What are commodities?Commodities Derivatives Risk Management

Models

Commodities - An Alternative AssetSeminar Cycle on Quantitative Finance - CRM-UAB

Madimon Consulting

Ramon Prat

20 December 2012

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

a different asset class

Stocks and Bonds can be valued on the basis of the netpresent value of expected cash flows

PV =

n∑i=1

CFi

(1 + ri )i

Commodities do not provide a claim on a ongoing stream ofrevenue and cannot be valued on the basis of PV.

Consume : ie corn as feedstock or food stockTransform : ie crude oil into diesel or gasoline

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Madimon Consulting Commodities - An Alternative Asset

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

What are commodities?Commodities Derivatives Risk Management

Models

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Commodities Risks

every commodity is traded in a spot market made oforiginators, marketers, manufacturers which face four types ofrisk:

Price : commodity, currency derivativesLogistics : freight derivativesDelivery : clearing houses

Credit : clearing houses

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

New Risks Associated with Hedging

Basis Risk: Cash prices and futures price might not beperfectly correlated

Roll Yield (Backwardation)/Cost(Contango)

Collateral Yield

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Equilibrium Relationship Between Spot Prices and ForwardPrices

F0,T = S0e(r−δt)t ; r=risk free rate; δ=convenience yield

if r > δ ⇒ contango

if r < δ ⇒ backwardation

Madimon Consulting Commodities - An Alternative Asset

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

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): treeBrownian Motion (continuous): Xt+1 = Xt + Wt+1

Black Scholes. . .

Non Markow Processes: multivariate statistics

ARMA Processes (discrete):Xt+1 = aXt + εt+1

Volatility Clustering Processes (continuous - Heston)GARCH Processes: σ2

t = σ2 + aσ2t−1 + bZ 2

t−1

. . .

Efficient Market Hipotesis implies stocks are Markowian.

But commodities usually exhibit seasonality . . .

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Neutral Probabilities versus Real Probabilities

Neutral Probabilities: Martingales

Cox-Ross-Rubinstein: Binomial model (discrete): treeBrownian 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 riskneutral !!!

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Stochastic vs Deterministic

Stochastic ⇒ Interested in the path t → TdSt

St= (r − δ)dt + σdWt

Deterministic ⇒ Interested only in the value at TdSt

St= (r − δ)dt

if the purpose of the trade is the physical delivery will not beinterested in the path . . .

if the purpose is hedging a portfolio the path is crucial . . .

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

One stochastic variable or more than one stochasticvariable

Geometric Brownian motion: dFt = Ft(r − δ)dt + σdW Ft

Heston Model, stochastic return & stochastic volatility:

dFt =√

VtFtdW Ft

dVt = av (bv − Vt)dt + cv√

VtdW Vt

(W F ,W V )t = ρFV t

Modified Heston Model, stochastic return & stochasticinventory:

dFt =√

ItFtdW Ft

dIt = ai (bi − It)dt + cI√

ItdW It

(W F ,W I )t = ρFI t

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

Complete Markets vs Incomplete Markets

Complete ⇒ can be hedged

Plain Vanilla Options on EquitiesFutures 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

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

Futures Return with no drift: dFt

Ft= σdWt

. . .

Both: Underlying & Derivative

Cox-Ross-Rubinstein: Binomial model

Madimon Consulting Commodities - An Alternative Asset

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 inescapablydestined to have a positive drift

Other commodities such as some industrial products seemsthat can not increase in price, because when the marginalincome is higher than the marginal cost, producers increaseproduction 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

What are commodities?Commodities Derivatives Risk Management

Models

Discrete vs Continuous Time Models

Discrete time processes mostly used for risk - portfoliomanagement:

Ft1,t2(x1, x2, . . .) ≡ P{Xt1 ≤ x1,Xt2 ≤ x2 . . .}where P is the real probability 1

Continuous time models mostly used to price derivatives:

P̃t = E{P̃t+τ , τ ≥ 0} where the pricing processis a martingale which uses a Q risk neutralprobability

1The Cox-Ross-Rubinstein is a complete discrete model which uses riskneutral probability

Madimon Consulting Commodities - An Alternative Asset

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 behind2. Use real risk indicators3. Fit models to data, not data to models4. Listen to alternative stories5. Conduct behavioural self-assessments

Madimon Consulting Commodities - An Alternative Asset

What are commodities?Commodities Derivatives Risk Management

Models

March/April 2012 33

PDF #1

Persian & Ptolemaic canalRoman & Arab canalRoute in commonSuez canal (1869-present)passage through Bitter Lakes

Persian & Ptolemaic canalRoman & Arab canalRoute in commonSuez canal (1869-present)passage through Bitter Lakes

Madimon Consulting Commodities - An Alternative Asset