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Options and evaluating statements

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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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The solution provides an excellent response to the question being asked. It goes into a considerable amount of detail and explains the concepts being asked very well.

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The statement above is false. A call option on a portfolio of stocks is equally valuable as a portfolio of call options on each of the stocks in the portfolio. First, let us understand intuitively why this is the case. If this were not the case, then an arbitrage opportunity exists. An investor would buy individual call options on each of the stock's portfolio and then sell a call option on a portfolio of stock thereby making an arbitrage ...

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