An option provides the buyer the right to buy or sale the quantity of goods he or she wants at a fixed price known as the strike price. Since the process of buying an option is optional, the holder can choose not to buy or sale the assets. There are two options these are; right to buy and right to sale. Options can come in several varieties like; a put option, gives the seller an underlying price to sale an option (Bostock, 2004). A call option gives its holder the right to buy an option on its set price; these options depend on when the option is offered. Therefore, the paper aims at giving a theoretical analysis of option pricing theory. 2.2 Research questions The paper focuses on two main research questions; to determine the effects of option pricing theory and to explore ways of improving option pricing theory. 2.3 Significance of the research The research targets businessmen who take part in buying and selling of options using the option pricing theories. The research findings will provide them with the basis of calculating option prices. The study mainly delimits itself to the two option pricing theories (Black-Scholes model and binomial pricing option models). ...

Broadie and Detemple (2000) in their research provided a suggestion that binomial models are modified by replacing the binomial prices with the tree diagram analysis using the the Black-Scholes values, or by making it easy to payoff stocks at maturity, and the other option prices as usual. The major disadvantages of this model is that the option price converges; a result of changes that may take place in the prices. In order to obtain solutions that are exact, the Standard Richardson extrapolation may be applied . Burn (2003) states that, although the option pricing models were used. their patterns of convergent and rate of convergence for calculating the option ratios are not well described. Hull method and extended model can be used to come up with monotonic convergence using as the formula for coming up with deltas and gammas and deltas in this model.He adds that the models can be improved by introducing a more advanced formula, to improve the computation of the hedge ratios while calculation option pricing. The Central Limit Theorem, states that, the actual distribution of prices under the Black-Scholes model converges to its continuous-time limit. For instance, the price distribution of the model converges to a lognormal distribution. Similarly, binomial option prices calculated also converge to the Black-Scholes price. . N-Cumulative Standard normal distribution function r- rate of return (risk free) T-time (up to expiry in years) S-current stock price o- volatility of stock q- strike price Broadie and Detemple (2000) in their evaluation suggested for a binomial model called Binomial Black and Scholes model to price options. This model is identical to the Cox, Ross and Rubinsten (CRR) model apart from
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