On February 1st, September call option with exercise price of $55 written on Azt

Question

On February 1st, September call option with exercise price of $55 written on Aztec stock is sold for $4.375 per share and September put option with exercise price of $55 written the same stock is sold for $6 per share. At the time, T-bills coming due in September were price to yield 12%. Aztec stock was sold for $53 per share on February 1st.

1. If the call option, Aztec stock, and T-bills are correctly priced, what was the appropriate value of put option?

2. How to take advantage of this situation? Please show arbitrage profit using arbitrage table.

Explanation / Answer

You need to use the put-call parity relation:
C - P = S - K exp(-r dt) where
C and P are the call and put option's value
S = share price
K = strike
r = interest rate
dt = time to maturity = 8/12 year
In this case:
4.375 - P = 53 - 55/(1+0.08)
=> P = $2.3
You could profit from the situation by doing a reverse conversion: Sell short the stock, buy the (discounted) T-Bill, buy the call, sell the put.

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