Valuation of FX barrier options under stochastic volatility

This paper describes European-style valuation and hedging procedures for a class of knockout barrier options under stochastic volatility. A pricing framework is established by applying mean self-financing arguments and the minimal equivalent martingale measure. Using appropriate combinations of stochastic numerical and variance reduction procedures we demonstrate that fast and accurate valuations can be obtained for down-and-out call options for the Heston model.     

Valuation Ratios and Stock Return Predictability in South Africa: Is It There?

Using monthly South African data for January 1990 through October 2009, this paper, to the best of our knowledge, is the first to examine the predictability of real stock return based on valuation ratios, namely, price-dividend and price-earnings ratios. We cannot detect either short-horizon or long-horizon predictability; that is, the hypothesis that the current value of a valuation ratio is uncorrelated with future stock price changes cannot be rejected at both short and long horizons based on bootstrapped critical values constructed from linear representations of the data. We find, via Monte Carlo simulations, that the power to detect predictability in finite samples tends to decrease at long horizons in a linear framework. Although Monte Carlo simulations applied to exponential smooth-transition autoregressive models of the price-dividend and price-earnings ratios show increased power, the ability of the nonlinear framework in explaining the pattern of stock return predictability in the data does not show any promise at either short or long horizons, just as in the linear predictive regressions.     

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 Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives

This paper analyses the robustness of Least-Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

Valuation and incentive effects of hurdle rate executive stock options

Traditional executive stock options are often criticized for inherently weak links between pay and performance. Hurdle rate executive stock options represent a viable improvement. However, valuing these options presents extraordinary analytic difficulties. With a constant dividend yield the strike price becomes a path-dependent function of the stock price and exact analytic valuation is intractable. To solve this problem, we apply the Monte Carlo valuation approach developed by Longstaff and Schwartz (Rev Financ Stud 4:113–147, 2001) to estimate the value of path-dependent American options. We also extend the methodology to incorporate the theoretical framework by Ingersoll (J Bus 79:453–487, 2006) to permit subjective valuation influenced by an executive’s risk aversion.

最优多因子仿射利率期限结构模型选择

在利用NS模型估计出市场即期利率的基础上,采用卡尔曼滤波方法对多因子Vasieck和CIR模型进行参数估计,最后运用蒙特卡罗模拟方法对交易所国债价格进行模拟,并与实际价格进行比较,进而确定了符合我们国债市场的最优多因子仿射利率期限结构模型。研究结果表明：多因子CIR模型对数据的拟合效果及对国债价格模拟效果要明显优于多因子Vasicek模型;对于多因子CIR模型而言,因子个数增加并没有提高模型的价格模拟效果;两因子CIR模型具有最优的国债价格模拟效果。     

American option pricing with discrete and continuous time models: An empirical comparison

This paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We first of all show that with a particular choice of framework the parameters of the SV models can be estimated using simple maximum likelihood techniques. We then perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results show that, while the overall differences in performance are small, for the in the money put options on individual stocks the continuous time SV models do generally perform better than the discrete time GARCH specifications.