Abstract
In this paper, we partially review probabilistic and time series models in finance. Both discrete and continuous-time models are described. The characterization of the No-Arbitrage paradigm is extensively studied in several financial market contexts. As the probabilistic models become more and more complex to be realistic, the Econometrics needed to estimate them are more difficult. Consequently, there is still much research to be done on the link between probabilistic and time series models.
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References
Aguilar, O. and M. West (2000), Bayesian dynamic factor models and variance matrix discounting for portfolio allocation, Journal of Business and Economic Statistics, 18, 338–357.
Ahn, D.-H., R.F. Dittmar and A.R. Gallant (2002), Quadratic term structure models: theory and evidence, The Review of Financial Studies, 15, 243–288.
Ahn, D.-A., R.F. Dittmar, A.R. Gallant and B. Gao (2003), Purebred of hybrid?: Reproducing the volatility in term structure dynamics, Journal of Econometrics, forthcoming.
Aït-Sahalia, Y. (1996a), Nonparametric Pricing of Interest Rate Derivative Securities, Econometrica, 64, 527–560.
Aït-Sahalia, Y. (1996b), Testing Continuous-Time Models of the Spot Interest Rate, Review of Financial Studies, 9, 385–426.
Aït-Sahalia, Y. (2002), Maximum likelihood estimation of discretely sample diffusions: a closed form approach, Econometrica, 70, 223–262.
Aït-Sahalia, Y. and P.A. Mykland (2003), The effect of random and discrete sampling when estimating continuous-time diffusions, Econometrica, 71, 483–549.
Aït-Sahaila, Y. and A.W. Lo (2000), Nonparametric risk management and implied risk aversion, Journal of Econometrics, 94, 9–51.
Andersen, T.G. (1996), Return volatility and trading volume: an information flow interpretation of stochastic volatility, Journal of Finance, 51, 169–204.
Andersen, T.G. and T. Bollerslev (1997a), Intraday periodicity and volatility persistence in financial markets, Journal of Empirical Finance, 4, 115–158.
Andersen, T.G. and T. Bollerslev (1997b), Heterogenous information arrivals and return volatility dynamics: uncovering the long-run in high frequency returns, Journal of Finance, 52, 975–1005.
Andersen, T.G. and T. Bollerslev (1998), Deutsche mark-dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer-run dependencies, Journal of Finance, 53, 219–265.
Andersen, T.G. and J. Lund (1997), Estimating continuous-time stochastic volatility models of the short-term interest rate, Journal of Econometrics, 77, 343–377.
Andersen, T.G., L. Benzoni and J. Lund (2002), An empirical investigation of continuous-time equity return models, Journal of Finance, 57, 1239–1284.
Andersen, T.G., T. Bollerslev and A. Das (2001), Variance-ratio statistics and high-frequency data: testing for changes in intraday volatility patterns, Journal of Finance, 56, 305–327.
Back, K. and S.R. Pliska (1991), On the fundamental theorem of asset pricing with infinite state space, Journal of Mathematical Economics, 20, 1–18.
Baillie, R.T., T. Bollerslev and H.O. Mikkelsen (1996), Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 3–30.
Balbás. A., M.A. Mirás and M.J. Muñoz-Bouzo (2002), Projective system approach to the martingale characterization of the absence of arbitrage, Journal of Mathematical Economics, 37, 311–323.
Ball, C. and W. Torous (1985), On jumps in common stock prices and their impact on call option pricing, Journal of Finance, 40, 155–173.
Barberis, N., M. Huang and T. Santos (2001), Prospect theory and asset prices, The Quarterly Journal of Economics, 116, 1–53.
Barndorff-Nielsen, O.E. and N.G. Shephard (2001), Non-Gaussian OU processes and some of their uses in financial economics (with discussion), Journal of the Royal Statistical Society, series B, 63,167–241.
Barndorff-Nielsen, O.E. and N.G. Shephard (2002a), Econometric analysis of realized volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society, series B, 64, 253–280.
Barndorff-Nielsen, O.E. and N.G. Shephard (2002b), Lèvy based dynamic models for financial economics, Unpublished book manuscript.
Barone-Adessi, G., K. Giannopoulos and L. Vosper (1999), VaR without correlations for nonlinear portfolios, Journal of Future Markets, 19, 583–602.
Barone-Adessi, G. and K. Giannopoulos (2001), Non-parametric VaR techniques. Myths and realities. Economic Notes, 30, 167–181.
Bates, D.S. (1996), Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options, The Review of Financial Studies, 9, 69–107.
Bekaert, G., R. Hodrick and D. Marshall (2001), Peso Problem explanations for term structure anomalies, Journal of Monetary Economics, 48, 241–270.
Benartzi, S. and R. Thaler (1995), Myopic loss aversion and equity premium puzzle, Quarterly Journal of Economics, 110, 73–92.
Black, F. (1986), Noise, Journal of Finance, 3, 529–543.
Black, F. and M. Scholes (1973), The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637–650.
Bollerslev, T. (1986), Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307–327.
Bollerslev, T. (1990), Modelling the coherence in short-run nominal exchange rates: a Multivariate generalized ARCH approach, Review of Economics and Statistics, 72,498–505.
Bollerslev, T. (2001), Financial econometrics: Past developments and future challenges, Journal of Econometrics, 100, 41–51.
Bollerslev, T., R. F. Engle and J. Wooldridge (1988), A capital asset pricing model with time varying covariances, Journal of Political Economy, 96,116–131.
Bollerslev, T., R.F. Engle and D.B. Nelson (1995), ARCH models, in R.F. Engle and D. McFadden (eds.), The Handbook of Econometrics, vol. 4, North-Holland, Amsterdam.
Brannath, W. (1997), No arbitrage and martingale measures in option pricing, Dissertation zur Erlangung des akademischen Grades. Univertsität Wien.
Breidt, F.J., N. Crato and P.J.F. de Lima (1998), The detection and estimation of long memory in stochastic volatility, Journal of Econometrics, 83, 325–348.
Broto, C. and E. Ruiz (2002), Estimation methods for stochastic volatility: A survey, Working Paper.
Butsic, R.P. (1999), Capital allocation for property-liability insures: a catastrophe reinsurance application, Casualty Actuarial Society Forum, Spring 1999.
Campbell, J.Y., A.W. Lo and A.C. MacKinlay (1997), The Econometrics of Financial Markets, Princeton University Press, Princeton, New Jersey.
Carnero, M.A., D. Peña and E. Ruiz (2001a), Outliers and conditional autoregressive heteroscedasticity in time series, Estadística, 53, 143–213.
Carnero, M.A., D. Peña and E. Ruiz (2001b), Is stochastic volatility more flexible than GARCH?, Working Paper 01-08(05), Serie Estadística y Econometría, Universidad Carlos III de Madrid.
Cvitanic, J. and I. Karatzas (1996), Hedging and portfolio optimization under transaction costs: a martingale approach, Math. Fin. 6, 133–166.
Chateaunef, A., R. Kast and A. Lapied (1994), Market preferences revealed by prices: non-linear pricing in slack markets, in Machina, M. and B. Munier (eds), Models and experiments in risk and rationality, Kluwer, Dordrecht.
Chateaunef, A., R. Kast and A. Lapied (1996), Choquet pricing for financial markets with frictions, Mathematical Finance, 6, 323–330.
Chen, R.-R. and L. Scott (2002), Multi-factor Cox-Ingersoll-Ross models of the term structure: Estimates and tests from a Kalman filter, Journal of Real State Finance and Economics, forthcoming.
Chernov, M. and E. Ghysels (2000), A study towards a unified approach to the joint estimation of objective risk neutral measures for the purpose of option valuation, Journal of Financial Economics, 57, 407–458.
Chernov, M., A.R. Gallant, E. Ghysels and G. Tauchen (2000), A new class of stochastic volatility models with jumps. Theory and estimation, Working paper, Columbia University.
Chib, S., F. Nardari and N. Shephard (2002), Markov chain Monte Carlo methods for stochastic volatility models, Journal of Econometrics, 108, 281–316.
Christoffersen, P.F. and F. Diebold (2000), How relevant is volatility forecasting for financial risk management?, Review of Economics and Statistics, 82, 12–22.
Christoffersen, P.F., J. Hahn and A. Inuoe (2001), Testing and comparing Value-at-Risk measures, Journal of Empirical Finance, 8, 325–342.
Dai, Q. and K. Singleton (2000), Specification analysis of affine term structure models, Journal of Finance, 55, 1943–1978.
Dai, Q. and K. Singleton (2003), Term structure dynamics in theory and reality, Review of Financial Studies, forthcoming.
Dalang, R.C., A. Morton, W. Willinger (1989), Equivalent martingale measure and no arbitrage in stochastic securities market model, Stochastics and Stochastic Rep. 29, 185–202.
Danielsson, J. and G. de Vries (1998), Beyond the sample: Extreme quantile and probability estimations, Discussion paper 298, London School of Economics, London.
Davis, M.H.A. and A. Norman (1990), Portfolio selection with transaction costs, Math. Operation Research, 15, 676–713.
De Waegenaere A.M.B., R. Kast and A. Lapied (1996), Non-linear Asset Valuation on Markets with Frictions, CentER Discussion Paper 96112.
Delbaen, F. (1992), Representing martingale measures when asset prices are continuous and bounded, Math. Fin. 2, 107–130.
Delbaen, F. and W. Schachermayer (1994), A general version of the Fundamental Theorem of Asset Pricing, Math. Annalen 300, 463–520.
Delbaen, F. and W. Schachermayer (1998), The fundamental theorem of asset pricing for unbounded stochastic process, Mathematische Annalen, 312, 215–250.
Delbaen, F., Y. Kabanov and E. Valkeila (1998), Hedging under transaction costs in currency markets: a discrete-time model. Preprint.
Diebold, F.X. and M. Nerlove (1989), The dynamics of exchange rate volatility: a multivariate latent factor ARCH models, Journal of Applied Econometrics, 4, 1–21.
Dixit, A. (1993), The Art of Smooth Pasting, Harwood, Switzerland.
Duan, J.C. (1997), Augmented GARCH(p.q) process and its diffusion limit, Journal of Econometrics, 79, 97–127.
Duan, J.-C. and J.-G. Simonato (1999), Estimating and testing exponential-affine term structure models by Kalman filter, Review of Quantitative Finance and Accounting, 13, 111–135.
Duffee, G.R. and R.H. Stanton (2003), Estimation of dynamic term structure models, mimeo, U.C. Berkeley.
Duffie, D. and C.F. Huang (1986), Multiperiod security markets with differential information; martingales and resolution times, J. Math. Econom., 15, 283–303.
Duffie, D. and R. Kan (1996), A yield-factor model of interest rates, Mathematical Finance, 6, 379–406.
Duffie, D., J. Pan and K.J. Singleton (2000), Transform analysis and asset pricing for affine jump-diffusions, Econometrica, 68, 1343–1376.
Dufour, A. and R. Engle (2000), Time and the price impact of a trade, Journal of Finance, 55, 2467–2498.
Durham, G.B. and A.R. Gallant (2002), Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes, Journal of Business and Economic Statistics, 20, 297–316.
Eberlein, E. (2001), Application of generalized hyperbolic Lévy motions to finance, in Barndorff-Nilesen, O.E., T. Mikosch and S. Resnick (eds.), Lévy Processes-Theory and Applications, 319–337, Birkhauser, Boston.
Eberlein, E. and K. Prause (2002), The Generalized hyperbolic model: Financial derivatives and risk measures, in Mathematical Finance-Bachelier Congress 2000, Springer Verlag, forthcoming.
Elerian, O., S. Chib and N.G. Shephard (2001), Likelihood inference for discretely observed nonlinear diffusions, Econometrica, 69, 959–993.
Embrechts, P., C. Kluppelberg and T. Mikosch (1997), Modelling Extremal Events, Springer, Berlin.
Engle, R. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987–1007.
Engle, R. (2000), The econometrics of ultra high frequency data, Econometrica, 68,1–22.
Engle, R. (2001), Financial econometrics — A new discipline with new methods, Journal of Econometrics, 100, 53–56.
Engle, R. (2002a), New frontiers for ARCH models, forthcoming in Journal of Applied Econometrics
Engle, R. (2002b), Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics, 20, 339–350.
Engle, R. and G.G.J. Lee (1999), A long run and short run component model of stock return volatility, in Engle, H. and H. White (eds), Cointegration, Causality and Forecasting, Oxford University Press, Oxford.
Engle, R. and S. Manganelli (1999), CaViar: Conditional Autoregressive Value at Risk by regression quantiles. Discussion paper, University of California, San Diego.
Engle, R.F. and J. R. Russell (1998), Autoregressive conditional duration: A new model for irregularly spaced transaction data, Econometrica, 66, 1127–1162.
Engle, R., D. Lilien and R. Robins (1987), Estimating time-varying risk premia in the term structure: the ARCH-M model, Econometrica, 55, 391–407.
Epsein, L.G. and S.E. Zin (2001), The independence axiom and asset returns, Journal of Empirical Finance, 8, 537–572.
Eraker, B. (2001), MCMC Analysis of Diffusion Models with Applications to Finance, Journal of Business and Economic Statistics, 19, 177–191.
Eraker, B., M. Johannes and N. Polson (2003), The impact of jumps in volatility and returns, Journal of Finance, forthcoming.
Gallant, A.R. and J.R. Long (1997), Estimating Stochastic Differential Equations Efficiently by Minimum Chi-Squared, Biometrika, 84, 125–141.
Gallant, A.R. and G. Tauchen (1996), Which moments to match?, Econometric Theory, 12, 657–681.
Gallant, A.R. and G. Tauchen (1998), Reprojecting partially observed systems with application to interest rate diffusion, Journal of the American Statistical Association, 93,10–24.
Ghysels, E. and S. Ng (1998), A semiparametric factor model of interest rates and tests of the affine term structure, Review of Economics and Statistics, 80, 535–548.
Ghysels, E. and G. Tauchen (2003), Frontiers of financial econometrics and financial engineering, Journal of Econometrics, forthcoming.
Ghysels, E., A.C. Harvey and E. Reanult (1996), Stochastic Volatility, in J. Knight and S. Satchell (eds.), Handbook of Statistics, 14, 119–191, North-Holland, Amsterdam.
Gibbons, M., S. Ross and J. Shanken (1989), A test of the efficiency of a given portfolio, Econometrica, 57, 1121–1152.
Gouriéroux, C.A., A. Monfort and E. Renault (1993), Indirect Inference, Journal of Applied Econometrics, 8, S85–S118.
Gourieroux, C.A. and J. Jasiak (2001), Financial Econometrics, Princeton University Press, Princeton.
Granger, C.W.J., Z. Ding and S. Spear (2000), Stylized facts on the temporal and distributional properties of absolute returns: An update, Working paper, University of California, San Diego.
Guermat, C. and R.D.F. Harris (2002), Forecasting value at risk allowing for time variation in the variance and kurtosis of portfolio returns, International Journal of Forecasting, 18, 409–419.
Hansen, L. and K. Singleton (1982), Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations models, Econometrica, 50, 1269–1288.
Hansen, L. and J. Scheikman (1995), Back to the future: Generating moment implications for continuous-time Markov processes, Econometrica, 63, 767–804.
Harrison, M. and D. Kreps (1979), Martingales and arbitrage in multiperiod security markets, Journal of Economic Theory, 20, 381–408.
Harrison, M. and S. Pliska (1981), Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes Appl., 11, 215–260.
Harvey, A.C. (1998), Long memory in stochastic volatility, in J. Knight and S. Satchell (eds.), Forecasting Volatility in Financial Markets, Butterworth-Haineman, Oxford.
Harvey, A.C. and N.G. Shephard (1996), Estimation of an asymmetric stochastic volatility model for asset returns, Journal of Business and Economic Statistics, 14, 429–434.
Harvey, A.C., E. Ruiz and N.G. Shephard (1994), Multivariate stochastic variance models, Review of Economic Studies, 247–264.
Harvey, C.R. (2001), The specification of conditional expectations, Journal of Empirical Finance, 8, 573–637.
Harvey, C.R. and G. Zhou (1990), Bayesian inference in asset pricing tests, Journal of Financial Economics, 26, 221–254.
Hausman, J., A. Lo and C. MacKinlay (1992), An ordered probit analysis of transaction stock prices, Journal of Financial Economics, 31, 319–379.
He, C. and T. Terasvirta (1999), Properties of moments of a family of GARCH processes, Journal of Econometrics, 92, 173–192.
Hentschel, L. (1995), All in the family: Nesting symmetric and asymmetric GARCH models, Journal of Financial Economics, 39, 71–104.
Heston, S. (1993), A closed-form solution for options with stochastic volatility with applications to bond currency options, Review of Financial Studies, 6, 327–343.
Hong, H. and J.C. Stein (1999), A unified theory of underreaction, momentum trading and overreaction in asset markets, Journal of Finance, 54, 2143–2184.
Hull, J. and A. White (1987), The pricing of options on assets with stochastic volatilities, Journal of Finance, 42, 281–300.
Jacquier, E., N.G. Polson and P.E. Rossi (1994), Bayesian analysis of stochastic volatility models, Journal of Business and Economic Statistics, 12, 371–417.
Jacquier, E., N.G. Polson and P.E. Rossi (1995), Models and prior distributions for multivariate stochastic volatility, Technical report, Graduate School of Business, University of Chicago.
Jouini, E. and H. Kallal (1995a), Martingales and arbitrage in securities markets with transaction costs, Journal of Economic Theory, 66, 178–197.
Jouini, E. and H. Kallal (1995b), Arbitrage in securities markets with short-sales constraints, Math Fin., 5,197–232.
Jouini, E. and H. Kallal (1999), Viability and Equilibrium in Securities Market with Frictions, Math Fin., 9, 275–292.
Jouini, E. and C. Napp (2002), Arbitrage and Investment Opportunities, to appear in Finance and Stochastics.
J.P. Morgan (1996), Risk Metrics Technical Document, 4th edition, J.P. Morgan, New York.
Kabanov, Y. (1999), Hedging and liquidation under transaction costs in currency markets, Finance and Stochastics, 3, 237–248.
Kabanov, Y. (2001), Arbitrage theory. Handbooks in Mathematical Finance, Option Pricing: Theory and Practice, 3–42.
Kabanov, Y. and D. Kramkov (1994), No arbitrage and equivalent martingale measures: An elementary proof of the Harrison-Pliska theorem, Theory Prob. Appl., 39
Kabanov, Y., M. Rasonyi and C. Striker (2001), No-arbitrage criteria for financial markets with efficient friction, Finance and Stochastics, 6, 371–382.
Kandel, S., R. McCulloch and R. Stambaugh (1995), Bayesian inference and portfolio efficiency, Review of Financial Studies, 8, 1–53.
Karatzas, I. and S.E. Shreve (1991), Brownian Motion and Stochastic Calculus, 2nd ed., Springer, New York.
Kessler, M. (2000), Estimation of an ergodic diffusion from discrete observations, Scandinavian Journal of Statistics, 24
Kessler, M. and M. Sørensen (1999), Estimating equations based on eigenfunctions for discretely observed diffusion process, Bernoulli, 5, 299–314.
Kim, S., N.G. Shephard and S. Chib (1998), Stochastic volatility: likelihood inference and comparison with ARCH models, Review of Economic Studies, 65, 361–393.
King, M., E. Sentana and S. Wadhwany (1994), Volatility and links between national stock markets, Econometrica, 62, 901–933.
Koopman, S.J. and E.H. Uspensky (2002), The stochastic volatility in mean model: Empirical evidence from international stock markets, Journal of Applied Econometrics
Kreps, D. (1981), Arbitrage and equilibrium in economies with infinitely many commodities, J. Math. Econ. 8, 15–35.
Ledoit, O., P. Santa-Clara and M. Wolf (2003a), Flexible multivariate GARCH modeling with an application to international stock markets, Review of Economics and Statistics, forthcoming.
Lintner, J. (1965), The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47, 13–37.
Lo, A. W. (1988), Maximum likelihood estimation of generalized Itô processes with discretely sampled data, Econometric Theory, 4, 231–247.
Lo, A. and A.C. MacKinlay (1990), An econometric analysis of nonsynchronous trading, Journal of Econometrics, 45, 181–212.
Lobato, I.N. and N.E. Savin (1998), Real and spurious long-memory properties of stock-market data, with discussion, Journal of Business and Economic Statistics, 16, 261–283.
Lobato, I., J.C. Nanverkis and N.E. Savin (2001), Testing for autocorrelation using a modified Box-Pierce Q test, International Economic Review, 42, 187–205.
Luenberger, D.G. (2002a), A correlation pricing formula, Journal of Economics Dynamics & Control, 26, 1113–1126.
Luenberger, D.G. (2002b), Arbitrage and universal pricing, Journal of Economics Dynamics & Control, 26, 1613–1628.
McNeil, A. and R. Frey (2000), Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach, Journal of Empirical Finance
Merton, R. C.(1990), Continuous-time Finance, Blackwell, Cambridge.
Merton, R.C. (1976), Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3, 125–144.
Merton, R.C. (1980), On estimating the expected return on the market: An exploratory investigation, Journal of Financial Economics, 8, 323–361.
Müller, U.A., M.M. Dacorogna, R.D. Davé, R.B. Olsen, O.V. Pictet and J.E. von Weizsächer (1997), Volatilities at different time resolutions-analysing the dynamics of market components, Journal of Empirical Finance, 4, 213–239.
Nelson, D.B. (1990), ARCH models as diffusion approximations, Journal of Econometrics, 45, 7–38.
Nelson, D.B. (1991), Conditional Heteroskedasticity in asset returns: A new approach, Econometrica, 59, 347–370.
Nelson, D.B. (1992), Filtering and forecasting with misspecified ARCH models I: Getting the right variance with the wrong model, Journal of Econometrics, 52, 61–90.
Nelson, D.B. (1994), Asymptotically optimal smoothing with ARCH models, Econometrica, 63
Nelson, D.B. and D.P. Foster (1994), Asymptotic filtering theory for univariate ARCH models, Econometrica, 62, 1–41.
Panjer, H.H. (editor) (1998), Financial Economics, The Actuarial Foundation, Schaumburg, IL.
Pearson, N.D. and C. Smithson (2002), VaR. The state of play, Review of Financial Economics, 11,175–189.
Pedersen, A.R., (1995), A new approach to maximum-likelihood estimation for stochastic differential equations based on discrete observations, Scandinavian Journal of Statistics, 22, 55–71.
Pham H. and N. Touzi (1999), The fundamental theorem of asset pricing with cone constraints, Journal of Mathematical Economics, 31, 265–279.
Pitt, M. and N. Shephard (1999), Time varying covariances: a factor stochastic volatility approach (with discussion), in. Bernardo, J., Berger, J.O., Dawid, A.P., Smith, A.F.M. (eds.), Bayesian Statistics, 6, 547–570, Oxford University Press, Oxford.
Ray, B.K. and R.S. Tsay (2000), Long-range dependence in daily stock volatilities, Journal of Business and Economic Statistics, 18, 254–262.
Romano, J.L. and L.A. Thombs (1996), Inference for autocorrelations under weak assumptions, Journal of American Statistical Association, 91, 590–600.
Rydberg and N.G. Shephard (2003), Dynamics of trade-by-trade price movements: decomposition and models, Journal of Financial Econometrics, forthcoming.
Ruiz, E. and L. Pascual (2002), Bootstrapping financial time series, Journal of Economic Surveys, 16, 271–300.
Schachermayer, W. (1992), A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time, Insurance: Mathematics and Economics, 11,4, 249–257.
Schachermayer, W. (1994), Martingale measures for discrete time processes with infinite horizon, Math. Finance, 4, 25–55.
Schachermayer, W. (2002), The Fundamental Theorem of Asset Pricing under proportional transaction costs in finite discrete time, Working paper.
Schmeidler, D. (1989), Subjective probability and expected utility without additivity, Econometrica, 52, 571–587.
Sentana, E. and G. Fiorentini (2001), Identification, estimation and testing of conditionally heteroskedastic factor models, Journal of Econometrics, 102, 143–164.
Sharpe, W.F. (1964), Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance 19, 425–442.
Shephard, N.G. (1996), Statistical aspects of ARCH and stochastic volatility, in Cox, D.R., D.V. Hinkley and O.E. Barndorff-Nielsen (eds), Time Series Models In Econometrics, Finance and other Fields, Chapman & Hall, London.
Striker, C. (1990), Arbitrage et lois de martingale, Ann. Inst. H. Poincaré Prob. Statist., 26, 451–460.
Szego, G. (2002), Measures of risk, Journal of Banking and Finance, 26, 1253–1272.
Taylor, S.J. (1986), Modeling Financial Time Series, John Wiley, Chichester.
Taylor, S. J. (1994), Modeling stochastic volatility, Mathematical Finance, 4, 183–204.
Terasvirta, T. (1996), Two stylized facts and the GARCH(1,1) model, Stockholm School of Economics, Working Paper 96.
Tsay, R.S. (2002), Analysis of Financial Time Series, Wiley, New York.
Tse, Y.K. (2000), A test for constant correlations in a multivariate GARCH model, Journal of Econometrics, 98, 107–127.
Tse, Y.K. and A.K.C. Tsui (2002), A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlation, Journal of Business and Economic Statistics, 20, 351–362.
Venter, G.G. (1991), Premium implications of reinsurance without arbitrage, ASTIN Bulletin, 21,223–230.
Vlaar, P. J.G. (2000), Value at Risk models for Dutch bond portfolios, Journal of banking and Finance, 24, 1131–1154.
Wang, S. S. (2000), A class of distortion operators for pricing financial and insurance risks, Journal of Risk and Insurance, 67, 15–36.
Wang, S. S. (2001), A two factor model for pricing of risks, Working Paper, June 2001.
Wang, Y. (2002), Asymptotic nonequivalence of GARCH models and diffusions, The Annals of Statistics, 30, 754–783.
Zakodian, J.M. (1994), Threshold heteroskedastic models, Journal of Economic Dynamics and Control, 18, 931–955.
Zhang, M.Y., J.R. Russell and R.S. Tsay (2001), A nonlinear autoregressive conditional duration model with applications to financial transaction data, Journal of Econometrics
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Balbás, A., Romera, R., Ruiz, E. (2005). An Overview of Probabilistic and Time Series Models in Finance. In: Baeza-Yates, R., Glaz, J., Gzyl, H., Hüsler, J., Palacios, J.L. (eds) Recent Advances in Applied Probability. Springer, Boston, MA. https://doi.org/10.1007/0-387-23394-6_2
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