As an option trader, you are constantly looking for opportunities to make an arb
ID: 2708225 • Letter: A
Question
As an option trader, you are constantly looking for opportunities to make an arbitrage transaction. Suppose you observe the following prices for options on ABCD co stock: $3.18 for a call with an exercise price of $60, and $3.38 for a put with an exercise price of $60. Both options expire in exactly six months, and the price of a six month T-Bill is $97(for face value of $100).
A) using the put-call-spot parity condition, demonstrate graphically how you could synthetically recreate the payoff structure of a share of ABCD stock in six months using a combination of puts, calls, and T-Bills transacted today.
B) Given the current market prices for the two otions and the T-bill, calculate the no-arbitrage price of a share of ABCD stock.
C) If the actual market price of ABCD stock is $60, demonstrate the arbitrage transaction you could create to take advantage of the discrepancy. Be specific as to the positions you would need to take in each security and the dollar amount of your profit.
Explanation / Answer
Put call parity states that
(Price of Call) - (Price of Put) = (Price of stock) e ^( - dividend rate X time in years) - (Exercise or Strike Price) e ^( - risk free rate X time in years)
To replicate a share of stock, just isolate that variable. Since there is no dividend, it's simple.
Stock = Put - Call - (Exercise or Strike Price) e ^( - risk free rate X time in years).
In other words buy a put, sell a call, and buy 60 dollars worth of T bills.
We can use the price of a T bill to get the risk free rate.
97 X e ^ (0.5 X risk free rate) = 100, or e ^ ( - risk free rate X time in years) = .97.
If we want r, then we can do this:
2 X ln (100/97) = .06092
To find the non arbitrage price of the stock, we plug in the values we have into the Put Call Parity formula and solve.
3.18 - 3.38 = S - (60 X .97)
S = 58
If the price of the stock is 60, then it is overvalued by Put Call parity and we would want to SELL the stock to take advantage,
Then to make up for the sold stock, you would BUY a put and SELL a call and BORROW 60 dollars at the risk free rate.
Your loss would be $58, as calculated before, and you would gain $60, leaving you a net $2 profit with this transaction.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.