Here is the project I have to do in Financial Risk course... Thanks in advance for help !

So far, we have seen that we can combine options to make strategies that allow us to bet on the trend or the volatility of a particular stock. However, there are strategies that allow us to bet on both trend and volatility. These strategies are similar to Straddle, but differ from it in the number of options to be purchased.

• Complete the table with the names of these combinations (HINT: Look for two combinations, and fill in the spaces with their standard and reverse versions).
• Describe the strategies you have indicated. To do so, build the table that indicates the result of the strategy at each moment, and draws its behaviour, as well as that of its components separately, in a graph.
• What are the implications, in general, of buying more or fewer units of options?

3. We now know that we can replicate a futures contract with a long position in a call and a short position in a put. However, while we know that both products have a price, we also know that there is nothing to pay to enter into a futures contract. Therefore, we could conclude that both the price and the call () and the price of the put () must be equal ( = ). Suppose you are replicating a futures contract in its initial stage, using a call and put. Prove that the price of the call and the put must be equal:

a. Using arbitrage arguments (it is recommended to build the corresponding payoff table).

b. Through a mathematical demonstration, using formulas that have been seen throughout the course.