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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.  相似文献   

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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.  相似文献   

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This article presents and extends the first known model in real options, proposed in Tourinho (1979), and provides thoughts on addressing issues that are still outstanding 30 years later. It discusses the need to ensure the existence of market equilibrium when applying real options valuation to price assets, once all agents behave as suggested by the solution to the pricing equation. It argues that this can be achieved by using a stochastic process for the price that is sufficiently general to respond to supply and demand imbalances in the market for the resource. Once the individual decision rules are derived, the parameters of the process must be determined to ensure market equilibrium exists. For reserves of natural resources, this can be done by using a mean-reverting process for the price of the commodity and ensuring that the long-term price to which it reverts equals the trigger price for development of the marginal reserve.  相似文献   

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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.  相似文献   

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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.  相似文献   

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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.  相似文献   

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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.
Charles Corrado (Corresponding author)Email:
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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。  相似文献   

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We focus on factors that drive the dynamics of commodity prices. We highlight the capital budgeting implications of three highly‐cited, nested, multi‐factor models for commodity prices that have been successful in empirical investigations. Competing assumptions regarding commodity prices and their convenience yields can account for differences close to 40% on average, and in excess of 60% in cases, in the valuation of typical natural resource investments. These value differences are found to increase with the maturity and the intrinsic value of the investment, and also with the level and the volatility of the resource's convenience yield. Resources such as oil or copper, that are used for production purposes, usually exhibit high and volatile convenience yields; thus our findings should be more relevant for decision‐makers in such sectors.  相似文献   

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This paper proposes a set of Value-at-Risk (VaR) models appropriate to capture the dynamics of energy prices and subsequently quantify energy price risk by calculating VaR and expected shortfall measures. Amongst the competing VaR methodologies evaluated in this paper, besides the commonly used benchmark models, a Monte Carlo (MC) simulation approach and a hybrid MC with historical simulation approach, both assuming various processes for the underlying spot prices, are also being employed. All VaR models are empirically tested on eight spot energy commodities that trade futures contracts on the New York Mercantile Exchange (NYMEX) and the constructed Spot Energy Index. A two-stage evaluation and selection process is applied, combining statistical and economic measures, to choose amongst the competing VaR models. Finally, both long and short trading positions are considered as it is of utmost importance for energy traders and risk managers to be able to capture efficiently the characteristics of both tails of the distributions.  相似文献   

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Abstract

Control variates are often used to reduce variability in Monte Carlo estimates and their effectiveness is traditionally measured by the so-called speed-up factor. The main objective of this paper is to demonstrate that a control variate can also be applied to reduce the bias stemming from the discretization of the state variable dynamics. This is particularly valuable when stochastic interest rate models are discretized, since bias reduction through more grid points is computationally expensive.  相似文献   

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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.  相似文献   

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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.  相似文献   

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In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.  相似文献   

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The purpose of this paper is to shed light on some of the flaws in the forecasting approach undertaken by the pension industry. Specifically, it considers the treatment of inflation and shows that the current modeling framework is too simplistic. I identify the flaws of the existing regulatory framework and provide an alternative full model framework constructed around the three-factor diffusion model recently proposed by the Danish Society of Actuaries. By use of a simulation study I compare the deterministic inflation scheme applied in the industry to a stochastic scheme and show that the real value of the pension saver’s investment portfolio at retirement is highly dependent on the inflation scheme. As the deterministic scheme does not take state variable correlations into account it overestimates the expected portfolio value in real terms compared to the stochastic scheme. Moreover, the deterministic scheme gives rise to a more heavy-tailed distribution implying a misestimation of downside risk and upside potential. Finally, it is shown in a realistic case study that the pension saver’s expected retirement payout profile is heavily affected.  相似文献   

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