1.You short one December futures contract when the futures price is $2,020 per
unit (day 0). Each contract is on 100 units and the initial margin per contract that you
provide is $4,000. The maintenance margin per contract is $3,000. During the next day
(day 1) the futures price rises to $2,024 per unit. What is the balance of your margin
account at the end of the day (day 1)? In the following day (day 2), the futures price
decreases to $2,016 per unit. What is the balance of your margin account at the end of
day 2?
2. ) A company has a $84 million portfolio with a beta of 1.2. The futures price for
a contract on an index is 2100. Futures contracts on $250 times the index can be traded.
What trade is necessary to reduce beta to 0.9? What trade is necessary to increase beta
from 1.2 to 1.8?
3. On March 1 a commodity’s spot price is $40 and its August futures price is
$49. On July 1 the spot price is $64 and the August futures price is $63.50. A company
entered into futures contracts on March 1 to hedge its purchase of the commodity on July
1. It closed out its position on July 1. What is the effective price (after taking account of
hedging) paid by the company?
4. Given that the crude oil price is $95 per barrel. The annual storage cost is $5 per
barrel paid at the end of each year. The risk free rate is 5% per annum with continuous
compounding. You should assume that the crude oil is a consumption commodity and there
is no way to borrow the crude oil for a short sale. But, of course, you can borrow or lend
money at the risk free rate. Based on the price formula in our textbook, the no arbitrage
price range for a two-year futures contract on the crude oil in a rational market should be
5. A call option on a stock has a delta of 0.5. A trader has sold 1,000 options.
What position should the trader take to hedge the position? If the stock price increases in
the next day, should the trader _____ (buy or sell) some shares to continue to hedge.
6. Consider an American put option on a non-dividend-paying stock where the
stock price is $500, the strike price is $600, the risk-free rate is 1% per month, the volatility
is 36% per annum, and the time to maturity is six months.
a. Calculate the up step size u, down step size d, growth factor per step a, and risk-neutral
probability of up move p for a two-step tree.
b. Value the option using a two-step tree, more specifically, please show the price of this
stock at each of the following node: A, B, C, D, E, and F. Please also show the value of
this put option at each of the following node: D, E, F, B, C, and A.
c. If this is an American Call option, what is the value of the call option at each of the
following node: D, E, F, B, C, and A.
The two-step tree is shown in the following figure. (the figure is the upload picture)
7. Please use Black-Scholes formula for this question and keep your answers to the
4 digits.) ABC is a non-dividend-paying stock that has the potential to bankrupt or to be
taken over. Current stock price is $100/share; the risk-free interest rate is 12% per annum
with continuous compounding; the volatility is 20% per month; and the time to maturity is
2 years. Your manager wants you to construct a strap using the at-the-money European
options. How much is the cost of constructing this strap? More specifically,
a. What is the value of S0, K, r, σ, T, d1 and d2 in the Black-Scholes formula?
b. What are N(d1) and N(d2) in the Black-Scholes formula? What is the price of this European
call option? What is the price of this European put option?
c. Suppose ABC goes to bankrupt at maturity and the stock price at maturity is $0, what is
the percentage return to your strap?
d. Suppose ABC price goes to $300/share at maturity, what is the percentage return to your strap?
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