Abstract
How much to spend on an option contract is the main problem at the task of pricing options. This become more complex when it comes to projecting the future possible price of the option. This is attainable if one knows the probabilities of prices either increasing, decreasing or remaining the same. Every investor wishes to make profit on whatever amount they put in the stock exchange and thus the need for a good formula that give a very good approximations to the market prices. This paper aims at introducing the concept of pricing options by using numerical methods. In particular, we focus on the pricing of a European put option which lead us to having American put option curve using Trinomial lattice model. In Trinomial method, the concept of a random walk is used in the simulation of the path followed by the underlying stock price. The explicit price of the European put option is known. Therefore at the end of the paper, the numerical prices obtained by the Black Scholes equation will be compared to the numerical prices obtained using Trinomial and Binomial methods.
Highlights
Trinomial model has been used in few options like American option, European option and in exotic options like lookback, barrier and Asian option
We present the results obtained in the calculation of the European put option by using a Trinomial Tree Method
The pricing of derivatives has been made easier by the development of Black-Scholes model
Summary
When a trinomial tree model is recombined, we get a trinomial lattice This means that all nodes that end up with the same prices at the same time will be taken to be one node. In this lattice every node has three possible paths to follow, going up, going down or remaining same. This is out of the results of multiplying the stock price at the node by either of the three factors u, d and m. The same process is repeated all the way till the price at time zero is gotten and that is the price of the options
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