MARKET IMPLIED GDP

HARRIS NTANTANIS & LARRY POHLMAN, PHD

SEPTEMBER 5, 2018

NORTHFIELD’S 30TH ANNUAL RESEARCH CONFERENCE

OUTLINE

Background

Research Question

Data

Research Approach

Estimation

Improving Conventional Forecasts

Results

Conclusions

BACKGROUND

• IN 2012, INVESTORS JOINED GREECE ON A SWAP AGREEMENT (PSI)

• NEW BONDS, SHORT-TERM NOTES AND A WARRANT FOR THE EXCHANGE OF THE PREVIOUS DEBT

• THE WARRANTS ARE A PUBLIC LISTED SECURITY WITH SOME SPECIAL FEATURES:

1. MULTIPLE ANNUAL EXERCISE DATES (TREAT IT LIKE A SERIES OF CAPLETS)

2. CASH-OR-NOTHING UP-AND-IN DUAL STRIKE LOOK BACK BARRIER

3. BARRIERS RESET ON A ANNUAL BASIS UNTIL 2020, STABLE THEREAFTER

4. PAYMENT IS CAPPED TO UP 1% OF THE NOTIONAL AMOUNT

5. LIFETIME: 2012-2042

BARRIERS FOR THE PAYMENT

WHEN BOTH GDP AND GDPR ARE ABOVE THE THESE THRESHOLDS A PAYMENT TAKES PLACE IN THE OF THE Q3 OF THE NEXT YEAR. GDP LEVEL AND REAL GDP GROWTH RATE ARE PUBLISHED BY EUROSTAT.

Barrier levels for warrant to be "in the money"

Reference Year

Reference Nominal GDP in

billion euros

Reference Real GDP Growth Rate

2014 210.10 2.35%2015 217.90 2.90%2016 226.35 2.85%2017 235.72 2.80%2018 245.47 2.60%2019 255.88 2.50%

2020-2041 266.47 2.00%

RESEARCH QUESTION

SINCE WARRANTS ARE LISTED, DO THEIR PRICES HAVE INFORMATION ABOUT GDP?

Two approaches:

• Regression pricing modeling

• Option Pricing

DATA• GDP NOMINAL AND REAL GDP GROWTH RATE

• WARRANT QUARTERLY AVERAGE OF DAILY PRICES

• QUARTERLY FROM 2012 TO PRESENT

• BASED ON THE BARRIERS WE ARE CALCULATING TWO MORE VARIABLES (SPREAD LEVEL AND RATE)

4.000

4.100

4.200

4.300

4.400

4.500

4.600

4.700

4.800

4.900

5.000

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

GD

PCha

inLi

nked

War

rant

Pric

e, G

DPR

ealG

row

th (‰

)

GPD

S &

GD

PSR

(%)

In sample Warrant Prices, GDP, GDPR, GDPS & GDPSR

Warrant Price GDPRealGrowth (‰) GDPSGDPSR (%) GDPChainLinked

RESEARCH APPROACH

• REGRESSION BASED

1 *t tGDP a b WP≡ +

1 *t tGDPR a b WP≡ +

OPTION PRICING MODELS

BLACK SCHOLES

BACHELIER (NEGATIVE VARIABLES)

REINER & RUBENSTEIN (BARRIER OPTIONS)

2

1ln( / ) / 2F K td

tσ

σ+

=

F Kdtσ

−=

( )rtc e KN d−=

2ln( / ) / 2F K tdtσ

σ+

=

1 2( ) ( )

( ) ( ) ( )

rtc FN d KN d e

c F K N d tn dσ

−= −

= − +

OPTION PRICING RESEARCH APPROACH• WARRANT PRICING, HAYMEN & KAT

,, , ,( , ; )i jrt l r

i j j i j i jc e K M d d ρ−=

2, , ,

,,

( ) ( ) / 2l l li j i j i j jl

i j lj i j

S X td

tσ

σ

− −=

2, , ,

,,

( ) ( ) / 2r r ri j i j i j jr

i j rj i j

S X td

tσ

σ

− −=

,

n

j i ji j

C c=

=∑

1, *l l li j i jS S σ+ =

1,i j

r r ri jS S σ

+= +

ESTIMATION

• CONVENTIONAL

(ESTIMATE)

(FORECAST)

• OPTION IMPLIED

FOR EVERY QUARTER I WE CALCULATE THE VALUES OF SL AND SR BY SOLVING SIMULTANEOUSLY FOR THE

AND THAT EQUATES THE CAP TO WARRANT PRICE. THE OPTION IMPLIED GDP (OIGDP) AND GDPR

(OIGDPR) EQUAL THE VALUES OF AND .

ljσ

rjσ jC

1,l

jS 1,r

jS

1 2* *exp( )w w wt t t tGDP a b WP b WP ε= + + +

1 2* *exp( )w w wt t tWIGDP a b WP b WP≡ + +

IMPROVING FORECASTS

• (BASIC AUTOREGRESSION EQUATION)

• (CONVENTIONAL FORECAST)

• (OPTION IMPLIED FORECAST)

1 1* ...t t tGDP a b GDP ε−= + +

1 1 2 1* *t t t tGDP a b GDP b WIGDP ε− −= + + +

1 1 2 1* *t t t tGDP a b GDP b OIGDP ε− −= + + +

RESULTS

ANOVA F Test

VariablesWarrant Implied

Option Implied

GDP1.00(0.00)

0.96(0.00)

GDPR1.00(0.00)

0.81(0.00)

GDPS1.00(0.00)

1.13(0.00)

GDPSPR1.00(0.00)

0.96(0.00)

CONCLUSIONS

Improve GDP forecasts

Both Conventional and Option Implied approaches

QUESTIONS?