1. Use European options to create a short forward position, where you agree today to sell a stock in three months at a (forward) price of K
2. A trader creates a long butterfly spread from options with strike prices of $90, $100, and $110 per share by trading a total of 20 option contracts (buy 5 contracts at $90, sell 10 contracts at $100 and buy 5 contracts at $110). Each contract is written on 100 shares of stock. The options are worth $15, $18, and $22 per share of stock, respectively.
What is the value of the butterfly spread at maturity as a function of the then stock price?
What is the profit of the butterfly spread at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.
3. A trader creates a long strangle with put options with a strike price of $90 per share, and call options with a strike of $105 per share by trading a total of 40 option contracts (buy 20 put contracts and buy 20 call contracts). Each contract is written on 100 shares of stock. The put option is worth $10.5 per share, and the call option is worth $6.5 per share.
What is the value of the strangle at maturity as a function of the then stock price?
What is the profit of the strangle at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.
4. The current price of a non-dividend-paying stock is $70. Over the next six months it is expected to rise to $80 or fall to $62. Assume the risk-free rate is zero. An investor sells a call option with a strike price of $72 per share. How would the investor hedge the call option position? Assume that the option is written on 100 shares of stock.
5. The current price of a non-dividend-paying stock is $70. Over the next six months it is expected to rise to $80 or fall to $62. Assume the risk free rate is zero. An investor buys a put option with a strike price of $72. How would the investor hedge the put option position? Assume that the option is written on 100 shares of stock.