美式看跌期权的两点Geske-Johnson近似定价法

在分数Black-Scholes模型下,应用两点Geske-Johnson定价法推导连续支付红利为常数的美式看跌期权的近似公式.首先假定期权没有提前实施,其价格为对应欧式看跌期权的价格;再将期权的实施时刻指定为两个时刻,通过中性风险定价法推导价格公式,然后利用两点Geske-Johnson定价法得到美式看跌期权价格的近似公式.最后给出一个数值算例,结果显示Hurst参数和到期日对价格的影响.     

美式利率期权定价的抛物型变分不等式

应用PDE方法对美式利率期权定价问题进行理论分析.在CIR利率模型下美式利率期权定价问题可归结为一个退化的一维抛物型变分不等式.通过引入惩罚函数证明了该变分不等式的解的存在唯一性,然后研究了自由边界的一些性质,如单调性,光滑性和自由边界在终止期的位置.     

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.     

模糊环境下美式看跌期权的定价研究

应用模糊集理论将无风险利率和波动率进行模糊化,以梯形模糊数替代精确值,将美式期权的定价模型扩展到美式期权模糊定价模型.得到了模糊风险中性概率表达式,并在此概率测度下推导出多期二叉树模糊定价模型,以及二叉树上各节点以梯形模糊数表示的模糊期权价值,以数值模拟演示了美式看跌期权的模糊定价过程.最后分析了不同风险偏好投资者在不确定环境下的套利决策行为,结果表明风险偏好大的投资者具有较高的置信水平、较小的主观模糊期权价格以及较大的无风险套利区间.     

分期付款购房模型及其抛物障碍问题

考虑常数利率条件下的分期付款购房模型,若风险资产市场价格服从几何布朗运动,则合约可以运用美式期权定价方法给出合理的价格.该文给出了分期付款购房合约定价的偏微分方程方法,得到一个一维抛物障碍问题,同时给出了贷款合约价格函数所联系的自由边界,并讨论了自由边界的单调性与有界性.     

跳跃-扩散过程下百慕大交换期权定价

在等价鞅测度下,利用条件期望等知识导出在风险中性定价模型中,标的资产服从跳跃-扩散过程时百慕大交换期权的解析定价公式,依此结合Richardson两点外推加速法得到美式交换期权近似解.提出的数值算例阐明提前执行特征具有重要经济价值.定价结果可以评估场外交易的金融期权价格尤其是实物期权定价.     

双指数跳扩散模型的美式二值期权定价

在股价满足红利连续支付的双指数跳扩散模型下,研究美式二值现金-无值看涨期权的定价问题.通过分解方法将其定价转化成求一个对应的永久美式期权价格和一个Cauchy问题的解,从而得到定价表达式.最后给出一个计算实例.     

基于不确定指数O-U过程带有浮动利率模型的亚式期权定价

不确定金融是不确定理论在现代金融领域的一种应用,在解决金融问题中发挥着越来越重要的作用。而利率是一个重要的经济指标,经常受到一些不确定因素的影响,在研究期权定价时,有必要考虑浮动利率。本文提出了一种新的不确定指数Ornstein-Uhlenbeck过程模型,假设利率服从不确定均值回复过程,研究了期权定价问题,运用α-轨道方法,分别推导了亚式看涨期权和看跌期权定价公式。最后,设计了计算期权价格的数值算法,并给出数值算例。     

分数布朗运动模型下美式两值期权的定价

在标的资产服从分数布朗运动模型的条件下,研究美式两值现金或无值看涨期权的定价问题.将定价问题分解为一个对应永久美式期权的价格和一个Cauchy问题的解,得到定价公式.     

Option pricing under joint dynamics of interest rates, dividends, and stock prices

This paper proposes a unified framework for option pricing, which integrates the stochastic dynamics of interest rates, dividends, and stock prices under the transversality condition. Using the Vasicek model for the spot rate dynamics, I compare the framework with two existing option pricing models. The main implication is that the stochastic spot rate affects options not only directly but also via an endogenously determined dividend yield and return volatility; consequently, call prices can be decreasing with respect to interest rates.     

A spectral-collocation method for pricing perpetual American puts with stochastic volatility

Based on the Legendre pseudospectral method, we propose a numerical treatment for pricing perpetual American put option with stochastic volatility. In this simple approach, a nonlinear algebraic equation system is first derived, and then solved by the Gauss-Newton algorithm. The convergence of the current scheme is ensured by constructing a test example similar to the original problem, and comparing the numerical option prices with those produced by the classical Projected SOR (PSOR) method. The results of our numerical experiments suggest that the proposed scheme is both accurate and efficient, since the spectral accuracy can be easily achieved within a small number of iterations. Moreover, based on the numerical results, we also discuss the impact of stochastic volatility term on the prices of perpetual American puts.     

Stochastic volatility asymptotics of stock loans: Valuation and optimal stopping

A stock loan, or equity security lending service, is a loan which uses stocks as collateral. The borrower has the right to repay the principal with interest and regain the stock, or make no repayment and surrender the stock. Therefore, the valuation of stock loan is an optimal stopping problem related to a perpetual American option with a negative effective interest rate. The negative effective interest rate makes standard techniques for perpetual American option pricing failure. Using a fast mean-reverting stochastic volatility model, we applied a perturbation technique to the free-boundary value problem for the stock loan price. An analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion.     

具有复合泊松损失和随机利率的巨灾期权定价

分析了带有复合泊松损失过程和随机利率的巨灾看跌期权的定价问题.资产价格通过跳扩散过程刻画,该过程与损失过程相关.当利率过程服从CIR模型时,获得了期权定价的显式解,并给出相关证明.通过一个实例,讨论了资产价格与期权价格的关系.     

American Call Options Under Jump‐Diffusion Processes – A Fourier Transform Approach

We consider the American option pricing problem in the case where the underlying asset follows a jump‐diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro‐partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary.     

Lie-algebraic approach for pricing moving barrier options with time-dependent parameters

In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.     

Mean-reverting stock model with floating interest rate in uncertain environment

As an application of uncertainty theory in the field of finance, uncertain finance is playing a more and more important role in solving the financial problems. This paper proposes a mean-reverting stock model with floating interest rate to investigate the uncertain financial market. The European option and American option pricing formulas of the stock model are derived by using the Yao–Chen formula. Besides, some numerical algorithms are designed to compute the prices of these options based on the pricing formulas.     

A drift‐free simulation method for pricing commodity derivatives

Having in view the pricing of commodity derivatives in Libor Market Model (LMM) setting, we first analyze the set of basic rates we need to formulate the model by using the spanning tree concept taken from graph theory. Next, we present an efficient procedure for Monte Carlo simulation of the dynamics of the rates associated to LMM, avoiding the presence of the rates dependent drifts (drift‐free simulation) and the presence of negative deflated bond prices and negative forward rates. The method is based upon a new parameterization of the martingales introduced by Glasserman and Zhao and it is extended to a Cross‐Market Model for commodities. Finally, a particular example of commodity derivative (spread option) pricing problem is considered. Copyright © 2014 John Wiley & Sons, Ltd.     

随机利率下期权定价

本文在随机利率的基础上,考虑股票价格过程和利率过程分别为扩散过程和Ito过程,并且在相关的假设下,运用鞅方法推导出欧式期权价值过程所满足的微分方程;以及利率满足一种特殊方程时,运用最优停止的鞅方法,得到了随机利率下美式期权的价格和最优停时.     

美式看跌期权定价的一种混合数值方法

本文对美式看跌期权的定价提供了一种新的混合数值方法,即快速傅里叶变换法加龙格-库塔法.首先将美式看跌期权价格所满足的Black-Scholes微分方程定解问题转化为一个标准的抛物型初、边值问题,然后通过傅里叶变换,使之转换为一个不带股价变量的常微分方程初值问题,再利用龙格-库塔法对其进行数值求解.数值实验表明,本文算法是一种快速的高精度的算法.