# Evaluation of Various Numerical Methods for Option Pricing Model

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In finance, a derivative is a financial instrument whose value is derived from one or more underlying assets. An option is a contract which gives the owner the right, but not the obligation, to buy or sell the asset at a specified strike price at the specified date. The derivative itself is just a contract between two or more parties. Its value is determined by fluctuations in the value of the underlying asset. This price is chosen so that the value of the contract to both sides is zero at the outset, which means that the price is fair, so neither party is taking advantage of the other. Hence, numerical methods are needed for pricing options in cases where analytic solutions are either unavailable or not easily computable. The subject of …show more content…
In finance, a derivative is a financial instrument whose value is derived from one or more underlying assets. An option is a contract which gives the owner the right, but not the obligation, to buy or sell the asset at a specified strike price at the specified date. The derivative itself is just a contract between two or more parties. Its value is determined by fluctuations in the value of the underlying asset. This price is chosen so that the value of the contract to both sides is zero at the outset, which means that the price is fair, so neither party is taking advantage of the other. Hence, numerical methods are needed for pricing options in cases where analytic solutions are either unavailable or not easily computable. The subject of numerical methods in option pricing is very broad. A wide range of contracts exist and in many cases several models can be applied in the valuation.

Although the option valuation has been studied at least since nineteenth century, the contemporary approach is based on the Black-Scholes model which was first published in 1973. Fischer Black and Myron Scholes derived a partial differential equation, now called Black-Scholes equation, which governs the price of the option over time. The key idea was to hedge perfectly the option by buying and selling the underlying asset in just the way and consequently “eliminate risk”. Many empirical tests have shown the Black-Scholes price is fairly close to the observed price. The formula led to a boom in