What are commodities?
Commodities Derivatives Risk Management
Models
Markow 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. What are commodities?
Commodities Derivatives Risk Management
Models
Neutral 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. What are commodities?
Commodities Derivatives Risk Management
Models
Stochastic 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. What are commodities?
Commodities Derivatives Risk Management
Models
One stochastic variable or more than one stochastic
variable
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. What are commodities?
Commodities Derivatives Risk Management
Models
Complete 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. What are commodities?
Commodities Derivatives Risk Management
Models
Modeling 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. What are commodities?
Commodities Derivatives Risk Management
Models
Drift / 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. What are commodities?
Commodities Derivatives Risk Management
Models
Discrete 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. What are commodities?
Commodities Derivatives Risk Management
Models
Some 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. 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