A company will lose$50,000 for each 1 cent decrease in the price per gallon of jet fuel over the next two months. The company plans to hedge its exposure to jet fuel with heating oil futures. Jet fuel price changes have a 0.7 correlation with heating oil futures price changes. Jet fuel price changes have a standard deviation of $3 and price changes in heating oil futures have a standard deviation of $2.Each futures contract is on 25,000 gallons.

a) What is the optimal hedge ratio?

b) What is the company's exposure measured in gallons of the new fuel?

c) What position measured in gallons should the company take in heating oil futures?

d) How many heating oil futures should be traded?

e)Should the company take long or short futures positions?Why?

Following information about an existing bond is available:

Principal Time to maturity (in years)Annual coupon ($)Price ($)1001094

Additionally, assume that the zero rate for two years is 7% with continuous compounding.

a) Calculate the zero rate (with continuous compounding) for one year.

b)What is the equivalent one-year zero rate withsemiannualcompounding?

c) What is the forward rate (with continuous compounding) for the period between one and two years?

d) The rate that can be locked in between year 1and year 2 with a Forward Rate Agreement (FRA)is 8.2%.Is there an arbitrage opportunity?If yes,please explain (withoutcalculations)howyoucan earn a risk-free profit.