Standard Oil

A bond issued by Standard Oil some time ago worked as follows. The holder received no

interest. At the bond's maturity, the company promised to pay $$1,000$ plus an additional

amount based on the price of oil at that time. The additional amount was equal to the

product of $170$ and the excess $($if any$)$ of the price of a barrel of oil at maturity over $$25.$

The maximum additional amount paid was $$2,550($which corresponds to a price of $$40$

per barrel$).$

What is the price of the bond? If your answer is $1234\mathrm{.}56,$ write it as $1235.$

Assumptions

The interest rate is $0\%.$

The maturity of the bond is $1$ year.

The current oil price is $$25$ per barrel.

The volatility of the log price return of oil is $20\%.$