The Sickness Experience of the Valkyrian Insurance Company, 1929-48

Abstract

1. Introduction.     

The distributions of the first and second order moments,the partial correlation coefficients and the multiple correlation coefficient in samples from a normal multivariate population

Abstract

1. When the frequency function of a statistical variable is known, one of the most important tasks of Theoretical Statistics is to find the frequency functions of some simple functions of this variable. The most important are the first and second order moments in a sample containing a certain number of values of the variable.     

Sell in May and go away: the evidence in the international equity index futures markets

There are teeth in the old saw     

Large sample validity of the binomial distribution for lives with unequal mortality rates

Abstract

Let us consider a group of n lives which are observed during some time or age interval. Suppose that the following conditions are satisfied: 1. The probability of death within the interval considered has the same value q for each person of the group.

2. These lives represent statistically independent observations (with respect to mortality).

     

Derivation of the Wishart distribution of the second order sample moments by straightforward integration of a multiple integral

1. Introduction.

In his textbook of statistics Kendall classifies the methods of deducing exact sampling distributions into four groups:

• (a) straightforward evaluation of the integral in question by ordinary analytical processes such as a convenient change of variable;

• (b) the use of geometrical terminology;

• (c) the use of characteristic functions; and

• (d) other analytical methods.

     

Are tightened trading rules always bad? Evidence from the Chinese index futures market

This paper investigates the impact of tightened trading rules on the market efficiency and price discovery function of the Chinese stock index futures in 2015. The market efficiency and the price discovery of Chinese stock index futures do not deteriorate after these rule changes. Using variance ratio and spectral shape tests, we find that the Chinese index futures market becomes even more efficient after the tightened rules came into effect. Furthermore, by employing Schwarz and Szakmary [J. Futures Markets, 1994, 14(2), 147–167] and Hasbrouck [J. Finance, 1995, 50(4), 1175–1199] price discovery measures, we find that the price discovery function, to some extent, becomes better. This finding is consistent with Stein [J. Finance, 2009, 64(4), 1517–1548], who documents that regulations on leverage can be helpful in a bad market state, and Zhu [Rev. Financ. Stud., 2014, 27(3), 747–789.], who finds that price discovery can be improved with reduced liquidity. It also suggests that the new rules may effectively regulate the manipulation behaviour of the Chinese stock index futures market during a bad market state, and then positively affect its market efficiency and price discovery function.     

A Note on Gaussian Estimation of the CKLS and CIR Models with Feedback Effects for Japan

In this note we extend the Gaussian estimation of two factor CKLS and CIR models recently considered in Nowman, K. B. (2001, Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom, Asia Pacif. Financ. Markets 8, 23–34) to include feedback effects in the conditional mean as was originally formulated in general continuous time models by Bergstrom, A. R. (1966, Non-recursive models as discrete approximations to systems of stochastic differential equations, Econometrica 34, 173–182) with constant volatility. We use the exact discrete model of Bergstrom, A. R. (1966, Non-recursive models as discrete approximations to systems of stochastic differential equations, Econometrica 34, 173–182) to estimate the parameters which was first used by Brennan, M. J. and Schwartz, E. S. (1979, A continuous time approach to the pricing of bonds, J. Bank. Financ. 3, 133–155) to estimate their two factor interest model but incorporating the assumption of Nowman, K. B. (1997, Gaussian estimation of single-factor continuous time models of the term structure of interest rates, J. Financ. 52, 1695–1706; 2001, Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom, Asia Pacif. Financ. Markets 8, 23–34). An application to monthly Japanese Euro currency rates indicates some evidence of feedback from the 1-year rate to the 1-month rate in both the CKLS and CIR models. We also find a low level-volatility effect supporting Nowman, K. B. (2001, Gaussian estimation and forecasting of multi-factor term structure models with an application to Japan and the United Kingdom, Asia Pacif. Financ. Markets 8, 23–34).     

Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

May the course of the tuberculosis-mortality chiefly be explained by the movements of the infection-curve (tuberculin-curve)?

Abstract

Let us suppose that we have a population which is kept constant by the birth of 10,000 children annually, and that this has been the case for a number of years.     

The variance part of the credibility premium without the jackknife

Abstract

The present paper brings some criticisms to a method introduced by Zehnwirth for estimation of the credibility factor in the variance part of the credibility premium, and an alternative method is proposed.     

A novel Monte Carlo approach to hybrid local volatility models

We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014, 14, 1899–1922], Piterbarg [Risk, 2007, April, 84–89], Tataru and Fisher [Quantitative Development Group, Bloomberg Version 1, 2010], Lipton [Risk, 2002, 15, 61–66]—and the local volatility model incorporating stochastic interest rates—see e.g. Atlan [ArXiV preprint math/0604316, 2006], Piterbarg [Risk, 2006, 19, 66–71], Deelstra and Rayée [Appl. Math. Finance, 2012, 1–23], Ren et al. [Risk, 2007, 20, 138–143]. For both model classes a particular (conditional) expectation needs to be evaluated which cannot be extracted from the market and is expensive to compute. We establish accurate and ‘cheap to evaluate’ approximations for the expectations by means of the stochastic collocation method [SIAM J. Numer. Anal., 2007, 45, 1005–1034], [SIAM J. Sci. Comput., 2005, 27, 1118–1139], [Math. Models Methods Appl. Sci., 2012, 22, 1–33], [SIAM J. Numer. Anal., 2008, 46, 2309–2345], [J. Biomech. Eng., 2011, 133, 031001], which was recently applied in the financial context [Available at SSRN 2529691, 2014], [J. Comput. Finance, 2016, 20, 1–19], combined with standard regression techniques. Monte Carlo pricing experiments confirm that our method is highly accurate and fast.     

A review of the collective theory of risk

Abstract

1. Ackermann, W. G. 1939. Eine Erweiterung des Poissonschen Grenzwertsatzes und ihre Anwendung auf Risikoprobleme der Sachversicherung. Berlin.     

An inequality satisfied by the Gamma function

Abstract

1. Summary

For all real values of α and λ satisfying α + λ > 0, α ≠ 0, α ≠ 1, λ > 0 the following inequality involving the Gamma function holds:

This follows from a general inequality for the variance of regular unbiased estimators given by Cramér [1].     

One-state variable binomial models for European-/American-style geometric Asian options

Abstract

This paper is concerned with geometric Asian options whose pay-offs depend on the geometric average of the underlying asset prices. Following the Cox et al (1979 J. Financial Economics 7 229-63) arbitrage arguments, we develop one-state variable binomial models for the options on the basis of the idea of Cheuk and Vorst (1997 J. Int. Money Finance 16 173-87). The models are more efficient and faster than those lattice methods (for the options) proposed by Hull and White (1993 J. Derivatives 1 21-31), Ritchken et al (1993 Manage. Sci. 39 1202-13), Barraquand and Pudet (1996 Math. Finance 6 17-51) and Cho and Lee (1997 J. Financial Eng. 6 179-91). We also establish the equivalence of the models and certain difference schemes.     

Nucleation of market shocks in the Sornette–Ide model*

Abstract

The Sornette–Ide differential equation of herding and rational trader behaviour together with very small random noise is shown to lead to crashes or bubbles where the price change goes to infinity after an unpredictable time. About 100 time steps before this singularity, a few predictable roughly log-periodic oscillations are seen.

A statistical analysis of DJ, S&P and Sofix (the share index for Bulgaria) shows higher fluctuations in the Sofix. This is consistent with the assumption that higher noise levels lead to shorter times between crashes. The higher level of fluctuations for the Sofix is consistent with Maslov's results comparing share indices for emerging and established markets (Maslov 2001 Physica A 301 397)     

A stronger version of Gautschi's inequality satisfied by the gamma function

Abstract

Let X be a random variable defined on a probability space, and E denote the expectation operator.     

On the asymptotic behavior of the mixed poisson process

Abstract

The recent note by Pfeifer (1982) suggests that it might be useful to point out the intuitive nature of the limit theorems in question.     

Stochastic processes and practical working models or why is the Polya process approach defective in modem practice and how cope with its deficiencies?

Abstract

1. One of the principal aims of mathematical statistics is the creation of theoretical models of probabilistically governed events or series of events. These models are mostly constructed by bringing together in suitable arrangements different elements from the tool-kit of general methods and premanufactured simple pieces of work at hand and known by the research worker.     

No-arbitrage bounds for the forward smile given marginals

We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek [Financ. Stochastics, 2015, 19, 189–214] and by Hobson and Neuberger [Math. Financ., 2012, 22, 31–56]. We recast this dual approach as a finite-dimensional linear program, and reconcile numerically, in the Black–Scholes and in the Heston model, the two approaches.     

Empirical Bayes approach to statistical estimation in the Paretian law

Abstract

The two-parameter Pareto distribution of a random variable (r.v.) X with probability density function (p.d.f.)