Consider the stock XYZ, which pays no dividends. It is currently trading at $14.
ID: 2806888 • Letter: C
Question
Consider the stock XYZ, which pays no dividends. It is currently trading at $14.93 per share. The following questions refer to options and futures on this stock that expire on 3/15/2018. You may assume that this is exactly 3 months or 0.25 years from now in calculation.
a. Zero-coupon T-bills expiring on 3/15/2018 are currently selling for 99.5013. what is the risk-free spot interest rate?
b. What is the future price of XYZ.
c. A call with a strike equal to the value found in part(b) is selling for $1.20. What is the price of a put with the same strike?
d. You want to make a synthetic short future with a contract price of $16/share. How can you do this using only puts and calls?
e. How much do you pay, or are you paid, at initiation to create this synthetic future?
Explanation / Answer
1
100*e^(-0.25*r)=99.5013
=>r=2%
2
14.93*e^(0.25*2%)=15
3
Put price=1.2+15*e^(-0.25*2%)-14.93=1.195
4
Sell call, Buy put