Assessing the Least Squares Monte-Carlo Approach to American Option Valuation

A detailed analysis of the Least Squares Monte-Carlo (LSM) approach to American option valuation suggested in Longstaff and Schwartz (2001) is performed. We compare the specification of the cross-sectional regressions with Laguerre polynomials used in Longstaff and Schwartz (2001) with alternative specifications and show that some of these have numerically better properties. Furthermore, each of these specifications leads to a trade-off between the time used to calculate a price and the precision of that price. Comparing the method-specific trade-offs reveals that a modified specification using ordinary monomials is preferred over the specification based on Laguerre polynomials. Next, we generalize the pricing problem by considering options on multiple assets and we show that the LSM method can be implemented easily for dimensions as high as ten or more. Furthermore, we show that the LSM method is computationally more efficient than existing numerical methods. In particular, when the number of assets is high, say five, Finite Difference methods are infeasible, and we show that our modified LSM method is superior to the Binomial Model.  

商业银行操作风险的统计特征及其资本模拟实证

本文通过对近年我国发生的商业银行操作风险事件的统计,得出了我国商业银行操作风险的重要特征,包括:内部欺诈及其导致的操作风险损失所占比重最大,操作风险资本的顺经济周期效应表现明显,欺诈性操作风险与地区法治水平呈现背离走势等.在对操作风险事件各损失类型发生的频率和损失金额分布进行拟合的基础上,运用蒙特卡洛模拟方法对我国商业银行操作风险资本进行10 231次模拟计算,结果显示,在置信水平为99.9%的条件下,我国整个商业银行业在拨备了3 163亿元的操作风险资本以后,大致可以抵御150年所遭遇的全部操作风险损失带来的冲击.  

亚式期权定价的模拟方法研究

由于算术平均价格亚式期权的定价没有解析公式，所以文章用Monte Carlo模拟方法通过Matlab软件编写程序对亚式期权进行了定价。发现在某些情况下，亚式期权的价值并不是国内外一些研究者所认为的低于相应的欧式期权的价值。  

Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model

We introduce the two-dimensional shifted square-root diffusion (SSRD) model for interest-rate and credit derivatives with (positive) stochastic intensity. The SSRD is the unique explicit diffusion model allowing an automatic and separated calibration of the term structure of interest rates and of credit default swaps (CDSs), and retaining free dynamics parameters that can be used to calibrate option data. We propose a new positivity preserving implicit Euler scheme for Monte Carlo simulation. We discuss the impact of interest-rate and default-intensity correlation and develop an analytical approximation to price some basic credit derivatives terms involving correlated CIR processes. We hint at a formula for CDS options under CIR + + CDS-calibrated stochastic intensity.Received: March 2004, Mathematics Subject Classification (2000): 60H10, 60J60, 60J75, 91B70JEL Classification: G13  

房地产开发企业违约概率压力测试研究——现金流蒙特卡洛模拟方法在银行中的应用

本文采用蒙特卡洛模拟方法,根据现金净额是否为负这一标准来判断房地产开发企业是否违约,在对企业的现金流进行随机模拟的基础上来计算企业的违约概率。压力测试的场景为房价下降,利率上升。压力传导途径为房价与利率变动导致企业销售收入变动,销售收入的改变导致企业的现金流量表发生变化。房价和利率对销售收入的冲击是随机的,企业的现金流也是随机的,本文通过随机模拟估算了企业的现金流为负的频率,以此作为企业违约的概率。压力测试表明,当房价下降幅度到达15%附近时,房地产开发商的违约概率开始急剧上升。  

Pricing growth-indexed bonds

Growth-indexed bonds have been suggested as a way of reducing the procyclicality of emerging-market countries’ fiscal policies and the likelihood of costly debt crises. Investor attitude surveys suggest that pricing difficulties are seen as a considerable obstacle. In an effort to reduce such concerns, this article presents a simple way of pricing growth-indexed bonds. As a pleasant by-product, the analysis tracks the quantitative implications of an increase in the share of growth-indexed bonds in total debt, measuring the ensuing decline in the probability of default and the reduction in the spreads at which standard bonds can be issued.  

Comparison of randomization techniques for low-discrepancy sequences in finance

This paper deals with comparisons of low-discrepancy sequences in terms of actual performance through numerical computation for option pricing. For that purpose, we construct a variety of randomized low-discrepancy sequences based on classical low-discrepancy sequences. A randomization structure by coordinate-wise and digit-wise permutations proves to give excellent results regardless of the classical low-discrepancy sequences. This paper represents only the author’s personal opinion, and has absolutely nothing to do with his affiliation.  

A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach

We developed a new scheme for computing “Greeks” of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for Deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.