PSTAT 170 INTRODUCTION TO MATHEMATICAL FINANCE QUIZ 2
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PSTAT 170 INTRODUCTION TO MATHEMATICAL FINANCE
QUIZ 2
AUGUST 15, 2022
Problem 1 (5 pt). On August 15, 2022 you could purchase 1.06 US dollars (USD) with one Swiss franc (CHF). The continuously compounded USD interest rate is 0.025 and the continuously compounded CHF interest rate is -0.005. You want to enter a forward contract on August 15, 2022, to purchase 100,000 CHF in exactly 9 months time. What is the forward price?
Problem 2 (10 pt). Rio Tinto’s stock price was $60.20 on August 12, 2022. A 6-month call option with strike $66.60 has a premium of $2.76, and a put option with the same strike and maturity has a premium of $8.98. Assume the continuously compound risk-free rate is 2.5%.
(a) Rio Tinto is expected to pay dividends in 2022 and 2023. Compute the present value of the dividends the company pays to its shareholders by February 12, 2023.
(b) A 6-month call option on Rio Tinto with strike K has a premium of $4.81, and a put option with the same strike and maturity has a premium of $5.33. Find the value of K .
Problem 3 (10 pt). A long straddle strategy involves buying a put and a call option with the same strike price and the same maturity. This is a bet on variance: if the stock price rises, the call will be profitable, and if the stock price falls, the put will be profitable. The price of Snap stock was $11.50 on August 12, 2022, and you enter into a long at-the-money straddle with a 3-month maturity. Assume the risk-free rate is 3%, and suppose that the combined premium for the call and put options is $1.97. Draw the P&L diagram for this long straddle strategy and compute the break-even prices of Snap.
Problem 4 (15 pt). The closing price of Intuitive Surgical shares was $236.02 on Thursday, August 11, 2022. Suppose you want to initiate a long position in an asymmetric butterfly spread with a maturity of one month. The long asymmetric
butterfly spread has the following payoff structure at maturity:
(1)
0 if S1/12 < 220
⎪
Asymmetric Butterfly Spread Payoff =
0 if S1/12 > 280 The payoff in equation (1) can be represented graphically as follows:
Payoff
220 240 280 S1/12
The following options maturing in one month are available:
Call |
Strike |
Put |
26.21 10.20 0.70 |
220 240 280 |
4.34 10.99 64.10 |
To simplify computations, assume that a year has 360 days; 30 days per month. The risk-free continuously compounded interest rate is 2% per year.
Note: An asymmetric butterfly spread can be created using either put or call options.
(a) What is the price of a long asymmetric butterfly spread that can be designed using the available call option contracts?
(b) What is the price of a long asymmetric butterfly spread that can be designed using the available call option contracts?
(c) Compare the premiums in (a) and (b). Which asymmetric butterfly strategy is more advantageous if you want to enter into a long position?
2022-09-06