An oil company has zero coupon notes outstanding that mature one year from now. that is, each note promises to make a single payment of $1000 one year from now with no coupon payments between now and then. unlike ordinary zeros, the note also promises investors a bonus payment equal to 15 times the amount by which the prevailing oil price on the maturity date exceeds $60 per barrel (for example, if the oil price is $62 at maturity, the holder receives $1000 plus 15 x $2 or $1030 in all; if the price of oil is below $60, the holder receives only $1000). the oil company’s investment bankers estimate that the oil company could instead have issued a conventional one‐ year zero at a yield of about 8%. suppose also that investors are convinced that the price of oil one year from now will be either $50 or $70 per barrel. annual risk free rate is 3% and the current oil price per barrel is $60.

suppose that investors do not have good idea about what oil price will be in the next year. but, they believe that the annual standard deviation of oil prices is 20%. how much do you think the notes are worth?