Homework 5
Q1. Put-call parity
a.
Does
put-call parity mean the put and the call option (of the same stock, with same
expiration, with same strike price) have the same value/price?
b.
If
not, for put and call to have the same prices, what must be the relationship
between the strike price and the current stock price?
Hint: Find the Apple option page
from Yahoo Finance and look for the strike price where the call and put price
are similar.
Q2.A European call option and a European put option on a
stock both have the same strike price of $45 and expire in 6 months. Currently,
the market call price is $10 and the put price is $6. The risk-free rate is 2%
per annum, and the current stock price is $49. Identify the arbitrage
opportunity open to the trader. All the interest rates are with continuous
compounding.
Hint: Arbitrage table from the class example.
Q3. Suppose the price of a non-dividend-paying stock is
currently $60, its volatility is 30%, and the risk-free rate for all maturities
is 2% per annum.
Use Derivagem (see Session 5) and price the following 3
European “put” options expiring in 3 months (=3/12 years). In Derivagem, choose
“Black-Scholes – European” for Option Type in D17 cell.
a.
a put with $50 exercise price
b.
a put with $55 exercise price
c.
a put with $60 exercise price
Your submission must include all 3 Derivagem screenshots or
the outputs.
Hint: If you price a “call” with $55 exercise price, the
price is $6.6906. See the Derivagem output below.
Q4: Graph the relationship between the stock prices at
expiration and the profits of a butterfly spread using 3 “put” options in Q3.
Hint: To graph, use the same method in Homework 4
spreadsheet. Use stock prices ranging between $45 and $65 with $1 increment.
Your final graphs should look similar to Figure 11.7 in the textbook.
