# Replicating portfolio of an option and to find inital price

I am very new to financial math so I am not sure how to do with this question. A friend sent me this question to practice but I am unsure how to begin. I read about call option . Can that be used for any option? Any help would be appreciated.

Consider the following discrete time one-period market model. The savings account is at \$1 at time 0 and \$$$\beta$$ at time 1. The stock price is given by $$S_0 = 1$$ and $$S_1 = \xi$$ where $$\xi$$ is a random variable taking two possible values $$u$$ and $$d$$, each with positive probability. Moreover, assume that $$0 < d < \beta < u$$. Find, with proof, the risk-neutral measure of this model. Does this model have arbitrage opportunities?

• Since you are new to financial maths and your question is about binomial tree model, perhaps you can read Steven Shreve's Stochastic Calculus for I: The Binomial Asset Pricing Model? The book's Chapter 1 covers your question. I learn binomial tree model from this book. If you would like to proceed to models in continuous time (such as Black-Scholes model, a famous option pricing model), you can read volume 2. – Idonknow Jun 17 '20 at 4:24
• thanks for the comment!! i will read through this. – starfire Jun 17 '20 at 4:32