Options Problem

Please help with the following problem.

Evaluate the following statement:
"A call option on a portfolio of stocks is more valuable than a portfolio of call options on each of the stocks in the portfolio".

II) Use your own data to set up a hypothetical example to substantiate the above statement (NB: you can use any pricing method, e.g. Black & Scholes, Binomial, Monte-Carlo, to price the options).

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... Thus, both needs to be priced the same in order for an arbitrage opportunity to cease.

Numerically, let us assume we have two stocks S1, S2. Their portfolio is S and the call option on the portfolio is C. The two call options on the two stocks are C1 and C2 respectively.

Further assume that S1 can be 20 in the up state and 10 in the down state (with equal probabilities), for a current price of 15 (assume risk free rate of 0%). Also ...