Question

The value of the shares of company A is currently at S0 = 500. The annual risk-free interest rate is 6% per annum (continuous compound). This company pays a dividend of 50 euros semiannually. The next payment will be made within 4 months

Calculate the current value of dividends Answer

Calculate the price of the future for a five-month contract. Reply

Calculate the value of the contract within a month if the strike (future transaction price) is K = 450 and the cash price within a month is S1 = 525 Answer

Now assume a futures contract on 100 shares that do not pay dividends. The share price is 15.10 and the market requires an initial guarantee of 15% of the value of the position with a maintenance balance of 150. What will be the value of the initial guarantee? Reply

If the next day the price rises to 15.5, what will be the value of the guarantee now? Reply Starting from the initial price of 15.1, it indicates from what price the buyer of the future will have to replace the guarantee Answer.

Answer 1

You have asked a question with multiple sub parts, in the same post. I have addressed the first four. Please post the balance sub parts separately.

Current value of dividend = D x e^{-r x t} = 50 x e^{-6% x 4/12} = $ 49.01

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Let the price of the future for a five-month contract, be F

Hence, F = S0 x e^rT - D0 x e^{r x (T - t)} = 500 x e^{6% x 5/12} - 50 x e^{6% x (5 - 4) / 12} = $ 462.41

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the value of the contract within a month if the strike (future transaction price) is K = 450 and the cash price within a month is S1 = 525 will be = S1 - PV(K) = 525 - 450 x e^{-r x t} = 525 - 450 x e^{-6% x (5 - 1) / 12} = $ 83.91

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the value of the initial guarantee = 15% x 100 x 15.10 = 226.50