On an efficient multiple time step Monte Carlo simulation of the SABR model

In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.     

RIDGE ESTIMATORS FOR PROBIT REGRESSION: WITH AN APPLICATION TO LABOUR MARKET DATA

In this paper we propose ridge regression estimators for probit models since the commonly applied maximum likelihood (ML) method is sensitive to multicollinearity. An extensive Monte Carlo study is conducted where the performance of the ML method and the probit ridge regression (PRR) is investigated when the data are collinear. In the simulation study we evaluate a number of methods of estimating the ridge parameter k that have recently been developed for use in linear regression analysis. The results from the simulation study show that there is at least one group of the estimators of k that regularly has a lower mean squared error than the ML method for all different situations that have been evaluated. Finally, we show the benefit of the new method using the classical Dehejia and Wahba dataset which is based on a labour market experiment.     

ON THE CONSISTENCY OF REGRESSION‐BASED MONTE CARLO METHODS FOR PRICING BERMUDAN OPTIONS IN CASE OF ESTIMATED FINANCIAL MODELS

In many applications of regression‐based Monte Carlo methods for pricing, American options in discrete time parameters of the underlying financial model have to be estimated from observed data. In this paper suitably defined nonparametric regression‐based Monte Carlo methods are applied to paths of financial models where the parameters converge toward true values of the parameters. For various Black–Scholes, GARCH, and Levy models it is shown that in this case the price estimated from the approximate model converges to the true price.     

Design of limited-stop bus service with capacity constraint and stochastic travel time

This paper develops a mathematical model for the optimal stopping design of limited-stop bus service, which allows each bus vehicle to skip some stops. To better reflect the reality, this paper considers the vehicle capacity and stochastic travel time. Also, vehicles are all allowed to skip stops whereas any stop is not allowed to be skipped by two consecutive vehicles. A hybrid artificial bee colony (ABC) and Monte Carlo method is developed to solve the optimal stopping strategy. Finally, the model and solution method are validated by a numerical example, and a sensitivity analysis is performed on the passenger demand.     

基于福州市降水量数据研究降水期权定价

为应对干旱、洪涝等降水事件给相关经济主体带来的风险,基于1953年1月至2016年12月福州市月均累积降水量数据,运用威尔克斯法对降水量进行建模,利用蒙特卡罗模法对降水期权进行定价从而得到降水期权价值,并提出发展我国降水期权的政策建议。     

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.     

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.     

How effective are heuristic solutions for electricity planning in developing countries

Heuristic algorithms have been widely used to provide computationally feasible means of exploring the cost effective balance between grid versus off grid sources for universal electrification in developing countries. By definition in such algorithms however, global optimality is not guaranteed. We present a computationally intensive but globally optimal mixed integer non-linear programming (MINLP) model for electricity planning and use it in a Monte Carlo simulation procedure to test the relative performance of a widely used heuristic algorithm due to [28]. We show that the overall difference in cost is typically small suggesting that the heuristic algorithm is generally cost effective in many situations. However we find that the relative performance of the heuristic algorithm deteriorates with increasing degree of spatial dispersion of unelectrified settlements, as well as increasing spatial remoteness of the settlements from the grid network, suggesting that the effectiveness of the heuristic algorithm is context specific. Further, we find that allocation of off grid sources in the heuristic algorithm solution is often significantly greater than in the MINLP model suggesting that heuristic methods can overstate the role of off-grid solutions in certain situations.     

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.