1. Put-call parity
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?
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.
2. 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.
3. 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.
a put with $50 exercise price
a put with $55 exercise price
a put with $60 exercise price
Hint: If you price a “call” with $55 exercise price, the price is $6.6906. See the Derivagem output below.
4. Graph the relationship between the stock prices at expiration and the profits of a butterfly spread using 3 “put” options in Q3.