Money and Mathematics by Ralf Korn & Bernd Luderer

Author:Ralf Korn & Bernd Luderer
Language: eng
Format: epub
ISBN: 9783658346775
Publisher: Springer Fachmedien Wiesbaden

If you now want to price a European call on the stock, your computations start at the end. At that stage, the final payments of the call at time T are known. They are given by

for i = 0.1, …, N (i. e. for all possible final share prices), which are then equal to the price of the option at time T.

It can also be shown in the N-period binomial model that the valuation of options takes place under the risk-neutral measure Q. Here Q is uniquely determined by the independence and identical distribution of the individual price increases of the stock. For Q to be risk neutral it is then required that the probability q for the strong rise of the share price is given by

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