Question

an investor buys 25 contracts of S&P 500 futures.Each for the delivery of 250 units. The spot price of the index is 1900. The future price iof the index is the forward price. The continuously compunded risk free rate is .04, index pays no dividends. After one day the spot price remains at 1900. Calculate the market to market of that day.

Answer 1

Contact Size = 250 units

Number of Contracts = 25

Let, T_{​​​​​0} = Date of Entering Contract

T_{​​​​​1} = Day after T_{​​​​​​0}​​​

E = Date of Expiry

Spot Price on T₀ = 1900

Future Price on T₀ = 1900 * e^{(0.04 * (E-T_{​​​​0}​​​)/365)}

Spot Price on T_{​​​​​​1} = 1900

Future Price on T₁ = 1900 * e^{(0.04 * (E-T₁)/365}

We know, E - T₀ > E - T₁

Thus, FP on T₀ > FP on T₁

Therefore, Investor suffers a loss

MTM (Loss) = 1900 * [e^{(0.04 * 1/365)}-1] * 250 * 25

= 1900 * 0.00010960 * 250 * 25

= 1,301.441173