In this article, I incorporate the anchoring-and-adjustment heuristic into the Black-Scholes option pricing framework, and show that this is equivalent to replacing the risk-free rate with a higher interest rate. I show that the price from such a behavioralized version of the Black-Scholes model...

In this paper we derive the locally risk-minimizing hedging for a general contingent claim in an incomplete market via the generalized Clark-Ocone formula. Using this result in a stochastic volatility model, we study its connection with the hedge obtained via PDE approach. We see these hedging...

Leland's approach to the hedging of derivatives under proportional transaction costs is based on an approximate replication of the European-type contingent claim VT using the classical Black Scholes formulae with a suitably enlarged volatility. The formal mathematical framework is a scheme of...

This contribution to the Handbook of Computational Finance, Springer-Verlag, gives an overview on modeling implied volatility data. After introducing the concept of Black-Scholes-Merton implied volatility (IV), the empirical stylized facts of IV data are reviewed. We then discuss recent results...

In this short notice, we present structure of the perfect hedging. Closed form formulas clarify the fact that Black-Scholes (BS) portfolio which provides perfect hedge only at initial moment. Holding portfolio over a certain period implies additional cash flow, which could not be imbedded in BS...

We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a...

In some papers it have been remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular there are two problems which can be raise by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and other the pricing...

In this paper, we establish a link between quantum stochastic processes, and non-local diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi, Andreas Boukas, The Quantum Black-Scholes Equation, Global Journal of Pure and Applied Mathematics,...

To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges switched the option model from Black-Scholes to Bachelier in April 2020. This study reviews the literature on Bachelier's pioneering option pricing model and summarizes the practical...

This article investigates the delta hedging performance of the skewness and kurtosis adjusted Black-Scholes model of Corrado and Su (1996) and Brown and Robinson (2002). The empirical tests in the FTSE 100 index option market show that the more sophisticated skewness and kurtosis adjusted model...