Question

Calculate the forward price of an investment asset which has a spot price of USD80.00 and six-month (exactly 0.5 year) interest rates are 5% on a continuously compounded basis and the six-month storage costs for the asset amount to 1% on an annualized basis. The asset pays continuous income at the rate of 2% on an annualized basis.                                                          

Answer 1

1 % annualised return on storage cost can be converted to continuously compounded rate by the formula

e^c = 1.01

c= ln (1.01) = 0.00995 or 0.995%

2 % annualised return of income can be converted to continuously compounded rate by the formula

eⁱ = 1.02

i= ln (1.02) = 0.01980 or 1.9803%

So, the forward price of the asset can be calculated as

F =S * e ^{( r+ c- i) * t}

where S is the spot price, r is the continuously compounded interest rate

c is the continuously compounded storage cost , and i is the continuously compounded income, t is the time in years

F = 80 * e^{( 0.05 + 0.00995-0.019803) *0.5}

   = 80 * 1.020276

= USD 81.62