Suppose the current ABC stock price is $50 and an option trader speculates this price will fall below $50 soon. Which set of actions is the best strategy for him? buy the Stock and write a $50 call O buy $40 call and short $60 call short $40 put and buy $60 put O buy $50 call and buy $50 put
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- Suppose you construct a strategy based on options on a stock that is currently selling for $100. The strategy is as follows: Buy one call option having an exercise price of $95. Sell two calls having an exercise price of $100. Buy one call option having an exercise price of $105. All of the options are written on the same stock and all have the same expiration date. Compute the payoff (the dollars you receive) from this strategy at the expiration date for each of the following alternative stocks prices: $90, $95, $98, $100, $102, $105, and $110. What additional information would be required to determine whether your strategy had been profitable? What is the name of this strategy?You use the Black-Scholes-Merton model for a put option on a stock. You calculate N(d1) = 0.60 and N(d2) = 0.56. a) What is the delta of the put option? Solution for A = -0.40 b) You short 100 put options. How would you hedge your delta exposure using the underlying stock? How many shares would you need to buy or sell?You use the Black-Scholes-Merton model for a put option on a stock. You calculate N(d1) = 0.60 and N(d2) = 0.56. a) What is the delta of the put option? b) You short 100 put options. How would you hedge your delta exposure using the underlying stock? How many shares would you need to buy or sell?
- Label the following for this diagram: a. Name of options payoff b. Identify whether positive or negative premium c. Identify breakeven point d. What is the profit or loss when stock price is S60 at maturity e. Suppose you have this options position, should you exercise your right (if any) assuming that the stock price is $60 at maturity? Option Payoffs and Profits Long put $40 $20 $0 Option Payoff Option Profit Exerche Price $20 S40 $20 $40 S60 $80. Stock Price At Maturity Payoff and ProfitSuppose that put options on a stock with strike prices $18 and $20 cost $2 and $3.50, respectively. How can the options be used to create a bull spread? Construct atable that shows the profit and payoff for the spread.A call option with a strike price of $100 costs $5. A put option with a strike price of $85 costs $4. Explain how a strangle can be created from these two options. What is the cost of this strategy? When should I exercise my options? For what range of future stock prices would the strategy lead to a gain and what is the maximum gain you can receive? Prove your answer by providing an example. 5 For what range of future stock prices would the strategy lead to a loss and what is the maximum loss you could sustain? Prove it by giving an example.
- A stock price is $30. An investor buys one call option contract on the stock with a strike price of $28 and sells a call option contract on the stock with a strike price of $27. The market prices of the options are $2 and $1.7, respectively. The options have the same maturity date. Describe the investor’s position and the possible gain/loss he will get (taking into account the initial investment). Make a graph of your gain/loss.Suppose you own a put option on Apple stock with a strike price of $150. Suppose it is the expiration date of the option and the current stock price of Apple is $75. What payoff will you receive from making an optimal exercise decision on your option? 1. -$75 2. $0 3. $75You buy a put and a call on a stock that expire at time T. They are European options. Both the put and the call have an exercise price of $50. Plot the cash flows at the time of expiry. This strategy has a name. What is it?
- Consider the following options, which have the same two-year maturity and are written on the same stock. The firm does not pay dividends. Put option P1 has a strike price Xp1 = $50 Put option P2 has a strike price Xp2 = $100 Call option C1 has a strike price Xc1 = $100 Call option C2 has strike price Xc2 = $50 Your broker offers two trading strategies that can be derived from the options above. Strategy A: Long two puts P1 and long two calls C1 Strategy B: Long two calls C2 and long two puts P2 A. Which strategy would you choose if the two strategies have the same costs? Explain your answer. You now collect more information about the available securities. The stock has an implied volatility of 45% p.a.. The current risk-free rate is 1% p.a. The current stock price is $56. B. Calculate the value of the call option C1 using the Black-Scholes formula. Explain why such a deep out-of-the-money option still has a positive valuere: C. Calculate the cost of strategy B using the Black-Scholes…Suppose you are a seller . At time t = 0 you get £C from the buyer where C is the risk-neutral price of the option. You then have to design a hedging strategy which would allow you to meet your financial obligation in one year’s time. Your portfolio should consist of two investments: you are allowed to buy the underlying shares and to deposit money in the bank. The price of the share evolves according to a geometric Brownian motion. State the formulae you will need to compute the number of shares in the portfolio and the capital deposited in the bank at any time t, 0 ≤ t ≤ 1.Consider a stock with the current market price equal to So. A trader buys a call option on the stock with exercise price K1 and short sells a put with exercise price. The trader also buys a put option on the stock with K2 and short sells a call with K2, with K2>K1. Her position is equivalent to A) Borrowing the present value of K2 - K1 B) Holding the stock and borrowing the present value of K2 – K1 C) Lending the present value of K2 – K1 D) Holding the stock and lending the present value of K2 – K1