Error analysis of finite difference and Markov chain approximations for option pricing

Mijatovi? and Pistorius proposed an efficient Markov chain approximation method for pricing European and barrier options in general one‐dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are nonsmooth, are rarely available. In this paper, we solve this problem for general one‐dimensional diffusion models, which play a fundamental role in financial applications. For such models, the Markov chain approximation method is equivalent to the method of lines using the central difference. Our analysis is based on the spectral representation of the exact solution and the approximate solution. By establishing the convergence rate for the eigenvalues and the eigenfunctions, we obtain sharp convergence rates for the transition density and the price of options with nonsmooth payoffs. In particular, we show that for call‐/put‐type payoffs, convergence is second order, while for digital‐type payoffs, convergence is generally only first order. Furthermore, we provide theoretical justification for two well‐known smoothing techniques that can restore second‐order convergence for digital‐type payoffs and explain oscillations observed in the convergence for options with nonsmooth payoffs. As an extension, we also establish sharp convergence rates for European options for a rich class of Markovian jump models constructed from diffusions via subordination. The theoretical estimates are confirmed using numerical examples.     

Tourism,terrorism and political violence in Tunisia: Evidence from Markov-switching models

This study investigates the impact of terrorist attacks and political violence on the number of tourist arrivals and overnight stays in Tunisia. The dataset employed consists of monthly data that covers the period from January 2000 to September 2016, which includes several political and terrorist attacks in Tunisia and the region. Empirically, we investigate the true data generating process (DGP) of these two proxies of tourism activity by accounting for four statistical properties that characterize these series: (1) seasonality, (2) unit roots, (3) breaks, and (4) long memory behavior.Our empirical findings show strong evidence of stationarity, five breaks in the tourist arrival time series and spurious long memory behavior. By estimating a 3-state Markov switching model consisting of the mean, trend, and variance, we find that the Tunisian Jasmine revolution and two recent terrorist attacks, one at the Bardo National Museum on March 18, 2015 and the other at the tourist resort at Port El Kantaoui, Sousse on June 26, 2015, played an important role in influencing the tourism activity of the country. Our empirical findings show also that local shocks have a more important impact than international shocks in influencing tourism activity. Interestingly, we find that the effects of terrorist shocks have a long duration compared to political violence shocks. Several security, marketing, and economic policies have been proposed and discussed in the paper.     

Bayesian selection of technology assumptions for the transformation from supply-use to input–output tables

ABSTRACT

In the construction of input–output models from supply-use tables, technology assumptions disambiguate how an industry uses inputs in the production recipe of multiple outputs. This paper uses Bayes' theorem to select technology assumptions, taking into account empirical observations. The paper presents a formulation to explore hybrids between product and industry technology assumptions in product-by-product tables. We then present Markov chain Monte-Carlo techniques to implement the Bayesian method for selecting technology assumptions. We apply the method in a case study using Eurostat supply-use tables of 2004 and 2005, exhibiting a volume of secondary products of less than 13%, and 59 products and industries per country. The results show that the choice of technology is not important, given that there is no strong evidence in favour of any of them.     

Leverage effect on stochastic volatility for option pricing in Hong Kong: A simulation and empirical study

This paper explores the importance of incorporating the financial leverage effect in the stochastic volatility models when pricing options. For the illustrative purpose, we first conduct the simulation experiment by using the Markov Chain Monte Carlo (MCMC) sampling method. We then make an empirical analysis by applying the volatility models to the real return data of the Hang Seng index during the period from January 1, 2013 to December 31, 2017. Our results highlight the accuracy of the stochastic volatility models with leverage in option pricing when leverage is high. In addition, the leverage effect becomes more significant as the maturity of options increases. Moreover, leverage affects the pricing of in-the-money options more than that of at-the-money and out-of-money options. Our study is therefore useful for both asset pricing and portfolio investment in the Hong Kong market where volatility is an inherent nature of the economy.     

Cost-effectiveness analysis of utidelone plus capecitabine for metastatic breast cancer in China

Abstract

Objective: To estimate the cost-effectiveness of utidelone plus capecitabine therapy compared to capecitabine alone in patients with metastatic breast cancer (MBC) resistant to anthracyclines and taxanes treatment in the Chinese context and provide a reference for the marketing of utidelone in China.

Methods: A Markov model was developed based on the NCT02253459 clinical trial to simulate the clinical course of patients with metastatic breast cancer who had received taxanes and anthracycline therapy. The quality-adjusted life years (QALYs) and Incremental Cost Effectiveness Ratio (ICER) were then analyzed to evaluate the benefits. Two-parametric Weibull distribution was conducted to fit PFS and OS curves by using R. Sensitivity analyses were performed to evaluate the stability of the model designed.

Results: The addition of utidelone increased the cost and QALYs by $13,370.25 and 0.1961, respectively, resulting in an increased ICER of $68,180.78 per QALY. The most sensitive influential parameter on ICER was the price of utidelone. At the threshold of willingness-to-pay (WTP) of $24,380 (3 per capita GDP of China), the cost of utidelone per 30?mg of less than $18.5, $33.7, and greater than $48.8 resulted in a 100%, 50%, and 0% possibility of cost-effectiveness, respectively. The addition of utidelone was not cost-effective when it was $115.4 per 30?mg—the price of its analog paclitaxel. In consideration of varied economics levels across China, cost-effectiveness could be achieved with the price of utidelone ranging from $5.2 to $35.9.

Limitations: The survival curves extended beyond the follow-up time horizon, of which data were generated not from the real analyses but from our established two-parameter Weibull survival model.

Conclusion: It is recommended that the price of utidelone would be less than $18.5 per 30?mg in order to obtain cost-effectiveness for metastatic breast cancer patients resistant to anthracyclines and taxanes treatment in China.     

Contagion effects and risk transmission channels in the housing,stock, interest rate and currency markets: An Empirical Study in China and the U.S.

This paper aims to investigate the crisis linkage and transmission channels within the housing, stock, interest rate and the currency markets in the U.S. and China in the past decade since the 2008 Subprime Mortgage Crisis. Two hybrid models, namely the SWARCH-EVT-Copula and the Bivariate SWARCH-EVT models, are proposed and applied in order to take into account (A) the high/low volatility regimes, (B) the interdependence structure inherited from the joint tail behaviours, as well as, (C) the risk spillover dynamics among financial sectors during market turmoils. We empirically show that the housing and stock markets share the strongest linkage and play central roles in the spreading of shocks. With a highly integrated system, the American financial sectors are under greater exposure to risk contagion and systemic risk during crises than the Chinese markets. Nevertheless, the exchange rate risk of Renminbi remains at an intensive level since its “crawl-like arrangement” and leads to increasing co-movements in the stock and interest rate markets since 2014.     

Modeling node heterogeneity in latent space models for multidimensional networks

Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This article introduces a class of models for multidimensional network data, where different levels of heterogeneity within and between networks can be considered. The proposed framework is developed in the family of latent space models, and it aims to distinguish symmetric relations between the nodes and node-specific features. Model parameters are estimated via a Markov Chain Monte Carlo algorithm. Simulated data and an application to a real example, on fruits import/export data, are used to illustrate and comment on the performance of the proposed models.     

A Markov‐switching analysis of Nigeria's business cycles: Are election cycles important?

The study examines Nigeria's business cycles between October 1998 and October 2017 and ascertains the importance of general elections cycles in engendering cyclical fluctuations in different measures of business cycles. A framework based on political business cycles theory was estimated with a dynamic Markov‐switching regression technique. The study finds that election cycles are adequate in predicting cycles in food prices, non‐farm prices, exports, and imports in Nigeria while a significant effect of election cycles on the stock market, general price level, and exchange rate could not be established. The study concludes that cycles in food, non‐farm prices, imports, and exports can be predicted by future general elections while re‐election seeking behaviour of politicians lacks the power to influence stock market performance and exchange rate in Nigeria. Hence, artificial business cycles that result primarily from politicians manipulating certain fiscal tools targeted at stimulating the economy only to increase the re‐election chances could be minimized if monetary and fiscal institutions are strong, effective, and truly independent. This will ensure that policies are not manipulated between elections by politicians but are well targeted at achieving a set of long‐term developmental goals.     

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting,incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.