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.     

随机利率下服从分数O-U过程的欧式幂期权定价

该文考虑了利率和标的资产价格的随机性和均值回复行为,把扩展的Vasick模型和分数O-U过程进行组合,在随机利率环境下,研究了标的资产价格服从分数O-U过程的两类欧式幂期权定价问题,得到相应的定价公式,并给出了欧式幂期权的看涨.看跌平价关系.     

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.     

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.     

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.     

混合分数布朗运动下永久美式期权的定价

假设标的资产由混合分数布朗运动驱动,利用分数It6公式得到了混合分数布朗运动环境下永久美式期权的Black-Scholes偏微分方程,并通过偏微分方程获得永久美式期权的定价公式.     

分数布朗运动环境下的幂期权定价

在等价鞅测度下,研究标的资产价格服从几何分数布朗运动的幂期权看涨、看跌定价公式及其平价公式.并与基于标准布朗运动的幂期权定价公式进行比较分析,进一步论证布朗运动只是分数布朗运动的一种特例,可基于分数布朗运动对原有的期权定价模型进行推广.     

标的资产服从一类混合过程的欧式未定权益定价

文中假设标的资产价格服从受分数布朗运动和泊松过程共同驱动的一类混合模型，并给出了基于这一模型的欧式未定权益定价的基本公式，以及欧式看涨、看跌期权和上限型欧式期权的定价公式。     

分数布朗运动的美式障碍期权定价

假定标的股票服从分数布朗运动,应用二次近似法和偏微分方程方法求出了美式下降敲出看涨、看跌障碍期权价格近似解以及最佳实施边界.最后,通过显式差分法比较近似解的准确性,并分析Hurst参数对期权价格和最佳实施边界S*的影响.     

具有随机利率的跳扩散模型下的脆弱期权的定价

本文研究了具有随机利率的跳扩散模型下考虑违约风险的欧式看涨和看跌期权的定价问题.当标的资产价值和交易对手的资产价值均服从含有共同跳跃的跳扩散模型,以及利率服从Vasicek模型时,利用跳扩散模型的Girsanov定理,给出了脆弱欧式看涨和看跌期权价格的显示表达式.     

随机利率下分数跳-扩散Ornstein-Uhlenbeck期权定价模型

假设股票价格遵循分数布朗运动和复合泊松过程驱动的随机微分方程,短期利率服从HullWhite模型,建立了随机利率情形下的分数跳-扩散Ornstein-Uhlenbeck期权定价模型,利用价格过程的实际概率测度和公平保费原理,得到了欧式看涨期权定价的解析表达式,推广了Black-Scholes模型.     

Pricing perpetual American options under a stochastic-volatility model with fast mean reversion

In this paper, we present a “correction” to Merton’s (1973) well-known classical case of pricing perpetual American puts by considering the same pricing problem under a general fast mean-reverting SV (stochastic-volatility) model. By using the perturbation method, two analytic formulae are derived for the option price and the optimal exercise price, respectively. Based on the newly obtained formulae, we conduct a quantitative analysis of the impact of the SV term on the price of a perpetual American put option as well as its early exercise strategies. It shows that the presence of a fast mean-reverting SV tends to universally increase the put option price and to defer the optimal time to exercise the option contract, had the underlying been assumed to be falling. It is also noted that such an effect could be quite significant when the option is near the money.     

From ruin theory to pricing reset guarantees and perpetual put options

We examine the joint distribution of the time of ruin, the surplus immediately before ruin, the deficit at ruin, and the cause of ruin. The time of ruin is analyzed in terms of its Laplace transform, which can naturally be interpreted as discounting. We present two financial applications – the pricing of reset guarantees for a mutual fund or an equity-indexed annuity, and the pricing of a perpetual American put option. In both cases, the logarithm of the price of the underlying asset is modeled as a shifted compound Poisson process. Hence the asset price process has downward discontinuities, with the times and amounts of the drops being random.     

基于分数O-U随机过程的新型亚式期权的定价

本文运用衍生证券理论的最基本原理(△对冲和无套利原理),研究了一种新型亚式期权的定价问题,该类型期权因具有常数平均值久期而不同于标准化情形.假设标的资产(气温)由分数Ornstein-Uhlenbeck过程驱动,这样假设对天气衍生品来说是合理的.本文得到了这种新型亚式期权的动态定价方程.     

Pricing perpetual American catastrophe put options: A penalty function approach

The expected discounted penalty function proposed in the seminal paper by Gerber and Shiu [Gerber, H.U., Shiu, E.S.W., 1998. On the time value of ruin. North Amer. Actuarial J. 2 (1), 48-78] has been widely used to analyze the joint distribution of the time of ruin, the surplus immediately before ruin and the deficit at ruin, and the related quantities in ruin theory. However, few of its applications can be found beyond except that Gerber and Landry [Gerber, H.U., Landry, B., 1998. On the discount penalty at ruin in a jump-diffusion and the perpetual put option. Insurance: Math. Econ. 22, 263-276] explored its use for the pricing of perpetual American put options. In this paper, we further explore the use of the expected discounted penalty function and mathematical tools developed for the function to evaluate perpetual American catastrophe equity put options. We obtain the analytical expression for the price of perpetual American catastrophe equity put options and conduct a numerical implementation for a wide range of parameter values. We show that the use of the expected discounted penalty function enables us to evaluate the perpetual American catastrophe equity put option with minimal numerical work.     

Discrete-Time Pricing and Optimal Exercise of American Perpetual Warrants in the Geometric Random Walk Model

An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.     

Vasicěk随机利率模型下指数O-U过程的幂型期权鞅定价

研究了Vasicěk随机利率模型中一维标准Brown运动与资产价格服从指数Ornstein-Uhlenbeck过程中一维标准Brown运动的相关系数为ρ(-1≤ρ≤1)的情形下的幂型期权鞅定价问题.推广了基于Vasicěk随机利率模型下基于Black-Scholes公式的两种幂型期权定价问题.并利用Girsanov定理和等价鞅测度,给出了基于Vasicěk随机利率模型下服从指数Ornstein-Uhlenbeck过程的两种欧式幂型期权鞅定价公式.     

股价服从指数O-U过程的多点重置期权定价

本文在风险中性定价原则下,得到了股价服从指数O-U(Ornstein-Uhlenbeck)过程的n个重置日期m个执行价格的重置期权定价,又在利率服从扩展Vasicek模型下,得到了n个重置日期m个执行价格的重置期权定价.     

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.     

Pricing perpetual American options under multiscale stochastic elasticity of variance

This paper studies pricing the perpetual American options under a constant elasticity of variance type of underlying asset price model where the constant elasticity is replaced by a fast mean-reverting Ornstein–Ulenbeck process and a slowly varying diffusion process. By using a multiscale asymptotic analysis, we find the impact of the stochastic elasticity of variance on the option prices and the optimal exercise prices with respect to model parameters. Our results enhance the existing option price structures in view of flexibility and applicability through the market prices of elasticity risk.