Numerical methods base on trinomial trees for option pricing

This paper investigates the approach to pricing European options, starting with one-step binomial tree pricing (a relatively simple way to calculate option value). In the next step, an additional possible rate of change of stock price is added to make the model more realistic, resulting in the one-step trinomial tree model. The model bounds the option price under the no-arbitrary principle. The paper then analyzes the circumstances under which options have a xed price by completing the market and giving the solution formula of option price through the model. Last, put-call parity is used to prove the rationality of one-step trinomial model so that the model eectively prevents the occurrence of risk-free arbitrage in the market. This helps traders to price options reasonably in the market and maintains the stability of the options market.