The interest rate per year is 3%. On February 14, call options on Exxon expiring on July 1 with an exercise price of 50 sold for $4.60, while put options with the same exercise price and expiration date sold for $1.55. You can go long or short 5,000 units in any asset mentioned above. The current price of Exxon is X. Graph your profits on July 1 as X goes from 45 to 57.
An asset can potentially last for five periods. Each period it has a 15% chance of disappearing. If the asset has not disappeared at the end of any period its owner is paid 15. After five periods, if the asset survives, its owner is paid 50. Given this, how much is this asset worth at the beginning of each period?