please help me finish the assignmentyou can write down or type no worry about that.ThanksDerivatives (Comm 4202)

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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