论文标题
非肢体市场的衍生品定价
Derivatives Pricing in Non-Arbitrage Market
论文作者
论文摘要
提出了一般的方法，用于建立一系列危险资产发展的Martingale措施。为危险资产的演变而制定了足够的条件，根据该资产，同等的Martingale措施与原始措施的措施是非空的。一组Martingale措施是由一组严格的Nonnege ative随机变量构建的，满足了某些条件。对于满足某些条件的非负随机变量的不平等现象。使用这些不等式，提出了针对非负超级马丁加尔的可选分解定理的新简单证明。引入了现场措施的家族，并为他们找到了代表。发现每个赛甲量度的条件是一组斑点测量值不可或缺的。根据非线性过程，例如Arch和Garch，引入了随机过程的参数家族，为此发现了非关注价格的间隔。该公式是根据合同的合同价格获得的，并选择了欧洲类型的参数过程。估算了引入的随机过程的参数，并发现了与期权合同的合同价格最少的估计值。
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent martingale measures to the original measure is a non-empty set. The set of martingale measures is constructed from a set of strictly nonneg ative random variables, satisfying certain conditions. The inequalities are obtained for the non-negative random variables satisfying certain conditions. Using these inequalities, a new simple proof of optional decomposition theorem for the nonnegative super-martingale is proposed. The family of spot measures is introduced and the representation is found for them. The conditions are found under which each martingale measure is an integral over the set of spot measures. On the basis of nonlinear processes such as ARCH and GARCH, the parametric family of random processes is introduced for which the interval of non-arbitrage prices are found. The formula is obtained for the fair price of the contract with option of European type for the considered parametric processes. The parameters of the introduced random processes are estimated and the estimate is found at which the fair price of contract with option is the least.
