Please include steps and explanations:

You can invest EUR 10000 in one of three different markets: the underlying market. futures and options. You expect the price of the underlying to increase within 3 months. Futures prices are positively correlated with the price of the undertying. The current price of the underlying asset is EUR 90 . The price of the futures contract is EUR 95 (expires in 3 months). Maintenance margin is \15 of the contract value and initial margin is \20 of the contract value. The price of a call option with a strike price of EUR 100 is EUR 3 per unit of the underlying, and the price of a put option with the same strike price is EUR 8 . Both options expire in 3 months. a) On the basis of the above description, decide whether you want to speculate, arbitrage or hedge. Briefly explain your choice. (1 point) b) What will be the effect (the nominal gains and the rate of return) of your strategy in (a) on the market for the underlying if the price of the underlying is EUR 105 in three month' time? What position should you take in this market? (2 points) c) What will be the effect (the nominal gains and the rate of return) of your strategy in (a) on the futures market if the price of the underlying is EUR 105 in three months' time? What position should you take in this market? \\( (2,5 \\) points) d) What will be the outcome of your strategy from point a) on the options market if the price of the underlying is EUR 105 in three months' time? What position should you take on this market (if there is more than one way to take a position, choose only one)? (2,5 points) e) Check and explain whether it is possible to arbitrage on futures contracts in the situation described in the problem. Assume that the underlying does no pay a dividend and that the risk-free rate in this market is \21.63 \\( \\left[e^{0.054075}=1.055564 ; e^{-0.054075}=0.947361\ ight](2 \\) points \\( ) \\)