Titlebook: Derivative Security Pricing; Techniques, Methods Carl Chiarella,Xue-Zhong He,Christina Sklibosios N Book 2015 Springer-Verlag Berlin Heide

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LIMN

Manipulating Stochastic Differential Equations and Stochastic Integralsis chapter derives those that are most frequently used. We also consider transformation of correlated Wiener processes to uncorrelated Wiener processes for higher dimensional stochastic differential equations.

Pessary

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The Continuous Hedging Argumentticle, we make use of Ito’s lemma to derive the expression for the option value and exploit the idea of creating a hedged position by going long in one security, say the stock, and short in the other security, the option. Alternative hedging portfolios based on Merton’s approach and self financing s

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The Martingale Approachexamples, including the Wiener process, stochastic integral, and exponential martingale. We then present the Girsanov’s theorem on a change of measure. As an application, we derive the Black–Scholes formula under risk neutral measure. A brief discussion on the pricing kernel representation and the F

Rustproof

The Partial Differential Equation Approach Under Geometric Brownian Motionhnique of the PDE approach is the Fourier transform, which reduces the problem of solving the PDE to one of solving an ordinary differential equation (ODE). The Fourier transform provides quite a general framework for solving the PDEs of financial instruments when the underlying asset follows a jump

NIB

Comprise

Option Pricing Under Jump-Diffusion Processesing asset price is driven by the jump-diffusion stochastic differential equations. By constructing hedging portfolios and employing the capital asset pricing model, we provide an option pricing integro-partial differential equations and a general solution. We also examine alternative ways to constru

Externalize

Partial Differential Equation Approach Under Geometric Jump-Diffusion Processsset price is driven by a jump-diffusion process. We take the analysis as far as we can for the case of a European option with a general pay-off and the jump-size distribution is left unspecified. We obtain specific results in the case of a European call option and when the jump size distribution is

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