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June, 2014

Real Options. The Recent Brazilian Real Estate Market : in search of stylized facts. 1) Real Options with Priced Regime-Switching Risk. Author: Marcelo Zeuli Pontifícia Universidade Católica (PUC) Rio de Janeiro Brasil. ADM 2834. June, 2014. MOTIVATION – US BUBBLES.

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June, 2014

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  1. Real Options The Recent Brazilian Real Estate Market : in search of stylized facts. 1) Real Options with Priced Regime-Switching Risk Author: Marcelo Zeuli Pontifícia Universidade Católica (PUC) Rio de Janeiro Brasil ADM 2834 June, 2014

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

  3. 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, UK TURALAY KENC: Central Bank of Turkey, Istiklal Caddesi 10, Ulus. 06100 Ankara, Turkey MARTIN SOLA: Universidad Torcuato Di Tella and Birkbeck College, School of Economics, Mathematics and Statistics, Birkbeck College, Malet Street, London WC1E 7HX, UK

  4. 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 returned to 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 the United 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 .

  5. Similarities with VaR Approach Operational: Optimal Capital VaR , CVar, AVaR, Real Options Theory Series: GARCH, TS, ... Tail measures: Levy, ... Fit: MLE, ... • Best fit optimizes Capital allocation • Risk Models: VaR Approach (Volatility Based Models)

  6. Cookbook

  7. Regime Switching (1990´s) • 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.

  8. Firm Values ponderated with inflation and monthly GDP

  9. Fipe Zap Series (Monthly Data)

  10. Fipe Zap Returns

  11. Fipe Zap Volatility

  12. Fipe Zap: Rats algorithm for the daily returns volatility (SPD1) SWGARCH (PP=50%):

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

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

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

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

  17. 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.

  18. Annex ANNEX

  19. “Crude” Monte Carlo Simulation

  20. Volatility (Fabozzi SW) '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 FunctionGRWPaths(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 = paths End Function

  21. SWGARCH 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:it pp(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; end end tempo_fim=datestr(now); save c:\atese\brandao\simulacao\resp_10_6_14.txt resp -ascii

  22. Unconditional Volatility, Currency Swaps (1999-2003) PTAX

  23. Loss Functions Example for SWGARCH (EM, Hamilton)

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

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