# Probability theory option. A New Look at Generalized Black-Scholes Formulae

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In reality, companies hardly change their valuations on a day-to-day basis, but their stock prices and valuations change nearly every second.

This difficulty in reaching a consensus about correct pricing for any tradable asset leads to short-lived arbitrage opportunities.

But a lot of successful investing boils down to a simple question of present-day valuation— what is the right current price today for an expected future payoff? Binominal Options Valuation In a competitive market, to avoid arbitrage opportunities, assets with identical payoff structures must have the same price.

Valuation of options has been a challenging task and pricing variations lead to arbitrage opportunities. Black-Scholes remains one of the most popular models used for probability theory option options but has limitations. They agree on expected price levels in a given time frame of one year but disagree on the probability of the up or down move.

Based on that, who would be willing to pay more price for the call option? Possibly Peter, as he expects a high probability of the up move.

Binominal Options Calculations The two assets, which the valuation depends upon, are the call option and the underlying stock. Suppose you buy "d" shares of underlying and short one call options to create this portfolio.

The net value of your portfolio will be d - The net value of your portfolio will be 90d.