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Assignment #3 – Due March 6, 2020
1. It is March 5, 2020. A stock index is traded at a level of 3123, the risk-free rate
is 2.53% with continuous compounding, and the dividend yield is 3.08%. What
is the futures price for an index futures contract that expires on September 18,
2020?
2. The USD-CAD exchange rate is 1.3283, the 6-month Canadian risk-free rate is
1.73%, and the 6-month U.S. risk-free rate is 0.8%. Both risk-free rates are continuously compounded. From a U.S. investor’s perspective, what is the futures
price for a USD-CAD currency futures contract that expires in six months?
3. A stock is expected to pay a dividend of \$1 per share in two months and in five
months. The stock price is currently traded at \$50 per share, and the 2-month,
3-month, 5-month, and 6-month risk-free rates are 3%, 3.025%, 3.05%, and
3.10% per annum with continuous compounding, respectively.
(a) What is the futures price on the stock? What is the initial value of the
futures contract to a long position holder?
(b) If the price of the stock is \$48 and the term structure of interest rates is
unchanged in three months, what will be the futures price and the value of
the short position in the futures contract?
4. A stock price is currently \$40. Over each of the next two three-month periods it
is expected to go up by 10% or down by 10%. The risk-free interest rate is 5%
per annum with continuous compounding.
(a) What is the value of a six-month European call option with a strike price of
\$42?
(b) What is the value of a six-month American put option with a strike price of
\$42?
5. Consider an option on a stock when the stock price is \$30, the exercise price is
\$29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum,
and the time to maturity is four months.
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(a) What is the price of the option if it is a European call or put based on the
Black-Scholes-Merton model?
(b) What is the price of the option if it is an American call or put based on a
two-period binomial model?
6. The price of a stock index futures contract is at 423.70, and the stock index level
is at 420.55. The three-month call option on the index with a strike price of 400
is traded at \$26.25, and the three-month put option with the same expiration
is traded at \$3.25. The three-month continuous compounding risk-free rate is
2.75%. Determine whether the futures and options are priced correctly in relation to each other. If they are not, construct a risk-free portfolio and show how
it will earn a rate better than the risk-free rate.
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