New analytic approach to address Put - Call parity violation due to discrete dividends

The issue of developing simple Black-Scholes type approximations for pricing European options with large discrete dividends was popular since early 2000's with a few different approaches reported during the last 10 years. Moreover, it has been claimed that at least some of the resulting expressions represent high-quality approximations which closely match results obtained by the use of numerics. In this paper we review, on the one hand, these previously suggested Black-Scholes type approximations and, on the other hand, different versions of the corresponding Crank-Nicolson numerical schemes with a primary focus on their boundary condition variations. Unexpectedly we often observe substantial deviations between the analytical and numerical results which may be especially pronounced for European Puts. Moreover, our analysis demonstrates that any Black-Scholes type approximation which adjusts Put parameters identically to Call parameters has an inherent problem of failing to detect a little known Put-Call Parity violation phenomenon. To address this issue we derive a new analytic approximation which is in a better agreement with the corresponding numerical results in comparison with any of the previously known analytic approaches for European Calls and Puts with large discrete dividends

The Analytical Solutions of European Options on Shares Pricing Models

The Black-Scholes options formula is the breakthrough in valuating options prices. However, the formula is heavily based on several assumptions that are not realistic in practice. The extensions of the assumptions are needed to make options pricing model more realistic. This paper has reviewed the relaxation of the formula to European options on shares with the focus on its analytical solutions. The assumptions that are relaxed are non-dividends assumption, constant interest rate, constant volatility, and continuous time

The use of the implied standard deviation as a predictor of future stock price variability: A review of empirical tests

Estimation;Securities;mathematische statistiek

Nonlinear models in option pricing : an introduction

Nonlinear Black-Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor's preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option price itself. This book consists of a collection of contributed chapters of well-known outstanding scientists working successfully in this challenging research area. It discusses concisely several models from the most relevant class of nonlinear Black-Scholes equations for European and American options with a volatility depending on different factors, such as the stock price, the time, the option price and its derivatives. We will present in this book both analytical techniques and numerical methods to solve adequately the arising nonlinear equations. The purpose of this book is to give an overview on the current state-of-the-art research on nonlinear option pricing. The intended audience is on the one hand graduate and Ph.D. students of (mathematical) finance and on the other hand lecturer of mathematical finance and and people working in banks and stock markets that are interested in new tools for option pricing

Nonlinear models in option pricing --- An introduction

Nonlinear Black-Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor's preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option price itself. This book consists of a collection of contributed chapters of well-known outstanding scientists working successfully in this challenging research area. It discusses concisely several models from the most relevant class of nonlinear Black-Scholes equations for European and American options with a volatility depending on different factors, such as the stock price, the time, the option price and its derivatives. We will present in this book both analytical techniques and numerical methods to solve adequately the arising nonlinear equations. The purpose of this book is to give an overview on the current state-of-the-art research on nonlinear option pricing. The intended audience is on the one hand graduate and Ph.D. students of (mathematical) finance and on the other hand lecturer of mathematical finance and and people working in banks and stock markets that are interested in new tools for option pricing