r options – real estate -june, 2014 1 june, 2014 real options adm 2834 author: marcelo zeuli...

R Options – Real Estate -June, 2014 11June, 2014June, 2014

Real OptionsReal Options

ADM 2834ADM 2834

Author: Marcelo Zeuli Pontifícia Universidade Católica (PUC)

Rio de JaneiroBrasil

The Recent Brazilian Real Estate Market :

in search of stylized facts.

1) Real Options with Priced Regime-Switching Risk

R Options – Real Estate -June, 2014 22

MOTIVATION – US BUBBLES

Stumpner, S (2013). Trade and the Geographic Spread of The Great Recession. Job Market Paper UC Berkeley. Jan.


RO section: Real Options with Priced Regime-Switching Risk

•Develops regime-switching risk premia model as well as regime dependent

factor risk premia to price real options. •Incorporates the observation that the underlying risky income streams of real

options are subject to discrete shifts over time as well as random changes. •Discrete shifts: systematic and unsystematic risk associated with changes in

business cycles or in economic policy regimes or events such as takeovers,

major changes in business plans. •Markov switching risk results in a delay in the expected timing of the

investment while the regime-specific factor risk premia make the possibility of a

regime shift more pronounced.

JOHN DRIFFILL, TURALAY KENC, and MARTIN SOLA, Int. J. Theor. Appl. Finan. 16, 1350028 (2013) [30 pages] DOI: 10.1142/S0219024913500283 JOHN DRIFFILL: School of Economics, Mathematics and Statistics, Birkbeck College, Malet Street, London WC1E 7HX, UKTURALAY KENC: Central Bank of Turkey, Istiklal Caddesi 10, Ulus. 06100 Ankara, TurkeyMARTIN SOLA: Universidad Torcuato Di Tella and Birkbeck College, School of Economics, Mathematics and Statistics, Birkbeck College, Malet Street, London WC1E 7HX, UK


John Driffill

John Driffill is a professor of economics at Birkbeck, University of London, specialising in international macroeconomics and labour economics.[1] He is the creator of the Calmfors-Driffill hypothesis.Driffill received his MA from Cambridge University and his PhD from Princeton University. From 1976 to 1989 he lectured at Southampton University. Appointed professor at Queen Mary and Westfield College in 1990, he returnedto Southampton University as Professor in 1992, and became Professor at Birkbeck in 1999.[2]

He is ranked top 5% author on the website IDEAS on several definitions of citations, and the Wu index.[3]

Works• Costs of inflation, 1988• The term structure of interest rates : structural stability and macroeconomic policy changes in the UK, 1990• Real interest rates, nominal shocks, and real shocks, 1997• No credit for transition : the Maastricht treaty and German unemployment, 1998• Product market integration and wages : evidence from a cross-section of manufacturing establishments in theUnited Kingdom, 1998• Delegation of monetary policy : more than a relocation of the time-inconsistency problem, 2003• Monetary policy and lexicographic preference ordering, 2004

References[1] http:/ / www. ems. bbk. ac. uk/ faculty/ driffill/[2] http:/ / www. ems. bbk. ac. uk/ faculty/ driffill/ cv/[3] http:/ / ideas. repec. org/ e/ pdr24. html

.


Similarities with VaR Approach

TheorySeries: GARCH, TS, ...Tail measures: Levy, ...

Fit: MLE, ...

Operational:Optimal Capital

VaR , CVar, AVaR,Real Options

• Best fit optimizes Capital allocation

• Risk Models: VaR Approach (Volatility Based Models)


Cookbook

OPERATION ALGORITHM Source

Unconditional Volatility ICSS Inclán and Tiao (1994)

ARCH/GARCH effects GARCH Haas (2004) modified.

ARCH/GARCH+ Volatility Level Change

SWGARCH Haas (2004) modified.

Real OptionsGARCH/SWGARCH+ At Risk/Binomial

Drifill (2013)


• Hamilton (1990) utilizes the EM algorithm to obtain the maximum likelihood

estimation (MLE) of the procedures parameters subject to discrete changes in their

self-regression parameters. • Many of the movements in the assets prices appear from specific identifiable events:

level, variance regression or the proper dynamics of a self-regression - being subject

to occasional and discrete changes. • The probability law that governs such changes is openly declared and it is supposed

that these changes exhibit a proper dynamic conduct. • Cai (1994) recommends SWGARCH models in place of SWARCH models:

SWGARCH models combine GARCH with regime changes: models offer a direct

estimate of the maximum likelihood, are analytically treatable and allow a

procedural breakdown of the conditional variance. • Gray: High price levels generate high volatility levels. GRAY, S. F. Modeling the

Conditional Distribution of Interest Rates as a Regime-Switching Process. Journal

of Financial Economics, 42, 1996, p. 27- 62.

Regime Switching (1990´s)


Firm Values ponderated with inflation and monthly GDP


Fipe Zap Series (Monthly Data)


Fipe Zap Returns


Fipe Zap Volatility


Fipe Zap: Rats algorithm for the daily returns volatility (SPD1)

ICSS Algorithm ----73 obs. from 2 to 74 -------------

Number of Change Points found:

NT hat = 1 from obs. (date) to obs. (date)

KAPPA(i) st.dev.

2( 2 ) 15 ( 15 ) 0.00856

16( 16 ) 74 ( 74 ) 0.00389

param Max sec third fourth

ct 0,6847 0,7701 0,8956 0,8424ar 0,5546 0,9411 0,4825 0,4970ma 0,0060 0,1315 0,4427 0,7624ct1 0,0001 0,0001 0,0001 0,0000ct2 0,0002 0,0001 0,0002 0,0001a1 0,1465 0,9937 0,7538 0,9144a2 0,0745 0,3410 0,1319 0,1627g1 0,4607 0,8996 0,3559 0,4281g2 0,3704 0,2375 0,3959 0,0419MLE 897,3030 829,4422 828,9193 809,3047

SWGARCH (PP=50%):


Put Price: 49.8% under 25% threshold (SPD1)


Strike Price versus GDP projection (Rio de Janeiro and São Paulo)


Put Price: 27.3% under 10% threshold (RJ and SP)


Preliminary Results/ Possible Conclusions

•Warning: 90% bulish market, accordin to FIPE Zap.

•FIPE Zap: few “open” data x “high frequency” internal data

•Stylized Fact: Markov switching risk results in a delay in the expected timing

of the investment while the regime-specific factor risk premia make the

possibility of a regime shift more pronounced.

•Strike Price versus GDP projection: bubbles or opportunity?

•Real Options with Markov – Markov approach is not new: a slow knowledge

diffusion issue.

•FIPE Zap index: good news, but time=0 is recent. •Remember: Rozenbaum, S., Brandão, E.T., Rebello, A., Fortunato, G. (2008). Lançamentos Imobiliários

Residenciais: Determinação do Valor da Opção de Abandono Prevista no Código do Consumidor.


AnnexAnnex

ANNEX


“Crude” Monte Carlo Simulation

~.)(.)).(2

1( 2

.tTtTr

tT eSS

}0,.max{.1 ~.)(.)).(

2

1(

1

).(2

KeSN

eCtTtTr

t

N

n

tTrt

FormulasFormulas


'generate sample paths initialPaths = GRWPaths(initPrice, r, sigma, T, numSteps, numPaths) 'Transpose results of GRWPaths (matrix is the other way around) For iStep = 1 To numSteps For iPath = 1 To numPaths paths(iPath, iStep) = initialPaths(iStep + 1, iPath) Next Next

Volatility (Fabozzi SW)

Function GRWPaths(initPrice As Double, _ r As Double, sigma As Double, T As Double, numSteps As Variant, numPaths As Variant) Randomize Dim iPath, iStep As Integer Dim paths() As Variant ReDim paths(1 To numSteps + 1, 1 To numPaths) For iPath = 1 To numPaths paths(1, iPath) = initPrice For iStep = 2 To numSteps + 1 paths(iStep, iPath) = paths(iStep - 1, iPath) * _

Exp((r - 0.5 * sigma ^ 2) * (T / numSteps) + _

sigma * (T / numSteps) ^ (1 / 2) * (Application.NormSInv(Rnd))) Next Next GRWPaths = pathsEnd Function


load('c:\atese\brandao\simulacao\zap.mat');y = input ('Serie :');it = input('Numero de iteracoes: ');% ***** it ideal de 10; ***** initseed=rng;rng(initseed);tempo_init=datestr(now);resp=zeros(2,18);k=2;v=1;cont=0;pp= zeros(1,13);% iniciais?? ct= 0.0006641;ar = 0.72791; ma = 0.7533;ct=0.00023423;ar=0.640700984;ma=-0.667862747;%mle=0;for i=1:itpp(1:13)=rand(1,13); i cont=2; [ans1,est2,P]=arma_swg_norm(pp,y,k,v); % [ans2,est1,P]=arma_swg_stbl(pp,y,k,v); [ans3,est3,P]=arma_swg_cts(pp,y,k,v); % [ans4,est4,P]=arma_garch_stbl(pp,y,k,v); [ans5,est5,P]=arma_garch_cts(pp,y,k,v); %resp(cont,1:13)=pp; resp(cont,1:9)=pp(1:9); resp(cont,10)=P(1,1);resp(cont,11)=P(2,1);resp(cont,12)=P(1,2);resp(cont,13)=P(2,2); % resp(cont,15)=ans2;% resp(cont,16)=ans3; resp(cont,17)=ans4; resp(cont,18)=ans5; resp(cont,14)=ans1;if ans1 > mle save c:\atese\brandao\simulacao\resp_d10_6_14.txt resp -ascii ; end if ans1 > mle mle=ans1; endendtempo_fim=datestr(now);save c:\atese\brandao\simulacao\resp_10_6_14.txt resp -ascii

SWGARCH


Unconditional Volatility, Currency Swaps (1999-2003)


Loss Functions Example for SWGARCH (EM, Hamilton)


Unconditional Volatility Examples. Comparing Brasil x USA (interest rates)

r options – real estate -june, 2014 1 june, 2014 real options adm 2834 author: marcelo zeuli...

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