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Symmetries of the Black–Scholes–Merton Equation for European Options
AbstractThe aim of the present paper is the clarification of the result of A. Paliathanasis, K. Krishnakumar, K.M. Tamizhmani and P.G.L. Leach on the...
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Black–Scholes–Merton Model for Option Pricing
In this chapter, we start off the discussion of option pricing or derivatives modelling with the pioneering work by Black, Scholes and Merton who...
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Risk-Neutral Pricing Framework
The risk-neutral pricing framework is about the analysis and techniques for derivatives hedging and pricing. The pioneer work of Black, Scholes and...
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Options and Volatilities
This chapter summarizes the main building blocks that make up the business of volatility trading. It starts by covering remarkable contributions of...
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Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment
In this paper, we deal with the problem of European vulnerable option pricing under the mixed fractional Brownian motion with stochastic corporate...
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High Mathematics Meets High Finance
Mathematics in finance has prehistoric origins, in fact it is argued that an accounting system of clay tokens used for prehistoric commerce were...
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The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations
The goal of this article is to provide a detailed introduction to infinite-horizon investment–consumption problems for agents with preferences...
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High Mathematics Meets High Finance
Mathematics in finance has prehistoric origins, in fact it is argued that an accounting system of clay tokens used for prehistoric commerce were...
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Black–Scholes–Merton Model for Option Pricing
In this chapter, we start off the discussion of option pricing with the pioneering work by Black, Scholes and Merton who proposed the first hedging...
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The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. II: Existence, uniqueness and verification for \(\vartheta \in (0,1)\)
In this article, we consider the optimal investment–consumption problem for an agent with preferences governed by Epstein–Zin (EZ) stochastic...
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Vulnerable European Call Option Pricing Based on Uncertain Fractional Differential Equation
This paper presents two new versions of uncertain market models for valuing vulnerable European call option. The dynamics of underlying asset,...
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A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options
After the discovery of fractal structures of financial markets, fractional partial differential equations (fPDEs) became very popular in studying...
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Pricing European Double Barrier Option with Moving Barriers Under a Fractional Black–Scholes Model
Analysis of financial time series shows the existence of the long memory in financial markets. Fractional stochastic models can be a suitable tool...
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Barrier Option Pricing in Regime Switching Models with Rebates
This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific...
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A robust numerical solution to a time-fractional Black–Scholes equation
Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying...
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A Terminal Condition in Linear Bond-pricing Under Symmetry Invariance
In this paper, we examine a general bond-pricing model with respect to its solutions that satisfy a given terminal condition. Firstly, we obtain...
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Pricing Models Beyond Black-Scholes
In the previous chapters we presented several pricing and hedging problems both in a discrete- and in a continuous-time setting. The basic model...
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Efficient Numerical Scheme for Generalized Black–Scholes Equations on Piecewise Uniform Shishkin-Type Mesh
In this paper, we propose numerical techniques for solving generalized Black–Scholes partial differential equations. The proposed numerical method is...
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Introduction
This monograph gives a concise exposition of our recent industry-academic collaboration on a general framework of portfolio theory. In particular, it...
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Modeling, or where do differential equations come from
Partial differential equations describe numerous phenomena in nature, technology, medicine, economics, ... In this first chapter we shall describe...