The binomial option pricing model is a financial market model with a stock and a risk-free bank account. It is used for the valuation of stock options. The main question of this thesis is whether the plain-vanilla European option pricing formula can be expressed in closed form. This is important because a closed-form solution increases the effectiveness of the calculations. The formula mentioned above contains a hypergeometric series. To find closed-form expressions for hypergeometric series, we use Gosper's algorithm. The key feature of the algorithm is the so-called completeness. This means that it either returns a sum in closed form or tells us that there is no such form. In the end, we conclude that the binomial option pricing formula for plain-vanilla European options has no such closed form.
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