论文标题
带有方差伽马信息的定价
Pricing with Variance Gamma Information
论文作者
论文摘要
在基于信息的Brody，Hughston和Macrina的基于信息的定价框架中，市场过滤$ \ {\ Mathcal f_t \} _ {t \ geq 0} $由信息过程$ \ {ξ_T_T\} _ { f_t $ - 可衡量的随机变量$ x_t $已“显示”。现金流量$ h_t $是为了取决于市场因子$ x_t $，并且有人认为以$ t $为$ h_t $的金融资产的估值。相对于$ \ Mathcal f_t $，在[0，t）$的任何时间的$ t \ in [0，t）$随时随地的值$ s_t $相对于$ \ MATHCAL F_T $的折扣，在[0，t）$中的值$ s_t $，在这种情况下，预期在风险中性措施且利率是恒定的。然后$ s_ {t^ - } = h_t $，而$ s_t = 0 $ for $ t \ geq t $。在一般情况下，一个人的现金流量数量可计，每个现金流都可以取决于市场因素的向量，每种现金流量与信息流程相关。在目前的工作中，我们基于方差 - 伽马过程构建了一个新的市场过滤模型。通过将特定类型的布朗随机桥与伽马过程从属于该信息过程。该过滤是由信息过程与与伽马级相关的伽马桥一起生成的。我们表明，由此产生的扩展信息过程具有Markov的财产，因此可以用来对各种不同的金融资产进行定价，其中一些示例进行了详细讨论。
In the information-based pricing framework of Brody, Hughston and Macrina, the market filtration $\{ \mathcal F_t\}_{t\geq 0}$ is generated by an information process $\{ ξ_t\}_{t\geq0}$ defined in such a way that at some fixed time $T$ an $\mathcal F_T$-measurable random variable $X_T$ is "revealed". A cash flow $H_T$ is taken to depend on the market factor $X_T$, and one considers the valuation of a financial asset that delivers $H_T$ at $T$. The value $S_t$ of the asset at any time $t\in[0,T)$ is the discounted conditional expectation of $H_T$ with respect to $\mathcal F_t$, where the expectation is under the risk neutral measure and the interest rate is constant. Then $S_{T^-} = H_T$, and $S_t = 0$ for $t\geq T$. In the general situation one has a countable number of cash flows, and each cash flow can depend on a vector of market factors, each associated with an information process. In the present work, we construct a new class of models for the market filtration based on the variance-gamma process. The information process is obtained by subordinating a particular type of Brownian random bridge with a gamma process. The filtration is taken to be generated by the information process together with the gamma bridge associated with the gamma subordinator. We show that the resulting extended information process has the Markov property and hence can be used to price a variety of different financial assets, several examples of which are discussed in detail.
