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Showing 1 to 6 of 6 for “"Black-Scholes Equation"”.
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Calibration of Option Pricing in Reproducing Kernel Hilbert Space
A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem …
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The Martingale Approach to Financial Mathematics
… of <em>Q</em> and a stochastic differential equation that models the dynamics of the assets of our market, known as the Ito formula, in order to derive the classic Black-Scholes Equation.</p>
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The Effects of Dilutions and Payout Policy on Equity- and Stock-linked Call Options on a Firm with Leverage
… methods utilising a generalised version of the Black-Scholes equation are then used to value and compare call options on total equity and call options on share price. Under the presented model, dilutions have little to no effect on stocklinked call option value in firms with low levels of …
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Novel fitted schemes based on mimetic finite difference method for options pricing
… approximate solutions of partial differential equations (PDEs) describing financial models since only a few of them have analytical solutions. Indeed, in the pricing of derivative securities such as European options, the underlying PDE, the so called Black-Scholes equation, is known to have a …
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Optimal Trading Strategies Under Arbitrage
… the non-uniqueness of the partial differential equation corresponding to the Black-Scholes equation. In order to apply these analytic tools, sufficient conditions are derived for the necessary differentiability of expectations indexed over the initial market configuration. The phenomenon of …
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Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance
… problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many …