Does patience pay? : empirical testing of the option to delay accepting a tender offer in the U.S. banking sector

We examine the empirical predictions of a real option-pricing model using a large sample of data on mergers and acquisitions in the U.S. banking sector. We provide estimates for the option value that the target bank has in waiting for a higher bid instead of accepting an initial tender offer. We find empirical support for a model that estimates the value of an option to wait in accepting an initial tender offer. Market prices reflect a premium for the option to wait to accept an offer that has a mean value of almost 12.5% for a sample of 424 mergers and acquisitions between 1997 and 2005 in the U.S. banking industry. Regression analysis reveals that the option price is related to both the price to book market and the free cash flow of target banks. We conclude that it is certainly in the shareholders best interest if subsequent offers are awaited. JEL Classification: G34, C1

Application of Operator Splitting Methods in Finance

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generalizations thereof. An overview of various operator splitting methods is presented for the efficient numerical solution of these problems. Splitting schemes of the Alternating Direction Implicit (ADI) type are discussed for multidimensional problems, e.g. given by stochastic volatility (SV) models. For jump models Implicit-Explicit (IMEX) methods are considered which efficiently treat the nonlocal jump operator. For American options an easy-to-implement operator splitting method is described for the resulting linear complementarity problems. Numerical experiments are presented to illustrate the actual stability and convergence of the splitting schemes. Here European and American put options are considered under four asset price models: the classical Black-Scholes model, the Merton jump-diffusion model, the Heston SV model, and the Bates SV model with jumps

Interest rate models with Markov chains

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Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements

This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundary conditions are illustrated for European vanilla options, digital call and American put options. The convection dominated Heston model for vanishing volatility is efficiently solved utilizing the adaptive dGFEM. For fast solution of the linear complementary problem of the American options, a projected successive over relaxation (PSOR) method is developed with the norm preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option pricing by conducting comparison analysis with other methods and numerical experiments

Does Patience Pay? Empirical Testing of the Option to Delay Accepting a Tender Offer in the U.S. Banking Sector

We examine the empirical predictions of a real option-pricing model using a large sample of data on mergers and acquisitions in the U.S. banking sector. We provide estimates for the option value that the target bank has in waiting for a higher bid instead of accepting an initial tender offer. We find empirical support for a model that estimates the value of an option to wait in accepting an initial tender offer. Market prices reflect a premium for the option to wait to accept an offer that has a mean value of almost 12.5% for a sample of 424 mergers and acquisitions between 1997 and 2005 in the U.S. banking industry. Regression analysis reveals that the option price is related to both the price to book market and the free cash flow of target banks. We conclude that it is certainly in the shareholders best interest if subsequent offers are awaited.Option-pricing Model, Mergers and Acquisitions, U.S. Banking Industry