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The current level of a broad stock market index is 1,474. Its dividend yield is 3% and the standard deviation of index returns is 20%. An American put option on the stock expires in 0.4 years. Its strike price is $1,480. The risk-free rate is 7% (annual, continuously compounded). Value the option using a binomial model with 2 periods of length 0.2 years each. What is the risk-neutral probability of an up movement? Report your answer in four decimal places

Consider call options on the same stock with the same maturity date. You bought two call options with strike prices of $54 and $90 for $6.09 and $1.69, respectively, and sold two call options with a strike price of $72 for $2.93 each.  What is your profit if the stock price is $81 on the expiration date? Report your answer in two decimal places

A put option on a stock with a current price of $100 has a strike price of $114 and currently sells for $16.39. What is the time value of the option?

The difference between a European and an American option is that the European option

The current price of a non-dividend-paying stock is $64.77 and you expect the stock price to either go up by a factor of 1.143 or down by a factor of 0.887 each period for 2 periods over the next 0.2 years. Each period is 0.1 years long. A European call option on the stock expires in 0.2 years. Its strike price is $65. The risk-free rate is 7% (annual, continuously compounded). What is the current value of the option? Report your answer in two decimal places

A protective put consists of a _____.

You wrote (sold) a put contract with a strike price of $50 and an expiration date in 6 months. The current stock price is $48 and the contract is for 100 shares. How big is your maximum loss (payoff)?

Bill buys a single call option with an exercise price of $40 for $7.37 from Simon. What is Simon’s profit if the stock price is $50 on the expiration date of the option?

You sold (wrote) 1 call option on IBM stock with an exercise price of $30 for $7.76 and bought 1 call option on the same stock with an exercise price of $40 for $2.45. Both options expire in 5 months. Such a portfolio is called a bear spread.  What is your total profit if the stock price is $100 in 5 months (in $)? Report your answer in two decimal places.

You wrote (sold) a put contract with a strike price of $50 and an expiration date in 6 months. The current stock price is $48 and the contract is for 100 shares. How big is your maximum gain/payoff (aside from the premium)?