Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm

In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete‐ and continuous‐time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete‐time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by with being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous‐time optimal stopping problems and derive the corresponding complexity bounds. Although we cannot prove semitractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example.     

Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds

In this paper, we study the excursions of Bessel and Cox–Ingersoll–Ross (CIR) processes with dimensions . We obtain densities for the last passage times and meanders of the processes. Using these results, we prove a variation of the Azéma martingale for the Bessel and CIR processes based on excursion theory. Furthermore, we study their Parisian excursions, and generalize previous results on the Parisian stopping time of Brownian motion to that of the Bessel and CIR processes. We obtain explicit formulas and asymptotic results for the densities of the Parisian stopping times, and develop exact simulation algorithms to sample the Parisian stopping times of Bessel and CIR processes. We introduce a new type of bond, the zero‐coupon Parisian bond. The buyer of such a bond is betting against zero interest rates, while the seller is effectively hedging against a period where interest rates fluctuate around 0. Using our results, we propose two methods for pricing these bonds and provide numerical examples.     

Is There a Causal Effect of Working Part‐Time on Current and Future Wages?

In this paper, I study the causal effects of part‐time work on current and future wages. To estimate these effects, I use a random effects model with a wage equation capturing the employment history and a dynamic multinomial probit component for the choice of employment status. Exclusion restrictions from the institutional context are exploited to support identification. The results suggest that working part‐time with few hours has a large causal effect on current wages, but more extensive part‐time work does not reduce current wages. However, both types of part‐time work lead to negative long‐term wage effects.     

A Monte-Carlo approach to estimating the effects of selected airport capacity options in London

The issue of future airport capacity in London is currently the subject of much political debate in the UK. Although realistic estimates of the effects of capacity enhancement may be desirable, such estimates are difficult. Through the use of Monte Carlo simulation, this paper quantifies and compares the relative capacity enhancements that may be afforded by the construction of a new hub airport in the Thames Estuary, additional runways at Heathrow, Gatwick and Stansted and changes to operating practices at Heathrow. The simulations show that a new hub airport would be the most effective way to increase capacity, although the reported financial and environmental costs of such a development indicate a comparatively poor rate of return. Proposed new runways at Heathrow, Gatwick and Stansted and the removal of runway alternation at Heathrow provide more modest increases in capacity.     

Decision-making in incomplete markets with ambiguity—a case study of a gas field acquisition

We apply utility indifference pricing to solve a contingent claim problem, valuing a connected pair of gas fields where the underlying process is not standard Geometric Brownian Motion and the assumption of complete markets is not fulfilled. First, empirical data are often characterized by time-varying volatility and fat tails; therefore, we use Gaussian generalized autoregressive score (GAS) and GARCH models, extending them to Student’s t-GARCH and t-GAS. Second, an important risk (reservoir size) is not hedgeable. As a result, markets are incomplete which makes preference free pricing impossible and thus standard option pricing methodology inapplicable. Therefore, we parametrize the investor’s risk preference and use utility indifference pricing techniques. We use Least Squares Monte Carlo simulations as a dimension reduction technique in solving the resulting stochastic dynamic programming problems. Moreover, an investor often only has an approximate idea of the true probabilistic model underlying variables, making model ambiguity a relevant problem. We show empirically how model ambiguity affects project values, and importantly, how option values change as model ambiguity gets resolved in later phases of the projects. We show that traditional valuation approaches will consistently underestimate the value of project flexibility and in general lead to overly conservative investment decisions in the presence of time-dependent stochastic structures.     

随机数在随机事件与概率教学中的应用探索

本文对在随机事件与概率中的常见问题提出了一种新的借助于计算机实现的解决思路,即通过机器自动产生随机数后构建相应的数学模型,再通过编程计算得到最后结果。该方法既为概率论的教学带来了创新性思维,也为当前的教师提出了新的挑战。     

OUTPUT FLUCTUATIONS PERSISTENCE: DO CYCLICAL SHOCKS MATTER?

The aim of this paper is to identify the different sources of persistence of output fluctuations. We propose an unobserved components model that allows us to decompose GDP series into a trend component and a cyclical component. We let the drift of the trend component switch between different regimes according to a first‐order Markov process. To calculate an appropriate p‐value for a test of linearity we propose a bootstrap procedure, which allows for general forms of heteroscedasticity. The performance of the bootstrap is checked by means of a Monte Carlo simulation. Our study concerns the USA. We find that cyclical shocks appear to play an important role on the observed persistence of output.     

The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics

This paper investigates the role of stochastic volatility and return jumps in reproducing the volatility dynamics and the shape characteristics of the Korean Composite Stock Price Index (KOSPI) 200 returns distribution. Using efficient method of moments and reprojection analysis, we find that stochastic volatility models, both with and without return jumps, capture return dynamics surprisingly well. The stochastic volatility model without return jumps, however, cannot fully reproduce the conditional kurtosis implied by the data. Return jumps successfully complement this gap. We also find that return jumps are essential in capturing the volatility smirk effects observed in short-term options.

跳跃随机波动的阈值模型风险值的贝叶斯估计

文章基于一类跳跃随机波动的阈值模型风险值估计贝叶斯分析,在给定先验分布下,以马尔科夫链蒙特卡洛方法估计模型中的未知参数,并给出了MCMC模拟算法,进而讨论了风险值的预测。根据模拟结果,我们得知,如果没有考虑金融时间序列的外生冲击导致的跳跃行为,将会高估风险值,因此考虑跳跃行为后,将增加风险值估计的精度。