Option pricing and Esscher transform under regime switching

Summary We consider the option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion (GBM). That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the underlying risky asset, depend on unobservable states of the economy which are modelled by a continuous-time Hidden Markov process. The market described by the Markov-modulated GBM model is incomplete in general and, hence, the martingale measure is not unique. We adopt a regime switching random Esscher transform to determine an equivalent martingale pricing measure. As in Miyahara [33], we can justify our pricing result by the minimal entropy martingale measure (MEMM).We would like to thank the referees for many helpful and insightful comments and suggestions.Correspondence to: R. J. Elliott  

银行业前瞻性贷款损失准备金计提方法的研究

在信贷市场信息不完全和历史成本会计法的条件下,银行前瞻性地计提贷款准备金具有必然性.本文从贷款定价的角度分析了银行计提贷款准备金的基本原理,基于对前瞻性的贷款准备金计提方法的理论依据、国际银行业的实施现状及所存在问题的考察,提出了基于马尔可夫链预测思想的前瞻性的贷款准备金的新思路,并分析了其运作机理及可行性.  

Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain

We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. Partial observation means that only the prices are observable. For the investors objective of maximizing the expected utility of the terminal wealth we derive an explicit representation of the optimal trading strategy in terms of the unnormalized filter of the drift process, using HMM filtering results and Malliavin calculus. The optimal strategy can be determined numerically and parameters can be estimated using the EM algorithm. The results are applied to historical prices.Received: March 2004, Mathematics Subject Classification (2000): 91B28, 60G44JEL Classification: G11Supported by NSERC under research grant 88051 and NCE grant 30354.  

中国商业银行操作风险损失分布甄别与分析：基于贝叶斯MCMC频率方法

确切的操作风险损失分布保障了风险度量的准确性。对银行操作风险损失数据的分析,国外学者一致认为操作风险分布近似泊松分布或负的贝奴里分布。基于中国商业银行1994～2008年的操作风险损失数据,通过对操作风险损失分布的检验、贝叶斯马尔科夫蒙特卡洛频率分析,发现中国商业银行操作风险损失分布近似服从广义极值分布(Generalized Extreme Value)。  

Jump Spillover in International Equity Markets

In this article we study jump spillover effects between a numberof country equity indexes. In order to identify the latent historicaljumps of each index, we use a Bayesian approach to estimatea jump-diffusion model on each index. We look at the simultaneousjump intensities of pairs of countries and the probabilitiesthat jumps in large countries cause jumps or unusually largereturns in other countries. In all cases, we find significantevidence of jump spillover. In addition, we find that jump spilloverseems to be particularly large between countries that belongto the same regions and have similar industry structures, whereas,interestingly, the sample correlations between the countrieshave difficulties in capturing the jump spillover effects.  

A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility

We show that, for three common SARV models, fitting a minimummean square linear filter is equivalent to fitting a GARCH model.This suggests that GARCH models may be useful for filtering,forecasting, and parameter estimation in stochastic volatilitysettings. To investigate, we use simulations to evaluate howthe three SARV models and their associated GARCH filters performunder controlled conditions and then we use daily currency andequity index returns to evaluate how the models perform in arisk management application. Although the GARCH models produceless precise forecasts than the SARV models in the simulations,it is not clear that the performance differences are large enoughto be economically meaningful. Consistent with this view, wefind that the GARCH and SARV models perform comparably in testsof conditional value-at-risk estimates using the actual data.  

Portfolio selection with qualitative input

We formulate a mean-variance portfolio selection problem that accommodates qualitative input about expected returns and provide an algorithm that solves the problem. This model and algorithm can be used, for example, when a portfolio manager determines that one industry will benefit more from a regulatory change than another but is unable to quantify the degree of difference. Qualitative views are expressed in terms of linear inequalities among expected returns. Our formulation builds on the Black-Litterman model for portfolio selection. The algorithm makes use of an adaptation of the hit-and-run method for Markov chain Monte Carlo simulation. We also present computational results that illustrate advantages of our approach over alternative heuristic methods for incorporating qualitative input.  

基于滚动窗口马尔科夫链预测模型的股票指数波动情况研究

文章运用基于滚动窗口的马尔科夫链预测模型，对上证综指的变动进行研究，创新地给出概率转移矩阵、极限概率以及预测准确率的时变特征，并首次给出马尔科夫链预测模型的最优窗口长度和状态定义阀值。研究揭示，大盘波动幅度与大盘的极限概率有着密切的关系；股指期货推出后大盘平盘概率占据主导地位，平稳性显著提高，马尔科夫链预测模型的预测准确率也有了较大提高。