Estimation of affine asset pricing models using the empirical characteristic function. (English) Zbl 0973.62096
Summary: The known functional form of the conditional characteristic function (CCF) of discretely sampled observations from an affine diffusion is used to develop computationally tractable and asymptotically efficient estimators of the parameters of affine diffusions, and of asset pricing models in which the state vectors follow affine diffusions. Both ‘time-domain’ estimators, based on Fourier inversion of the CCF, and ‘frequency-domain’ estimators, based directly on the CCF, are constructed. A method-of-moments estimator based on the CCF is shown to approximate the efficiency of maximum likelihood for affine diffusion and asset pricing models.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 91B28 | Finance etc. (MSC2000) |
Keywords:
affine asset pricing; efficient estimation; empirical characteristic function; conditional characteristic function; affine diffusionReferences:
| [1] | Ait-Sahalia, Y., 1999. Maximum likelihood estimation of discretely sampled diffusions: a closed-form approach. Working Paper, Princeton University. |
| [2] | Andersen, T., Benzoni, L., Lund, J., 1998. Estimating jump-diffusions for equity returns. Working paper, November. |
| [3] | Andersen, T., Lund, J., 1996. Stochastic volatility and mean drift in the short term interest rate diffusion: sources of steepness, level and curvature in the yield curve. Working paper, February. |
| [4] | Backus, D., Foresi, S., Telmer, C., 1996. Affine models of currency prices. Working paper, New York University. |
| [5] | Bakshi, G.; Cao, C.; Chen, Z.: Empirical performance of alternative option pricing models. Journal of finance 52, 2003-2049 (1997) |
| [6] | Ball, C.; Torous, W.: A simplified jump process for common stock returns. Journal of financial and quantitative analysis 18, 53-65 (1983) |
| [7] | Bates, D.: Jumps and stochastic volatility: exchange rate processes implicit in PHLX deutschemake options. Review of financial studies 9, 69-107 (1996) |
| [8] | Bates, D., 1997. Post-’87 Crash Fears in S&P 500 Futures Options. NBER Working paper. · Zbl 0942.62118 |
| [9] | Brandt, M., Santa-Clara, P., 2001. Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. Working paper, Wharton School. |
| [10] | Carrasco, M., Florens, J., 1997. Generalization of GMM to a continuum of moment conditions. Working paper, Ohio State University. · Zbl 0968.62028 |
| [11] | Chacko, G., Viceira, L., 1999a. Dynamic consumption and portfolio choice with stochastic voltality. Working paper, Harvard University. |
| [12] | Chacko, G., Viceira, L., 1999b. Spectral GMM estimation of continuous-time models. Working paper, Harvard University. · Zbl 1026.62085 |
| [13] | Chen, R.; Scott, L.: Maximum likelihood estimation for a multifactor equilibrium model of the term structure of interest rates. Journal of fixed income 3, 14-31 (1993) |
| [14] | Cox, J.; Ingersoll, J.; Ross, S.: A theory of the term structure of interest rates. Econometrica 53, No. 2, 385-407 (1985) · Zbl 1274.91447 |
| [15] | Dai, Q.; Singleton, K.: Specification analysis of affine term structure models. Journal of finance 55, 1943-1978 (2000) |
| [16] | Das, S., 2000. The surprise element: jumps in interest rate diffusions. Working paper, Harvard Business School. |
| [17] | Das, S.; Sundaram, R.: Of smiles and smirks: a term structure perspective. Journal of financial and quantitative analysis 34, 211-239 (1999) |
| [18] | Duffie, D.; Kan, R.: A yield-factor model of interest rates. Mathematical finance 6, 379-406 (1996) · Zbl 0915.90014 |
| [19] | Duffie, D.; Pan, J.; Singleton, K.: Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343-1376 (2000) · Zbl 1055.91524 |
| [20] | Duffie, D., Pedersen, L., Singleton, K., 2000. Modeling credit spreads on sovereign debt. Working paper, Stanford University. |
| [21] | Duffie, D.; Singleton, K.: Simulated moments estimation of Markov models of asset prices. Econometrica 61, 929-952 (1993) · Zbl 0783.62099 |
| [22] | Duffie, D.; Singleton, K.: An econometric model of the term structure of interest rate swap yields. Journal of finance 52, 1287-1321 (1997) |
| [23] | Epps, T., Singleton, K., 1982. A goodness of fit test for time series based on the empirical characteristic function. Working paper. · Zbl 0494.62050 |
| [24] | Feuerverger, A.: An efficiency result for the empirical characteristic function in stationary time series models. Canadian journal of statistics 18, 155-161 (1990) · Zbl 0703.62096 |
| [25] | Feuerverger, A.; Mcdunnough, P.: On some Fourier methods for inference. Journal of the American statistical association 76, 379-387 (1981) · Zbl 0463.62030 |
| [26] | Feuerverger, A.; Mcdunnough, P.: On the efficiency of empirical characteristic function procedures. Journal of the royal statistical society, series B 43, 20-27 (1981) · Zbl 0454.62034 |
| [27] | Fisher, M., Gilles, C., 1996. Estimating exponential affine models of the term structure. Working paper. |
| [28] | Gallant, A. R.; Long, J. R.: Estimation stochastic differential equation efficiently by minimum chi-square. Biometrika 84, 125-141 (1997) · Zbl 0953.62084 |
| [29] | Gallant, A. R.; Tauchen, G.: Which moments to match?. Econometric theory 12, 657-681 (1996) |
| [30] | Hansen, L.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029-1054 (1982) · Zbl 0502.62098 |
| [31] | Hansen, L.: A method of calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators. Journal of econometrics 30, 203-238 (1985) · Zbl 0588.62166 |
| [32] | Heathcote, C.: A test of goodness of fit for symmetric random variables. Australian journal of statistics 14, 172-181 (1972) · Zbl 0257.62030 |
| [33] | Heston, S.: A closed-form solution for options with stochastic volatility with applications to Bond and currency options. Review of financial studies 6, 327-344 (1993) · Zbl 1384.35131 |
| [34] | Jiang, G., Knight, J., 1999. Efficient estimation of the continuous time stochastic volatility model via the empirical characteristic function. Working paper, University of Western Ontario. |
| [35] | Jorion, P.: On jump processes in the foreign exchange and stock markets. Review of financial studies 1, 427-445 (1988) |
| [36] | Knight, J., Satchell, S., 1997. The cummulant generating function estimation method. Econometric Theory 170–184. |
| [37] | Knight, J., Yu, J., 1998. Empirical characteristic function in time series estimation. Working paper, University of Western Ontario. |
| [38] | Liu, J., 1997. Generalized method of moments estimation of affine diffusion processes. Working paper, Graduate School of Business, Stanford University. |
| [39] | Lukacs, E.: Characteristic functions. (1970) · Zbl 0201.20404 |
| [40] | Madan, D.; Seneta, E.: Simulation of estimates using the empirical characteristic function. International statistical review 55, 153-161 (1987) · Zbl 0616.62033 |
| [41] | Pan, J., 2000. ”Integrated” time series analysis of spot and options prices. Working paper, MIT. |
| [42] | Paulson, A.; Halcomb, E.; Leitch, R.: The estimation of the parameters of stable laws. Biometrica 62, 163-170 (1975) · Zbl 0309.62017 |
| [43] | Pearson, N. D.; Sun, T.: Exploiting the conditional density in estimating the term structure: an application to the Cox, ingersoll, and ross model. Journal of finance 49, No. 4, 1279-1304 (1994) |
| [44] | Pedersen, A.: A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scandinarian journal of statistics 22, 55-71 (1995) · Zbl 0827.62087 |
| [45] | Renault, E.; Touzi, N.: Option hedging and implied volatilities in a stochastic volatility model. Mathematical finance 6, 279-302 (1996) · Zbl 0915.90028 |
| [46] | Richardson, M.; Smith, T.: Tests of financial models in the presence of overlapping observations. Review of financial studies 4, 227-254 (1991) |
| [47] | Sandmann, G.; Koopman, S.: Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of econometrics 87, No. 2, 271-302 (1998) · Zbl 0937.62110 |
| [48] | Schmidt, P.: An improved version of the quandt-Ramsey MGF estimator for mixtures of normal distributions and switching regressions. Econometrica 50, 501-516 (1982) · Zbl 0504.62046 |
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