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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.

Now Priced at $25 (50% Discount)

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## Q : Determining the weighted average cost of capital

Assuming debt is risk-free, use the information given above to estimate the unlevered equity betas of each of these companies.