Option Pricing and Replication with Transactions Costs

TL;DR: In this paper, the reservation price of an option in an economy with more than one risky security and where trade involves transaction costs is examined. And the authors suggest an approach to compute reservation prices using convex optimization.

TL;DR: In this article, the nontrading region (NTR) in a mean-variance model with fixed, proportional, and quadratic trading costs is shown to be a singleton only for pure proportional costs, and utility loss from costs is approximately proportional at small cost levels, and approximately constant at large cost levels.

TL;DR: In this article, the authors address the problem of estimating and analyzing the residual risk that is not hedged by a discrete hedging strategy and propose alternative strategies to the classical delta hedging and optimization under the risk-neutral and historical probabilities.

Abstract: The classic text for understanding complex statistical probability An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivreLaplace theorem.

TL;DR: In this paper, a simple formula for the valuation of uncertain income streams consistent with rational risk averse investor behavior and equilibrium in financial markets is developed for the pricing of an option as a function of its associated stock.