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1.
We prove new error estimates for the Longstaff–Schwartz algorithm. We establish an $O(\log^{\frac{1}{2}}(N)N^{-\frac{1}{2}})$ convergence rate for the expected L 2 sample error of this algorithm (where N is the number of Monte Carlo sample paths), whenever the approximation architecture of the algorithm is an arbitrary set of L 2 functions with finite Vapnik–Chervonenkis dimension. Incorporating bounds on the approximation error as well, we then apply these results to the case of approximation schemes defined by finite-dimensional vector spaces of polynomials as well as that of certain nonlinear sets of neural networks. We obtain corresponding estimates even when the underlying and payoff processes are not necessarily almost surely bounded. These results extend and strengthen those of Egloff (Ann. Appl. Probab. 15, 1396–1432, 2005), Egloff et al. (Ann. Appl. Probab. 17, 1138–1171, 2007), Kohler et al. (Math. Finance 20, 383–410, 2010), Glasserman and Yu (Ann. Appl. Probab. 14, 2090–2119, 2004), Clément et al. (Finance Stoch. 6, 449–471, 2002) as well as others.  相似文献   

2.
As a corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463–520, 1994; Stoch. Stoch. Rep. 53:213–226, 1995; Math. Ann. 312:215–250, 1998), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict sigma-martingale density. This generalizes the continuous-path result of Choulli and Stricker (Séminaire de Probabilités XXX, pp. 12–23, 1996) to the càdlàg case and extends the recent one-dimensional result of Kardaras (Finance and Stochastics 16:651–667, 2012) to the multidimensional case. It also refines partially the second main result of Karatzas and Kardaras (Finance Stoch. 11:447–493, 2007) concerning the existence of an equivalent supermartingale deflator. The proof uses the technique of numéraire change.  相似文献   

3.
We consider the maximization of the long-term growth rate in the Black–Scholes model under proportional transaction costs as in Taksar et al. (Math. Oper. Res. 13:277–294, 1988). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341–1358, 2010) for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows one to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rate.  相似文献   

4.
We explore the implications for the optimal degree of fiscal decentralization when people’s preferences for goods and services—which classic treatments of fiscal federalism (Oates in Fiscal federalism, 1972) place in the purview of local governments—exhibit specific egalitarianism (Tobin in J. Law Econ. 13(2): 263–277, 1970), or solidarity. We find that a system in which the central government provides a common minimum level of the publicly provided good, and local governments are allowed to use their own resources to provide an even higher local level, performs better from an efficiency perspective relative to all other systems analyzed for a relevant range of preferences over solidarity.  相似文献   

5.
This paper develops and estimates an instrumental variables strategy for identifying the causal effect of securitization on the incidence of mortgage modification and foreclosure based on the early payment default analysis performed by Piskorsi et al. (J Financ Econ 97:360–397, 2010). Estimation results show that securitized mortgages are more likely to be modified and less likely to be foreclosed on by servicers. These results are consistent with the interpretation in Adelino et al. (2009) that low modification rates are not the result of contract frictions inherent in the mortgage securitization process.  相似文献   

6.
Option pricing under non-normality: a comparative analysis   总被引:1,自引:1,他引:0  
This paper carries out a comparative analysis of the calibration and performance of a variety of options pricing models. These include Black and Scholes (J Polit Econ 81:637–659, 1973), the Gram–Charlier (GC) approach of Backus et al. (1997), the stochastic volatility (HS) model of Heston (Rev Financ Stud 6:327–343, 1993), the closed-form GARCH process of Heston and Nandi (Rev Financ Stud 13:585–625, 2000) and a variety of Lévy processes including the Variance Gamma (VG), Normal Inverse Gaussian (NIG), and, CGMY and Kou (Manag Sci 48:1086–1101, 2002) jump-diffusion models. Unlike most studies of option pricing, we compare these models using a common point-in-time data which reflects the perspective of a new investor who wishes to choose between models using only the most minimal recent data set. For each of these models, we also examine the accuracy of delta and delta-gamma approximations to the valuation of both individual options and an illustrative option portfolio.  相似文献   

7.
We consider an equilibrium model à la Kyle–Back for a defaultable claim issued by a given firm. In such a market the insider observes continuously in time the value of the firm, which is unobservable by the market makers. Using the construction in Campi et al. (http://hal.archives-ouvertes.fr/hal-00534273/en/, 2011) of a dynamic three-dimensional Bessel bridge, we provide the equilibrium price and the insider’s optimal strategy. As in Campi and Çetin (Finance Stoch. 11:591–602, 2007), the information released by the insider while trading optimally makes the default time predictable in the market’s view at the equilibrium. We conclude the paper by comparing the insider’s expected profits in the static and dynamic private information case. We also compute explicitly the value of the insider’s information in the special cases of a defaultable stock and a bond.  相似文献   

8.
We study here the large-time behaviour of all continuous affine stochastic volatility models [in the sense of Keller-Ressel (Math Finan 21(1):73–98, 2011)] and deduce a closed-form formula for the large-maturity implied volatility smile. We concentrate on (rescaled) strikes around the money, which are the most common in practice, and extend the results in Forde and Jacquier (Finan Stoch 15(4):755–780, 2011) and Gatheral and Jacquier (Quant Finan 11(8):1129–1132, 2011).  相似文献   

9.
We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin et al. (Finance Stoch. 8:311–341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250–276, 2012) to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the G-expectation of Peng as earlier proved by Kusuoka (Ann. Appl. Probab. 5:198–221, 1995).  相似文献   

10.
We show, by means of an example, that in models where default is subject to both collateral repossession and utility punishments, opportunities for doing Ponzi schemes are not always ruled out and (refined) equilibria may fail to exist. This is true even if default penalties are moderate as defined in Páscoa and Seghir (Game Econ Behav 65:270–286, 2009). In our example, asset promises and default penalties are chosen such that, if an equilibrium does exist, agents never default on their promises. At the same time collateral bundles and utility functions are such that the full repayment of debts implies that the asset price should be strictly larger than the cost of collateral requirements. This is sufficient to induce agents to run Ponzi schemes and destroy equilibrium existence.  相似文献   

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