Derivatives in Supply Chain

Dailun Shi & William GreyIBM T. J. Watson Research Center

Richard DanielsUniversity of Georgia

Agenda

Background and Motivation Research Content Results Future Research Directions

Risk Management in The financial Services Industry

Portfolio management CAPM VAR for market and credit risk Credit rating/scoring methodologies Options pricing models Derivative products

Futures, swaps, options, floors, caps, etc.

Operational risk management techniques Risk-adjusted capital allocation

Supply Chain Risk Management Research at IBM T. J. Watson Center

Supply chain risk profiling Quantifying financial impacts of risks Risk assessment Risk management strategy - design and

implementationOperational managementFinancial management Insurance products OptionsOptions, Futures, Swaps

Derivatives in Supply Chain

Is there a need for options to manage supply chain risk?

Implications of introducing options into SCM: Behavioral Financial Information sharing Risk sharing

Problem Setting and Parameters

A single period two-party supply chain:

Highly perishable, short-life-cycle product Two replenishment modes: firm orders &

options Parameters:

D: stochastic demand with pdf f(D) and cdf F(D) W: wholesale price = unit cost of firm order C: unit cost of option, X: option exercise price R: product retail price, M: unit manufacturing cost P: penalty for defaulting on options

expediting cost vs. cash penalty

Supplier Retailer End Customers

The Newsvendor Problem

Overage risks of salvaging inventory at loss Price markdowns Inventory holding costs

Underage risks of unmet demand Lost profit Cost of expediting Customer ill will

Implications for the retailer Order less than in ISC Bear all overage risks Has some underage risks

Implications for the supplier Build to order No overage risks Substantial underage risks

Feasibility Conditions

Following conditions hold among parameters

M < W < C+X < R P M X > S

Those conditions ensure well-behaved profit functions, thus lead to unique optimal solutions

Sequence of Events

Background: procurement decisions is made before selling season, with no opportunity to replenish inventory once the season starts

Transaction terms (W, C, X, P) are determined At t=0

The retailer places orders Q and qThe supplier decides production quantity YThe supplier delivers Q units, holds (Y-Q) inventory

During the season t1The retailer exercises options ( q)The supplier delivers additional units to the

retailer

The Retailer’s Decisions

The retailer has two decision variables: number of firm orders Q and number of options q.

Total order quantity T = Q+q The retailer’s expected profit function:

The retailer’s optimal order quantities:

T

Q

QdDDFXRdDDFSRTCXRQWCXTQE )()()()()()(),(

0

XR

CXRTDTF

*)Pr(*)(

SX

WCXQDQF

*)Pr(*)(

The Supplier’s Decisions

Decision variable for the supplier: Y = the number of products to produce, and its range is Q*Y T*

The supplier’s expected profit function:

The unique maximum point of the expected profit function:

The supplier’s optimal production quantity Y*:

*

*)()()()(

)(*)(*)()(T

Y

Y

QdDDFPXdDDFSX

YMPqPCXQPWYE

SP

MPYDYF

*)*Pr(*)*(

****,

*****,*

****,

*

YTifT

TYQifY

QYifQ

Y

Results

Supply Chain Coordination Risk Sharing Information Sharing Supply Chain Contract Negotiation

Supply Chain Coordination

Double Marginality ProblemSeparate ownership of two supply chain

partiesNeither has control of the entire supply chainConflicting objectives Asymmetric information about demandsTotal supply chain profit is (R-M)Q, if Q is

producedWithout options, total product quantity:Integrated supply chain produces: Since M < W,

)(* 1

SR

WRFQ

)(1*

SR

MRFQI

** IQQ

Supply Chain Coordination (cont..)

Options introduce three more degrees of freedom (X, C and P), in addition to W

Conditions for the retailer to coordinate:

Conditions for the supplier to coordinate:

**** IQqQTSR

MR

XR

CXR

** TYXR

CXR

SP

MP

Risk Sharing

Options provide a tool for the retailer to manage demand uncertainty

Firm orders for demand relatively sure to sellOptions for products less likely to be neededHedge against both overage and underage risksPay a premium to purchase options

Options also benefit the supplierInducing the retailer to purchase more productsMust hold inventories for options

Bottom-line: both parties are better off

Risk Sharing (cont.)

Profits Improvement from Options

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

0 400 800 1200 1600 2000demand stdv

Pro

fit In

cre

ase

manufacturer (mean = 3000)

retailer (mean = 3000)

Chain (mean =300)

manufacturer (mean = 4000)

retailer (mean = 4000)

Chain (mean =4000)

Risk Sharing (cont.)

Two fundamental issues in supply chan optimization with options:

Set transaction parameters to maximize total profitsAllocate total profit equitably between the two parties

Observations:Coordination conditions ensure profits of ISCCoordination conditions provide no insight into total profit

allocationWholesale price W is not in the coordination conditionsW doesn’t effect T* and Y*Varying W is effective for total profit allocation

Two potential ways for the profit allocation:Set X, C, P, and W to ensure both parties better offDistribute profit based on “risk-adjusted profit”

Information Sharing

Fix contract terms (R, W, X, C, P and M), RHS of equations for T*, Q*, Y** are constant, denoting them CT*, CQ*, CY**

Assume normal demand with mean µ and stdv σ, we have: for Z = T*, Q*, and Y**

The implied θ in Y* = Q* + θq* is constant w.r.t to µ and σ

The above results are also true for non-normal demand Information implications of the 3rd result:

The retailer’s (Q*, q*) reveal demand information (µ,σ) completelyThe supplier always produces fixed percentage for options

)(1ZCZ

)(/

)()(

*

*

*1

*1

*1

T

QT

C

CC

T

q

Supply Chain Contract Negotiation

Contract terms and conditions are usually determined by:

Relative market powerIncentive considerationsPromotions

Understanding the impacts of contract parameters (R, X, C, W, P) on both parties’ profits is important

We have analytic results on related questionsThe following slides show graphic presentations

Impact of Option Cost C on Profits

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

10 12 14 16 18 20 22 24 26 28

Option Cost C

pro

fit In

cre

ase

manufacturer's gain

retailer's gain

supply chain gain

Impact of Exercise Price X on Profits

-4.0%

0.0%

4.0%

8.0%

12.0%

16.0%

20.0%

24.0%

28.0%

55 60 65 70 75 80

option exercise price X

Pro

fit Incr

ease

manufacturer's gain

retailer's gain

supply chain gain

Impact of Wholesale Price W on Profits

3000

18000

33000

48000

63000

78000

93000

108000

123000

138000

40 45 50 55 60 65Wholesale Price W

Pro

fits Manufacturer

Retailer

Total

Impact of Penalty Cost P on Profits

3.0%

6.0%

9.0%

12.0%

15.0%

18.0%

21.0%

24.0%

27.0%

40 45 50 55 60 65 70 75 80 85 90 95 100penalty cost P

% g

ain

of P

rofit

s

manufacturer's gain

retailer's gain

supply chain gain

P r o d u c t A v a i l a b i l i t y I n s u r a n c e

C o s t C a n d I n s u r a n c e I n c o m e

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

0 5 1 0 1 5 2 0

I n s u r a n c e C o s t C

Insura

nce I

ncom

e

I n s u r a n c e I n c o m e

I m p a c t o f C o s t s C o n P r o f i t s

- 1 8 . 0 %

- 9 . 0 %

0 . 0 %

9 . 0 %

1 8 . 0 %

2 7 . 0 %

3 6 . 0 %

4 5 . 0 %

5 4 . 0 %

0 5 1 0 1 5 2 0i n s u r a n c e c o s t c

% ga

in of

profit m a n u f a c t u r e r ' s g a i n

r e t a i l e r ' s g a i n

s u p p l y c h a i n g a i n

Future Research Directions

Supply chain option pricing Expand the framework to consider:

Multiple periodsMultiple suppliersMultiple buyers

Issues associated with creating markets to trade supply chain options