question archive A European call option and put option on a stock both have a strike price of 20 dollars and an expiration date of 3 months
A European call option and put option on a stock both have a strike price of 20 dollars and an expiration date of 3 months
Subject:FinancePrice:2.86 Bought3
A European call option and put option on a stock both have a strike price of 20 dollars and an expiration date of 3 months. Both sell for 3 dollars. The risk free rate for all maturities is 10% per year continuously compounded and remains unchanged over time. The current stock price is 19 dollars. A one dollar dividend is expected in one month. Identify the arbitrage opportunity open to a trader and provide the exact details of generating the quantity. Be very specific showing the exact trading strategy.
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Sell Call (CF = +3), borrow 19 (CF = +19).
Buy Put (CF = -3), buy share of stock( CF = -19).
Total CF = 3 + 19 - 3 - 19.
In 1 month, receive dividend, CF = +1.
In 3 months, either sell stock (S<20) and exercise your put: CF = +20
or sell stock (S >= 20) and pay the exercised call: CF = + 20
And pay off the Debt: CF = -19 e^[0.25x0.10]
Total CF = 1 e^[0.166x0.10] + 20 - 19 e^[0.25x0.10] = + 1.537
which is also 1.50 e^[0.25x0.10], the accumulated value of the risk-free profit from the other strategy Risk free point.
