On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

Continuity corrections for certain perpetual American and Bermudan options on multiple assets

In a general Feller martingale market with several assets, the existence of optimal exercise regions for multi-dimensional Bermudan options can be established by reference to Neveu's theory of Snell envelopes -- and also, as will be shown, more directly from standard martingale arguments combined with the strong Markov property. Based on this, in the framework of a log-Lévy martingale market, explicit formulae and asymptotic results on the perpetual American-Bermudan (barrier-like) put option price difference (``continuity correction'') near the exercise boundary will be proven, under the -- o…

Double continuation regions for American options under Poisson exercise opportunities

We consider the Lévy model of the perpetual American call and put options with a negative discount rate under Poisson observations. Similar to the continuous observation case as in De Donno et al. [24], the stopping region that characterizes the optimal stopping time is either a half-line or an interval. The objective of this paper is to obtain explicit expressions of the stopping and continuation regions and the value function, focusing on spectrally positive and negative cases. To this end, we compute the identities related to the first Poisson arrival time to an interval via the scale funct…

美式看跌期权价格有限差分近似的误差估计

Error estimates for finite difference approximations of American put option price

研究多资产美式看跌期权的有限差分近似，通过将最优停止问题转化为退化Hamilton-Jacobi-Bellman方程，证明了时间离散化参数误差阶为1/4、空间离散化参数误差阶为1/2，并估计了将问题限制在有界域引起的误差。