# Math Help - European call option

1. ## European call option

Consider a binomial model with one period and with parameters r(=interest rate) = 1/5, S_0 =
1, d = 3/4, u = 5/4. Compute the price of a European call option with strike price
K = 1, and find a replicating portfolio.
u(=upfactor) and d(=downfactor) are the following parameters: $u=\frac{S_0(H)}{S_0}$

$d=\frac{S_0(T)}{S_0}$

$S_1(H)=\frac{5}{4}$ $S_1(T)=\frac{3}{4}$

How can I determine the price at S_0 ?

2. ## Re: European call option

if you are working from first principles you can find the replicating porfolio first. the price is the cost of the replicating portfolio.

do you know how to find the replicating portfolio?

3. ## Re: European call option

Thank you very much for you answer, but I already solved the exercise.

I have an other exercise, where I have some problems, may you can help me with that:

Consider a model of a financial market consisting of one stock and one bond
with risk-free interest rate r > 0. Assume that the stock price at time 0 is a constant
S_0 > 0, and at time 1 can have any of the three values d,m and u , each with strictly positive probability, where we assume that 0 < d < m < u. On what conditions is this model free of arbitrage?
This model is known as a trinomial, and I have the following attempt:

S_0 is the start price and after a specific time I get three different results, each with different properies

$p_1 => S_0u$

$p_2 => S_0m$

$p_3 => S_0d$

and $p_1+p_2+p_3=1$

What are some examples for conditions that this is a model free of arbitrage?

4. ## Re: European call option

Does somebody has an idea?

5. ## Re: European call option

When the probability of an upward move (u) is greater than 50% by the amount that the probability of a downward move (d) is less than 50%, and a sideways move (m) is 50%. I assume you are doing this in class and not to trade, so write it on a blackboard as a time series and it should become very clear.