基于跳扩散过程的回望期权定价的数值算法

运用加权最小二乘蒙特卡洛模拟法(WLSM)研究标的资产服从跳扩散过程的美式回望期权定价问题,改进了Longstaff等提出的最小二乘模拟法.运用WLSM对美式回望期权进行定价,数值实验结果表明该方法具有较为显著的优势.     

美式障碍期权定价的总体最小二乘拟蒙特卡罗模拟方法

障碍期权的价格依赖于其标的资产的价格路径,实际市场中标的资产的价格变化存在跳跃现象。本文在跳跃扩散模型下使用总体最小二乘拟蒙特卡罗方法(TLSFM)对美式障碍期权定价问题进行了研究。TLSFM使用随机化的Faure序列并结合总体最小二乘回归方法,改进了Longstaff等提出的最小二乘蒙特卡罗模拟方法(LSM)。通过基于TLSFM与LSM和改进的三叉树方法的美式障碍期权定价结果的比较分析,说明了基于TLSFM的美式障碍期权定价具有结果稳定,时效性更强的优势。     

基于LSMC模型的煤炭资源价值定价研究

煤炭资源价值定价可以抽象为一种美式期权定价问题.最小二乘蒙特卡洛模拟(LSMC)方法是解决美式期权定价问题的一个有效途径.详尽地分析了Cortazar等人的基于资源价格、利率和便利收益随机变动的三因素定价模型,利用向量Ito定理提出了三因素模型中价格、利率和便利收益变量的递推公式.对LSMC方法原理进行了细致的阐述,总结出实现LSMC方法的完整过程,并在Matlab环境下编制了LSMC算法实现程序,进行算例计算.算例结果表明,LSMC方法用于资源定价是有效可靠的.研究为煤炭资源价值定价提供了一个完整具有可操作性的工具.     

基于偏最小二乘回归的美式期权仿真定价方法

本文应用最优停止理论给出了美式期权定价的一般理论框架，进而给出了美式期权普通多项式偏最小二乘仿真定价算法．解决丁当前普通最小二乘方法的理论缺陷．最后以数字实验演示了无红利美式股票卖权的价值计算，实验结果表明该方法是可行的．     

分数布朗运动环境下上证50ETF期权定价的实证研究

合理的期权价格是期权交易的前提.基于上证50ETF期权的最新数据,运用经典的BlackScholes定价模型、蒙特卡洛模拟期权定价方法和分数布朗运动定价模型对上证50ETF期权价格进行实证研究.结果表明:分数布朗运动定价模型相比较经典的Black-Scholes定价模型和蒙特卡洛方法在接近期权的实际成交价格时均方误差和均方比例误差更小,能够较为准确地、有效地模拟出上证50ETF期权的价格,从而对投资者的期权交易行为具有一定的指导作用,也为国内其他品种的期权定价研究提供参考.     

双跳跃仿射扩散模型的美式看跌期权定价北大核心CSCD

美式期权是一类具有提前实施权利的奇异型合约.2000年Duffie等人提出了一类双跳跃仿射扩散模型,假定标的资产及其波动率过程具有相关的共同跳跃,且波动率过程的跳跃大小服从指数分布.文章扩展了该模型,允许波动率过程的跳跃大小服从伽玛分布,并在具有跳跃风险的随机利率环境下研究美式看跌期权的定价.应用Bermudan期权和Richardson插值加速方法给出了美式看跌期权价格计算的解析近似公式.用数值计算实例,以最小二乘蒙特卡罗模拟法检验文章结果的准确性和有效性.最后,分析了常利率与随机利率情形下波动率过程中的相关系数对期权价格的影响.结果表明,相关系数对美式期权价格的作用是反向的.文章结果可以应用于利率与信用衍生品的定价研究.     

双跳跃仿射扩散模型的美式看跌期权定价

美式期权是一类具有提前实施权利的奇异型合约.2000年Duffie等人提出了一类双跳跃仿射扩散模型,假定标的资产及其波动率过程具有相关的共同跳跃,且波动率过程的跳跃大小服从指数分布.文章扩展了该模型,允许波动率过程的跳跃大小服从伽玛分布,并在具有跳跃风险的随机利率环境下研究美式看跌期权的定价.应用Bermudan期权和Richardson插值加速方法给出了美式看跌期权价格计算的解析近似公式.用数值计算实例,以最小二乘蒙特卡罗模拟法检验文章结果的准确性和有效性.最后,分析了常利率与随机利率情形下波动率过程中的相关系数对期权价格的影响.结果表明,相关系数对美式期权价格的作用是反向的.文章结果可以应用于利率与信用衍生品的定价研究.     

美式期权隐含波动率校准问题的研究

研究的是美式期权的隐含波动率校准问题.首先提出一个正则化的最小二乘方法,在对其惩罚问题研究后找到最小二乘问题的最优条件,并给出美式期权波动率校准问题的算法.最后,通过数值算例说明了方法的有效性.     

美式看跌期权定价的控制变量法及其估值效率研究

本文基于控制变量法原理,在Black-Scholes期权定价公式的基础上,采用CV-CRR方法为美式看跌期权定价.实证分析表明,运用控制变量法可以大大改进标准二叉树方法的运算速度和估值精度,提高了估值效率.     

混合高斯模型下带红利的永久美式期权定价

本文建立混合高斯模型下支付连续红利的永久美式期权定价模型.利用自融资策略和分数伊藤公式,得到永久美式期权价值所满足的偏微分方程.其次,由永久美式期权的实施条件与看涨-看跌期权的对称关系,获得看涨与看跌期权的定价公式与最佳实施边界.最后,利用平安银行的日收盘价对标的资产进行实证分析,结果表明:用混合高斯模型模拟出的股票价格与真实股票价格比较接近,能够反映股票的整体走势.     

GARCH模型中美式亚式期权价值的蒙特卡罗模拟算法

我们运用 Longstaff和 Schwartz最近提出的用蒙特卡罗模拟法计算美式期权的方法在 GARCH模型中求解美式亚式期权 ,我们的结果表明和其它数值方法相比 ,这个方法不仅有相当的精确度 ,而且使用简便并具有更广泛的适用性 ,对于 GARCH模型中运用格点法难以求解的浮动执行价格的美式亚式期权同样可以得到稳定解 .     

上证50ETF期权定价有效性的研究:基于B-S-M模型和蒙特卡罗模拟

上证50ETF期权作为中国资本市场上股票期权的第一个试点产品,其定价问题尤为重要。本文分别运用B-S-M期权定价模型和蒙特卡罗模拟方法对其定价进行实证研究,分析结果表明:1)IGARCH模型比传统的GARCH模型更能较好地拟合上证50ETF的波动率;2)当模拟次数为1000时,蒙特卡罗方法的效率一致地高于B-S-M模型,并且除了对偶变量技术的拟蒙特卡罗其他模型的精确度也都高于B-S-M模型;3)B-S-M模型和蒙特卡罗模拟方法都可以较为准确地、有效地模拟出上证50ETF期权价格。这些研究将为今后期权定价模型的发展和完善提供必要的参考和指引。     

Pricing Parisian down-and-in options

In this paper, we price American-style Parisian down-and-in call options under the Black–Scholes framework. Usually, pricing an American-style option is much more difficult than pricing its European-style counterpart because of the appearance of the optimal exercise boundary in the former. Fortunately, the optimal exercise boundary associated with an American-style Parisian knock-in option only appears implicitly in its pricing partial differential equation (PDE) systems, instead of explicitly as in the case of an American-style Parisian knock-out option. We also recognize that the “moving window” technique developed by Zhu and Chen (2013) for pricing European-style Parisian up-and-out call options can be adopted to price American-style Parisian knock-in options as well. In particular, we obtain a simple analytical solution for American-style Parisian down-and-in call options and our new formula is written in terms of four double integrals, which can be easily computed numerically.     

CEV模型和B-P混合驱动模型下亚式期权Monte Carlo模拟

对亚式期权在CEV模型和B-P混合驱动模型限制下进行Monte Carlo模拟定价,建立风险中性测度,模拟出不同弹性因子值下资产价格路径.为了得出优于标准的Monte Carlo模拟,应用方差缩减技术来提高期权定价的精度.最后对亚式期权定价模型进行数值案例分析,得出弹性因子取值、时间步长、模拟次数与期权价值变化的关系.     

Computational Methods for Pricing American Put Options

This work develops computational methods for pricing American put options under a Markov-switching diffusion market model. Two methods are suggested in this paper. The first method is a stochastic approximation approach. It can handle option pricing in a finite horizon, which is particularly useful in practice and provides a systematic approach. It does not require calibration of the system parameters nor estimation of the states of the switching process. Asymptotic results of the recursive algorithms are developed. The second method is based on a selling rule for the liquidation of a stock for perpetual options. Numerical results using stochastic approximation and Monte Carlo simulation are reported. Comparisons of different methods are made. This research was supported in part by the National Science Foundation and in part by the Wayne State University Research Enhancement Program.     

Efficiently pricing barrier options in a Markov-switching framework

An efficient Monte Carlo simulation for the pricing of barrier options in a Markov-switching model is presented. Compared to a brute-force approach, relying on the simulation of discretized trajectories, the presented algorithm simulates the underlying stock price process only at state changes and at maturity. Given these pieces of information, option prices are evaluated using the probability of Brownian bridges not to fall below some threshold level. It is illustrated how two methods of variance reduction, control variates and antithetic variates, further improve the algorithm. In a small case study, the algorithm is applied to the pricing of options with the EuroStoxx 50 as underlying.     

气温随机模型与我国气温期权定价研究

建立气温期权交易对于对冲天气风险,增加市场金融投资品种具有重要意义。本文主要参照均值回复模型,考虑气温的季节变化和长期趋势,建立反映气温变化的随机模型,应用1980至1999年北京日平均气温对模型参数进行估计。实证仿真以及模型验证结果表明,模型的相对误差较小,建立的气温随机模型能够对未来气温变化进行较好的模拟。蒙特卡罗方法能够对天气衍生产品进行合理定价。     

MC方差减小技术在算术平均亚式外汇期权定价中的应用

建立了利率和汇率波动率均为随机情形下算术平均亚式外汇期权的定价模型.由于其定价问题求解十分困难,运用蒙特卡罗(Monte Carlo)方法并结合控制变量方差减小技术进行模拟,有效地减小了模拟方差,得到了期权定价问题的数值结果.     

Mixing Monte-Carlo and Partial Differential Equations for Pricing Options

There is a need for very fast option pricers when the financial objects are modeled by complex systems of stochastic differential equations. Here the authors investigate option pricers based on mixed Monte-Carlo partial differential solvers for stochastic volatility models such as Heston’s. It is found that orders of magnitude in speed are gained on full Monte-Carlo algorithms by solving all equations but one by a Monte-Carlo method, and pricing the underlying asset by a partial differential equation with random coefficients, derived by Itô calculus. This strategy is investigated for vanilla options, barrier options and American options with stochastic volatilities and jumps optionally.     

Strong consistency of the empirical martingale simulation option price estimator

A simulation technique known as empirical martingale simulation （EMS） was proposed to improve simulation accuracy. By an adjustment to the standard Monte Carlo simulation, EMS ensures that the simulated price satisfies the rational option pricing bounds and that the estimated derivative contract price is strongly consistent with payoffs that satisfy Lipschitz condition. However, for some currently used contracts such as self-quanto options and asymmetric or symmetric power options, it is open whether the above asymptotic result holds. In this paper, we prove that the strong consistency of the EMS option price estimator holds for a wider class of univariate payoffs than those restricted by Lipschitz condition. Numerical experiments demonstrate that EMS can also substantially increase simulation accuracy in the extended setting.