英文标题：
《New Pricing Framework: Options and Bonds》
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作者：
Nick Laskin
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最新提交年份：
2014
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英文摘要：
  A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is assumed that asset price stochastic dynamics follows a Geometric Shot Noise motion. A new arbitrage-free integro-differential option pricing equation has been found and solved. The put-call parity has been proved and the Greeks have been calculated. Three additional new Greeks associated with market model parameters have been introduced and evaluated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. The new option pricing model has been generalized based on asset price dynamics modeled by the superposition of Geometric Brownian motion and Geometric Shot Noise. To model stochastic dynamics of a short term interest rate, the second model has been introduced and developed based on Langevin type equation with shot noise. A new bond pricing formula has been obtained. It has been shown that in diffusion approximation the developed bond pricing formula goes into the well-known Vasicek solution. The stochastic dynamic origin of the long-term mean and instantaneous volatility of the Vasicek model has been uncovered. A generalized bond pricing model has been introduced and developed based on short term interest rate stochastic dynamics modeled by superposition of a standard Wiener process and shot noise. Despite the non-Gaussianity of probability distributions involved, all newly elaborated models have the same degree of analytical tractability as the Black-Scholes model and the Vasicek model.
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中文摘要：
引入并详细阐述了一个包含散粒噪声随机过程的统一分析定价框架。已经开发了两个完全可解的新模型。第一种模式旨在评估期权价值。假设资产价格随机动态遵循几何散粒噪声运动。建立并求解了一个新的无套利积分微分期权定价方程。看跌期权奇偶性已经被证明，希腊人已经被计算出来。引入并评估了另外三个与市场模型参数相关的新参数。结果表明，在扩散近似下，发展的期权定价模型结合了著名的Black-Scholes方程及其解。Black-Scholes波动率的随机动力学起源已经被揭示。基于几何布朗运动和几何散粒噪声叠加的资产价格动力学模型，对新的期权定价模型进行了推广。为了对短期利率的随机动力学进行建模，第二个模型是基于带散粒噪声的朗之万型方程建立的。得到了一个新的债券定价公式。研究表明，在扩散近似下，所发展的债券定价公式进入了著名的Vasicek解。Vasicek模型的长期平均和瞬时波动率的随机动力学起源已经被揭示。在标准维纳过程和散粒噪声叠加的短期利率随机动力学模型基础上，引入并发展了广义债券定价模型。尽管所涉及的概率分布具有非高斯性，但所有新开发的模型都具有与Black-Scholes模型和Vasicek模型相同的分析可处理性。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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