Convergence of Jump-Diffusion Modelsto the Black–Scholes Model
Convergence of Jump-Diffusion Modelsto the Black–Scholes Model
复制标题
跳跃扩散模型与 Black-Scholes 模型的收敛
DOI：
10.1081/sap-120017536
复制
发表时间：
2003
影响因子：
1.3
通讯作者：
In
中科院分区：
文献类型：
--
作者：
Dowon Hong;In
本文考虑了一个资产价格的跳扩散模型，它被描述为一个由Lévy过程驱动的线性随机微分方程的解。这样的市场是不完全的，有许多等价的鞅测度。本文利用极小鞅测度对未定权益进行定价，并在局部风险最小化意义下构造了未定权益的套期保值策略。研究了当跳扩散模型收敛到Black-Scholes模型时，期权价格和局部风险最小化策略的成本的收敛问题。
We consider a jump-diffusion model for asset price which is described as a solution of a linear stochastic differential equation driven by a Lévy process. Such a market is incomplete and there are many equivalent martingale measures. We price a contingent claim with respect to the minimal martingale measure and construct a hedging strategy for the contingent claim in the locally risk-minimizing sense. We study the problem of convergence of option prices jointly with the costs from the locally risk-minimizing strategies when the jump-diffusion models converge to the Black–Scholes model.