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.     

On the source of contrarian and momentum strategies in the Italian equity market

This paper investigates the source of momentum profits, while inferring the validity of the assumptions underlying rational and behavioural theories. Using a unique sample of securities listed in the Italian Stock Exchange from 1950 to 1995, we observe that buying better performing stocks in the previous 3-12 months and selling worse performing stocks over the same period yields significant profits in the short term (less than 1 year). Results also hold when conditioned upon different risk specifications. On the other hand, the continuation effect seems to significantly revert over a longer period. More importantly, in contrast with Conrad and Kaul [Rev. Financ. Stud. 11 (1998) 489], bootstrap and Monte Carlo simulations show that momentum profits are more likely to be generated by stock returns time series properties rather than by their cross-sectional differences. While the overall findings cannot reject the market efficiency hypothesis, we argue that behavioural theory may be a possible “story” to interpret the continuation effect.     

Change in Volatility in the Won/U.S. Dollar Daily Exchange Rate:Stochastic Volatility Model

This study estimates the changes in volatility of the won/U.S. dollar dailyexchange rates before and after the Korean currency crisis, using the stochastic volatility model with the ARMAregression error term. We find that the persistence of volatility increased after the Koreancurrency crisis.     

互联网企业价值评估模型比较研究

基于互联网企业轻资产、高估值、迭代快以及风险大等特点,比较传统价值评估模型与Schwar-tz-Moon等实物期权价值评估模型,分别运用于评估案例企业泛微网络价值.结果发现,相较于传统现金流贴现模型,实物期权价值评估模型评估结果更接近于公司实际价值.三种实物期权模型敏感性分析表明:Schwartz-Moon模型评估误差最小,且模型稳健性最强,适用于不确定性高的互联网企业估值.     

股票资产组合VaR研究基于混合D藤Copula模型

本文在对上证市场五种股票资产组合的风险分析中以VaR作为风险度量指标,采用基于Pair Copula高维建模理论的混合D藤Copula模型,建立了反应多个资产组合相关结构的联合分布模型。该模型对传统D藤Copula建模方法作了进一步的改进,通过一定的选择标准,确定了D藤中每个Pair Copula函数的最优函数族,这样使得所建立的模型不仅考虑到了资产维数的影响,而且还能捕捉到组合内部因子间相关结构的差异性,从而改进后的模型能更好地描述资产组合的相关结构,并且能更精确地反映资产组合收益的实际分布。最后,以混合D藤Copula模型为基础,利用Monte Carlo方法计算了上证市场五种股票资产组合的VaR,并通过实证研究进一步证明了该模型的有效性。     

Investigating the stationarity of insurance premiums: international evidence

This article explores whether there is support for the stationarity hypotheses of life and non-life insurance premiums during the period 1979–2007 for 40 heterogeneous countries. The stationarity of insurance premiums affects insurance companies’ prediction on their future inflow of premium income, which affects the liquidity of insurance companies and their investment plans and thus is relevant to the insurers’ operation. This article employs the advanced nonlinear panel unit-root test with a sequential panel selection method to classify the entire panel into two groups: stationary countries and non-stationary countries. We apply Monte Carlo simulations to derive empirical distributions of the test, which allows us to correct for the finite-sample bias and to consider the cross-country effects. We find relatively stationary life insurance premiums in countries from the following groups: high-income, Europe, and common law origin; relatively stationary non-life insurance premiums exist in the following groups: low-income, Middle East and Africa, and common law origin. Evidence herein shows that different classifications, including income levels, geographic regions, regionally or economically integrated blocs, and legal system, affect the stationarity of life and non-life insurance premiums.     

Lognormal Approximation of Complex Path-Dependent Pension Scheme Payoffs

Abstract

This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation-based numerical experiments, and we point to several other potential practical applications of the paper's theoretical results.     

Least-squares Importance Sampling for Monte Carlo security pricing

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least-squares optimization procedure. With several numerical examples, we show that such Least-squares Importance Sampling (LSIS) provides efficiency gains comparable to the state-of-the-art techniques, for problems that can be formulated in terms of the determination of the optimal mean of a multivariate Gaussian distribution. In addition, LSIS can be naturally applied to more general Importance Sampling densities and is particularly effective when the ability to adjust higher moments of the sampling distribution, or to deal with non-Gaussian or multi-modal densities, is critical to achieve variance reductions.     

A new technique for calibrating stochastic volatility models: the Malliavin gradient method

We discuss the application of gradient methods to calibrate mean reverting stochastic volatility models. For this we use formulas based on Girsanov transformations as well as a modification of the Bismut–Elworthy formula to compute the derivatives of certain option prices with respect to the parameters of the model by applying Monte Carlo methods. The article presents an extension of the ideas to apply Malliavin calculus methods in the computation of Greek's.     

The affine Heston model with correlated Gaussian interest rates for pricing hybrid derivatives

In this article we define a multi-factor equity–interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model and we use a Gaussian multi-factor short-rate process. By construction, the model fits in the framework of affine diffusion processes, allowing fast calibration to plain vanilla options. We also provide an efficient Monte Carlo simulation scheme.