Consider a long position in a two-years forward contract The underlying asset is gold which incurs a net storage and security cost of 2 pa continuously compounded The total value of the underlying gol

(1) To calculate the forward price, we need to consider the carrying cost of the gold. The carrying cost is given by the formula:

Carrying cost = (Underlying value) * (Storage and security cost) * (Time to maturity)

In this case, the carrying cost is:

Carrying cost = $100 million * 2% * 2 years = $4 million

The forward price is calculated by adding the carrying cost to the underlying value:

Forward price = Underlying value + Carrying cost = $100 million + $4 million = $104 million

The initial value of the forward contract is zero since there is no upfront payment.

(2) To calculate the new forward price, we need to consider the new carrying cost. The carrying cost is:

Carrying cost = $120 million * 2% * 1 year = $2.4 million

The new forward price is calculated by adding the new carrying cost to the new underlying value:

Forward price = Underlying value + Carrying cost = $120 million + $2.4 million = $122.4 million

To calculate the new value of the forward contract, we need to consider the change in the underlying value. The change in the underlying value is:

Change in underlying value = New underlying value - Initial underlying value = $120 million - $100 million = $20 million

The new value of the forward contract is calculated by multiplying the change in underlying value by the present value of the carrying cost:

New value of the forward contract = Change in underlying value * e^(-rf * t)

Where rf is the risk-free rate of interest and t is the time to maturity. In this case, the time to maturity is 1 year.

New value of the forward contract = $20 million * e^(-6.09% * 1 year) = $20 million * e^(-0.0609) = $20 million * 0.9401 = $18.802 million