The Exact Value for European Options on a Stock Paying a Discrete Dividend

No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk-neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a derivative contract. Our results are illustrated with a vanilla credit default swap contract.

On optimal joint reflective and refractive dividend strategies in spectrally positive Lévy models

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively. In this paper, motivated by the behaviour of some dividend paying stock exchange companies, we determine the optimal dividend strategy when both continuous (refractive) and lump sum (reflective) dividends can be paid at any time, and if they are subject to di…

The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion

The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stocks that pay constant dividends when the payoff is a power function. Finally, lower bound of Asian options and some special cases are provided.

On perpetual American options in a multidimensional Black-Scholes model

We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a probabilistic characterization of the fair price in terms of a reflected BSDE, and an analytical one in terms of an obstacle problem. We also provide the early exercise premium formula.

障碍期权定价的高阶精确隐式方法

High-order accurate implicit methods for the pricing of barrier options

本文提出一种高阶精确隐式有限差分方法，通过概率最优边界条件处理连续和离散监测的各类障碍期权，显著提高定价速度和精度。

The early exercise premium representation for American options on multiply assets

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with val…