R Options – Real Estate -June, 2014 1 June, 2014 Real Options ADM 2834 ADM 2834 Author: Marcelo Zeuli Pontifícia Universidade Católica (PUC) Rio de Janeiro Brasil The Recent Brazilian Real Estate Market : in search of stylized facts. 1) Real Options with Priced Regime- Switching Risk
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R Options – Real Estate -June, 2014 1 June, 2014 Real Options ADM 2834 Author: Marcelo Zeuli Pontifícia Universidade Católica (PUC) Rio de Janeiro Brasil.
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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.
R Options – Real Estate -June, 2014 33
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
R Options – Real Estate -June, 2014 44
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
Strike Price versus GDP projection (Rio de Janeiro and São Paulo)
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Put Price: 27.3% under 10% threshold (RJ and SP)
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Put Price: 27.3% under 10% threshold (RJ and SP)
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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.
R Options – Real Estate -June, 2014 1818
AnnexAnnex
ANNEX
R Options – Real Estate -June, 2014 1919
“Crude” Monte Carlo Simulation
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FormulasFormulas
R Options – Real Estate -June, 2014 2020
'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
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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