TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON-NESTED MONTE CARLO

We present a generic non-nested Monte Carlo procedure for computing true upper bounds for Bermudan products, given an approximation of the Snell envelope. The pleonastic "true" stresses that, by construction, the estimator is biased above the Snell envelope. The key idea is a regression estimator for the Doob martingale part of the approximative Snell envelope, which preserves the martingale property. The so constructed martingale can be employed for computing tight dual upper bounds without nested simulation. In general, this martingale can also be used as a control variate for simulation of conditional expectations. In this context, we develop a variance reduced version of the nested primal-dual estimator. Numerical experiments indicate the efficiency of the proposed algorithms.     

Simulating Ruin Probabilities for a Class of Semimartingales by Importance Sampling Methods

We consider the problem of finding the probability of ruin when the risk process is assumed to be a special semimartingale with absolutely continuous characteristics. We show how the generalized Girsanov theorem can be used in connection with Monte Carlo simulation to obtain estimates of the ruin probabilities. It is shown by both analytical and numerical examples that these methods can be significantly better than ordinary simulations provided the new measure is chosen with some care.     

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: Patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with health care data, such assumptions unlikely hold. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.     

PRICING OF HIGH‐DIMENSIONAL AMERICAN OPTIONS BY NEURAL NETWORKS

Pricing of American options in discrete time is considered, where the option is allowed to be based on several underlyings. It is assumed that the price processes of the underlyings are given Markov processes. We use the Monte Carlo approach to generate artificial sample paths of these price processes, and then we use the least squares neural networks regression estimates to estimate from this data the so‐called continuation values, which are defined as mean values of the American options for given values of the underlyings at time t subject to the constraint that the options are not exercised at time t. Results concerning consistency and rate of convergence of the estimates are presented, and the pricing of American options is illustrated by simulated data.     

The long-horizon returns behaviour of the Portuguese stock market1

In the last few years several research studies have challenged the traditional weak-form efficiency tests of the stock market. These studies suggested an alternative to the random walk model, containing temporary and permanent components. If stocks follow such a model then the traditional tests, using returns computed for short intervals would be unable to detect them. To investigate the evidence for such models in the Portuguese stock market ten stock indexes were created. This is a pioneer study of the Portuguese stock market, and uses nominal, real and excess returns, computed for longer horizons. Three methodologies were used: variance ratios, ordinary least squares regressions and weighted least squares regressions. The statistical significance of the results was studied using traditional parametric tests as well as non-parametric tests. The evidence is mixed, as the presence of tendencies towards mean aversion and mean reversion were detected. Results also show that the evidence is very sensitive to the methodology used and the signifcance tests performed. These results, however, do not necessarily reject the weak-form market efficiency hypothesis.     

FAST MONTE CARLO GREEKS FOR FINANCIAL PRODUCTS WITH DISCONTINUOUS PAY‐OFFS

We introduce a new class of numerical schemes for discretizing processes driven by Brownian motions. These allow the rapid computation of sensitivities of discontinuous integrals using pathwise methods even when the underlying densities postdiscretization are singular. The two new methods presented in this paper allow Greeks for financial products with trigger features to be computed in the LIBOR market model with similar speed to that obtained by using the adjoint method for continuous pay‐offs. The methods are generic with the main constraint being that the discontinuities at each step must be determined by a one‐dimensional function: the proxy constraint. They are also generic with the sole interaction between the integrand and the scheme being the specification of this constraint.     

American options under stochastic volatility: control variates,maturity randomization & multiscale asymptotics

American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of an American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as Canadization. The volatility process is characterized by fast and slow-scale fluctuating factors. In particular, we study the case of an American put with a single underlying asset and use perturbative expansion techniques to approximate its price as well as the optimal exercise boundary up to the first order. We then use the approximate optimal exercise boundary formula to price an American put via Monte Carlo. We also develop efficient control variates for our simulation method using martingales resulting from the approximate price formula. A numerical study is conducted to demonstrate that the proposed method performs better than the least squares regression method popular in the financial industry, in typical settings where values of the scaling parameters are small. Further, it is empirically observed that in the regimes where the scaling parameter value is equal to unity, fast and slow-scale approximations are equally accurate.     

Equilibrium Heterogeneous-Agent models as measurement tools: Some Monte Carlo evidence

This paper discusses a series of Monte Carlo experiments designed to evaluate the empirical properties of Heterogeneous-Agent macroeconomic models in the presence of sampling variability. The calibration procedure leads to the welfare analysis being conducted with the wrong parameters. The ability of the calibrated model to correctly predict the long-run welfare changes induced by a set of policy experiments is assessed. The results show that, for the policy reforms with sizable welfare effects (i.e., more than 0.2%), the model always predicts the right sign of the welfare effects. However, the welfare effects can be evaluated with the wrong sign, when they are small and when the sample size is fairly limited. Quantitatively, the maximum errors made in evaluating a policy change are very small for some reforms (in the order of 0.02 percentage points), but bigger for others (in the order of 0.6 percentage points). Finally, having access to better data, in terms of larger samples, does lead to substantial increases in the precision of the welfare effects estimates, though the rate of convergence can be slow.     

Spurious deterministic seasonality and autocorrelation corrections with quarterly data: Further Monte Carlo results

Following recent work of Franses, Hylleberg and Lee (FHL), this paper analyses the consequences of fitting a deterministic seasonal model to a quarterly time series which can be (at least approximately) described by a seasonal unit root(s) model. Besides the distribution of the coefficient of determination, the empirical distributions of two commonly used statistics are also investigated through Monte Carlo experiments for small, moderately large and large samples. FHL's work is also extended allowing the possibility of residual autocorrelation corrections. The main conclusion that emerges from the results is that one should not try to measure the importance of deterministic seasonality nor test for its presence in the context of such (static) regression models, even when using some form of residual autocorrelation correction. A simple empirical application is provided to illustrate our results. First version received: July 1997/final version received: July 1998     

我国住房抵押贷款证券化产品定价模型

近年来,随着房地产业的迅猛发展,我国住房抵押贷款余额猛增,这不仅会给银行带来流动性风险,而且使我国住房金融市场的种种潜在的风险与漏洞逐渐地暴露出来。住房抵押贷款证券化(MBS)产品作为改革的切入点已经在我国起步。但是定价问题仍然是关注的焦点和难点。通过比较国外各种MBS定价的方法,根据我国的具体情况,运用蒙特卡罗模拟法,对我国的住房抵押贷款证券化产品进行实证分析,建立自己的测算模型。