Derive a Theoretical Price for Each of the Following Futures

question 32

Essay

Derive a theoretical price for each of the following futures contracts quoted in the United States and indicate why and how the market price should deviate from this theoretical value. In each case, consider one unit of underlying asset. The contract expires in exactly three months, and the annualized interest rate on three-month dollar London InterBank Offered Rate (LIBOR) is 12%.
All interest rates quoted are annualized.
$\begin{array}{c}\begin{array}{lll} \text {Contract}\\ \text {a. Gold Futures:}\\\\ \text {b. Currency Futures:}\\\\ \text {c. Eurodollar Futures: (3-month \( \$ \) LIBOR):}\\\\ \text {d. Stock Index Futures:}\\\\\end{array}\begin{array}{lll} \text {Useful Information}\\ \text {Spot gold price=\$ 300 per ounce; cost of storage= }\\ \text { \$ 0.50 per ounce per month}\\ \text {\$ / € spot exchange rate =1.10dollars per euro; }\\ \text {3-month euro interest rate =4 \% }\\ \text {6 -month \$LIBOR interest rate =10 \% }\\\\ \text {Current value of stock index =1,200 ; annual}\\ \text { dividend yield=2 \%} \end{array} \end{array}$

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Definitions:

Database Contracts

Contracts that specifically deal with the creation, use, and maintenance of databases, including licensing and access rights.

Unilateral Mistake

In contract law, a mistake made by only one of the contracting parties. Unilateral mistake does not offer sufficient grounds for recession or renegotiation.

Rescind Contract

The process of legally voiding a contract, thereby returning all the parties involved to their original state as if the contract had never occurred.

Firm Offer

In contract law, refers to an offer that remains valid for a specified period during which it cannot be withdrawn by the offeror.