Determining transaction costs in index arbitrage activity

Q1) Suppose the spot price of gold is $1700 per ounce. The futures price for delivery in six months is $1712, while the futures price for delivery in one year is $1720. The interest rate on 6-month loans is 1.00 percent (on an annual basis).

a) Ignoring transactions costs, does this represent an arbitrage opportunity? Why?

b) What is the implied interest rate for the first six months?

c) What is the implied forward rate six months hence? (Recall computing forward rates from bonds with different maturities)

d) Suppose the spot price of gold is, instead, $1706 per ounce. Assuming gold can be sold short at a transactions cost of $3 per ounce, describe an arbitrage strategy. What are the arbitrage gains, if any?

Q2) Suppose the spot price for Euro is $1.30, the futures price for delivery in 6 months is $ 1.29675. Assume that the 6 month borrowing/lending rate in Euro is 1.5 percent (annually, continuous compounding) and the corresponding rate in $ is 1.0 percent (annually, continuous compounding). (This is an FX application using the same cost of carry model).

a) Assume no transactions costs, do the above prices represent an arbitrage opportunity? Why?

Q3) Compute the 'fair' value of the two nearest to expiration futures contracts on the Hang - Seng Index (HSI) using HSI as the underlying asset

Answer the following questions:

a) What interest rate and dividend yield did you use?

b) Did the futures contract settle above or below HSI?

c) What are the transaction costs in index arbitrage activity?

d) What are the implied interest rates using the settlement prices?

e) What are the issues in doing index arbitrage (e.g. short selling)?

Options:

Q1) The first simple exercise that you should try is to draw payoff diagrams of various strategies. Get the web page http://www.cboe.com/DelayedQuote/QuoteTable.aspx for the closing prices of SPY options, or use the quotes on Bloomberg or Yahoo Finance.
Alternatively, use http://www.hkex.com.hk/rulereg/futrsksys/seriesprices.asp for prices of options trading on HKEX.
Here are a few possible strategies:

a) Buy the near term ATM (at-the-money) straddle.

b) Write the near term ATM call spread.

c) Buy the near term ATM put spread.

d) Write the near term ATM butterfly spread.

e) Buy 1 basket (SPX), Buy 1 near term ATM put

f) Buy 1 near term ATM put; Write 1 near term ATM call

g) Buy an ATM put spread; Buy an ATM call spread.

Q2)  What strategy will assure a profit if options on gold are priced as follows:

C(K= 1750, T1 = Apr ) > C(K= 1750, T2= June)
C(K= 1770, T1 = Apr ) > C(K= 1750, T1= Apr.)
C(K= 1750, T1 = Apr ) > C(K= 1770, T2= June)
C(K= 1750, T1 = Apr ) < C(S - PV(K))
P(K= 1750, T1 = Apr ) > C(K= 1750, T1= Apr)

Q3) The following three call options on gold, all expiring in three months, sell for:

    Exercise price            Option Price
    $1700                         $88
    $1750                         $57
    $1800                         $32

Consider the following position:

buy 1 call with K = 1700
sell (write) 2 calls with K = 1750
buy 1 call with K = 1800

What would be the values at expiration of such a spread for various prices of spot gold? What investment would be required to establish the spread? Given information about the prices of the $1700 and $1800 options, what could you predict about the price of the $1750 option?