Cruz, Lia Vaz

Duarte Silva, A. P.

English

Repositório Institucional da Universidade Católica Portuguesa

timematuritiesyields Completely Affine ResultsC A L I B R A T I N G    A N D    E S T I M A T I N GE X P O N E N T I A L – A F F I N E    M O D E L S    I NPedro Duarte Silva, Faculdade de Economia e Gestão, UCP – Porto Lia Vaz Cruz, IGFCSSpsilva@porto.ucp.pt lia.v.cruz@seg-social.ptHighly Flexible Models Modelling Term Structure of Interest Rates+ Main Applications Modelling Term Structure of Defaultable ClaimsReasonable Tractability Asset Pricing of DerivativesPopular Class of Continuous-Time Dynamic Models used in Financial ApplicationsFits model parameters to a panel of market prices over a period:Assumes model remains valid for the whole estimation periodStatistically based   +   Use of a larger set of information ↔↔Fits model parameters to a cross section of market prices Continuous update with evolving market conditions possibleNot statistically based  +  Limited amount of market information Hard Problem:  High Dimensionality + Identification Issues + Likelihoods (usually) of unknown formRequires Integration of Different Mathematical Tools: Optimization routines + ODE solvers + Linear algebra systemsComputationally Very Intensive    &     Rapidly Evolving LiteratureEstimation ProblemsProgram a “reasonable“ procedure in a formal (ex: C, Fortran) or high-level (ex: MathLab) language and “hope for the best”Current PracticeSeveral choices incorporating recent advances in literatureBuild an integrated set of  R functions and utilities for Exp-Affine Models: Calibration + Estimation + Analysis OUR PROPOSALCurrently includes Multi-Factor Models for Term Structure of Interest Rates with the possibility to choose:•Different Market Price of Risk Assumptions•Non or cross correlated errors•Estimation Method (quasi) maximum likelihood considering- All Yields measured with errors (Kalman Filter)- N Yields measured without errors- First N Principal Components measured without errorsPlanned Asset Pricing models including: Jumps  &  Stochastic VolatilityEstimate a 3-Factor Completely Affine Gaussian Model from a panel of German Yields (RtT):Open in R EstimTermSInt.R Estimated Parameters  +  Value Log-(quasi)Likelihood  +  State Variables(X)   + other possibilitiesDAI, Q. and SINGLETON, K. (2000), Specification Analysis of Affine Term Structure Models. Journal of Finance, 55, p. 1943-1978.DUFFIE, D. PAN, J. and SINGLETON, K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions, Econometrica, 68 (6), p. 1343-1376.R DEVELOPMENT CORE TEAM (2008). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing , Vienna, Austria. ISBN 3-900051- 07-0, URL http://www.R-project.orgE X P O N E N T I A L   – A F F I N E    M O D E L SC A L I B R A T I O N     & E  S T I M A T I O NE X A M P L ER e f e r e n c e sRun the EstIntRMod function with chosen Model and Inputs (initial parameters necessary):ResA03 <- EstIntRMod ( m = 0,  N = 3,  ntrials = 10,freepar = c(freeLDKappaDDg,delta0g,deltayg,lambda1g, sqrSigeg), freeparsd = c(freeLDKappaDDsd,delta0sd,deltaysd,lambda1sd,sqrSigesd),Yielddata = RtT,   tau = c(0.25,0.5,1,2,5,10),   h = 1/52, estmethod = ”fxyld”, fyi = c(1,4,6), MktPRpar = ”Completely” )Code Available - please contact -psilva@porto.ucp.ptESTIMATE OTHER SPECIFICATIONS AND COMPARE !!

Calibrating and estimating exponential-affine models in R

https://repositorio.ucp.pt/bitstream/10400.14/3763/1/Calibrating%20and%20Estimating%20Exponential%20Affine%20Models%20in%20R%20-%20Poster%20%28COMPSTAT%202008%29.pdf

Calibrating and estimating exponential-affine models in R

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Repositório Institucional da Universidade Católica Portuguesa