What is put-call parity and why does it hold

Question 1: What is put-call parity and why does it hold? Please show your proof?

Question 2: The following prices are observed. How are you going to profit from the opportunity?

• Stock A is selling for \$95.00
• Call options on stock A with exercise price of 90 and with April expiration are selling for \$9 per share
• Put options on stock A with exercise price of 90 and with April expiration are selling at \$2.5 per share
• At the current t-bill rate, \$89 invested today will grow to 90 at the option's maturity date.

Question 3:

The following prices are observed. Use an arbitrage strategy to get an arbitrage profit.

Stock A is selling for \$95.
Call options on stock A with an exercise price of 85 is selling for \$12 per share
Call options on stock A with an exercise price of 90 is selling for \$10 per share
Put options on stock A with an exercise price of 85 is selling for \$1.25 per share
Put options on stock A with an exercise price of 90 is selling for \$1.75 per share
At the current t-bill rate, \$89 invested today will grow to 90 at the option's maturity date and 84.06 invested today will grow to 85 at the option's maturity date.

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