4'. Options on a forward contract and on stocks You have gathered the following information regarding the values to-day (t = 0) of some vanilla options, maturing at T (>0), written on the forward contract X maturing at T' > T. The current price of this contract is 99. Strike 96 99 100 102 Call 3.45 158 ? 0.57 Put ? ? 2.13 3.54 a) Compute (with 2 decimals) the 3 missing values (?). b) Two ATMF calls written on stock Z expiring in 4 and 6 months, respectively, trade on the basis of 30% and 40% volatility, respectively. Compute (with 2 decimals) the BS value of these calls, as a percentage of the stock Z price, knowing that (here) you can use: N(d) = 0.5 + 0.4 d. Define carefully the continuously rebalanced arbitrage portfolio that could be constructed (in particular, define precisely the initial positions included in the portfolio. Hint: never be "directional"). c) You forecast that the price of stock Y will fluctuate wildly in the short run. What are the signs of the Gamma, Theta and Vega parameters of the portfolio that you consider building? Justify briefly your strategy