[a] Write the general formula (in terms of S, r, q, t, T) for the forward price of a stock.

S = S(t) = current stock price

r = interest rate (assumed constant)

q = dividend rate (assumed constant)

t = calendar time

T = delivery date

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[b] Write the general formula for V(S,t), the value of a forward contract (in terms of S, R, q, t, T, and L, where L is the delivery price).

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[c] L and T are fixed; t and S = S(t) are changing over time. Consider two basic sensitivities for V(S,t): V/S and V/t. Please compute these. The first one gives how much the contract value changes when the stock price moves up or down.

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[d] Suppose the stock price moves up $1: Which moves more the stock itself or the value of the forward contract?

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[e] Recall the put-call parity relationship that relates the prices of the European-style call and put (for the same strike K and same expiry T):

[PRICE OF K-STRIKE CALL (EXPIRY T)] [PRICE OF K-STRIKE PUT (EXPIRY T)] =

[PRICE OF FORWARD CONTRACT WITH DELIVERY PRICE K (DELIVERY DATE T)]

Can you explain why this is true?

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[f] What do we mean when we say: The price difference between the European put and European call (equal strike and expiry) is independent of model.

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[g] How about the sum of the option prices? Is that independent of model?

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EXTRA CREDIT

Suppose on 31-Dec-2019 you entered into a forward contract to buy one share of stock XYZ for delivery price = L = $50 with delivery date 31-Dec-2020. You enter t and S(t) into your formula for V(S,t) to figure out todays value of the contract. Now suppose you learn to your surprise that interest rates are not constant; they can change in an uncertain way over the time period from today to 31-Dec-2020.

[A] Assume that todays stock price and the interest rates that prevail today have not changed. Will the forward price that you compute today (for delivery date 31-Dec-2020) change because of your revised view that future interest rates are uncertain?

[B] Will V(S,t), the value of the forward contract, change? Why or why not?