Question

Let’s assume we are a heating oil delivery service company that sells 80,000 gallons of heating oil every month its clients. The firm wants to hedge its position buy entering into a contract to buy its heating oil at the end of each month for the following month. The firm has decided it only needs to hedge for the next 5 months as the demand for heating oil significantly falls off after that. What would be the swap price of the 80,000 gallons of heating oil at the end of each month for the next 5-months if the following information is true? (Risk-free rate is provided per annum with continuous compounding)

Month Forward Price Risk-Free Rate

1 $ 2.999 1.50%

2   $ 3.009 1.50%

3 $ 3.039 1.60%

4   $ 3.075 1.75%

5 $ 3.105 1.75%

Answer 1

Forward rate = Spot Rate X e^(r Xt) where, e= 2.7183 (Euler's number mathematical constant) r= risk free return t= time in years. Threrefore, Spot Rate = Forward Rate (e^(rXt)) Month Forward Rate Risk Free Rate Calcualion of Spot rate 1 2.999 0.015 2.995253567 =2.999/(2.7183^(0.015X1/12)) 2.995 2 3.009 0.015 3.001486845 =3.009/(2.7183^(0.015X2/12)) 3.001 3 5 3.039 3.075 3.105 0.016 0.0175 0.0175 3.026868199 3.057114597 3.082441568 =3.039/(2.7183^(0.016/3/12)) =3.075/(2.7183^(0.0175X4/12)) =3.105/(2.7183^(0.0175X5/12) 3.027 3.057 3.082 Spot rate