4. When a European put is priced higher than its upper bound, you can arbitrage by devising atrading strategy that consists ofa) Writing the European callb) Writing the corresponding European call and investing the proceeds at a risk-freeinterest ratec) Writing the European put and investing the proceeds at a risk-free interest rated) Holding the European put and borrowing at a risk-free interest rate
Question
- When a European put is priced higher than its upper bound, you can arbitrage by devising atrading strategy that consists ofa) Writing the European callb) Writing the corresponding European call and investing the proceeds at a risk-freeinterest ratec) Writing the European put and investing the proceeds at a risk-free interest rated) Holding the European put and borrowing at a risk-free interest rate
Solution
The correct answer is c) Writing the European put and investing the proceeds at a risk-free interest rate.
Here's why:
The upper bound of a European put option is the present value of the strike price. If the price of the put is higher than this, it means the put is overpriced.
To take advantage of this, you could write (or sell) the overpriced put. This means you receive the premium (the price of the put) upfront. You could then invest this premium at the risk-free interest rate.
This way, you're guaranteed to make a profit regardless of what happens. If the put is exercised, you have to pay the strike price, but you've already received more than this amount from selling the put. If the put isn't exercised, you keep the premium and make interest on it.
Similar Questions
The price of a stock, which pays no dividends, is $30 and the strike price of a one year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lower bound and no arbitrage opportunities if it is above the lower bound? A. $5.00 B. $4.98 C. $3.98 D. $5.98
23. Consider the following information for an individual stock:• Current share price is $10• Risk-free rate is 5% pa compounded continuously• Volatility of the stock returns (σ) is 30% pa• Strike price is $12• Time to maturity of the option is 9 mths• The firm is expected to pay dividend estimated at $1 per share in 2 mths, $1.40 pershare in 8 mths and $1.80 per share in 14 mths.Use the closed-form Black-Scholes model to price the European put option with the abovecharacteristicsa) 3.96b) 5.13c) 1.25d) None of the above.
The no-arbitrage condition is violated at option expiry when the value of an in-the-money:A.put option is below its exercise price.B.put option is below its exercise value.C.call option is below the price of its underlying.
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. (a) What is the price of the option if it is a European call? (1 mark) (b) What is the price of the option if it is an American call? (1 mark) (c) What is the price of the option if it is a European put? (1 mark) (d) Verify that put–call parity holds. (1 mark)
The Black-Scholes option pricing model states:a.The value of an at-the-money call and put is the same.b.The risk-free interest rate has no bearing on the option price.c.The option price is independent of the underlying stock's anticipated return on investment.d.The risk-free interest rate is the most challenging metric to measure.
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