Essentials Of Investments
11th Edition
ISBN: 9781260316193
Author: Bodie
Publisher: MCG
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Chapter 15, Problem 24PS
A put option with strike price
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The stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option
(same maturity and expiration date) is $6. The risk-free interest rate is 5%. Are these prices compatible with the absence of arbitrage opportunities? Why?
O1. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-Ro (T-t)) and this is not satisfied in this case.
O II. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship.
O II. No, because the put-call parity relationship for American options suggests that St - Ks t - Pt s St - K exp(-Ro (T-t)).
O V.It depends on whether the stock pays dividends or not.
The hedge ratio of an at-the-money call option on IBM is 0.36. The hedge ratio of an at-the-money put option is -0.64. What is the
hedge ratio of an at-the-money straddle position on IBM? (Negative answer should be indicated by a minus sign. Round your answe
to 2 decimal places.)
Hedge ratio
2. Calculate the put premium according to put-call parity which gives no arbitrage opportunity.
Explain what transaction would you do if the put premium is below/above the put premium you
calculated.
European call option premium: c = $2
Stock price today: So- $30
Life of option: T=0.5
Risk-free rate for maturity T with continous compounding: r= 8%
Strike price: K= Decide on the K value yourself (carefully).
No dividends paid during life of option.
Chapter 15 Solutions
Essentials Of Investments
Ch. 15.2 - Plot the rate of return to the call-plus-bills...Ch. 15.2 - Prob. 2EQCh. 15 - Prob. 1PSCh. 15 - Prob. 2PSCh. 15 - Prob. 3PSCh. 15 - Prob. 4PSCh. 15 - Prob. 5PSCh. 15 - Prob. 6PSCh. 15 - Prob. 7PSCh. 15 - The following diagram shows the value of a put...
Ch. 15 - You are a portfolio manager who uses Options...Ch. 15 - An investor purchases a stock for 38 and a put for...Ch. 15 - ll. Imagine that you are holding shares of stock,...Ch. 15 - Prob. 12PSCh. 15 - The common stock of the R.U.I.T. Corporation has...Ch. 15 - 14. The common stock of the C.A.L.L. Corporation...Ch. 15 - Prob. 15PSCh. 15 - Prob. 16PSCh. 15 - Prob. 17PSCh. 15 - Prob. 18PSCh. 15 - Prob. 19PSCh. 15 - In what ways is owning a corporate bond similar to...Ch. 15 - Prob. 21PSCh. 15 - Consider the following options portfolio: You...Ch. 15 - Consider the following portfolio. You write a put...Ch. 15 - A put option with strike price 300 on the Acme...Ch. 15 - You buy a share of stock, mite a one-year call...Ch. 15 - Joe Finance has just purchased a stock-index fund,...Ch. 15 - You write a call option with X=50 and buy a call...Ch. 15 - Devise a portfolio using only call options and...Ch. 15 - Prob. 29CCh. 15 - Prob. 1CPCh. 15 - Prob. 2CPCh. 15 - Prob. 3CPCh. 15 - Prob. 4CPCh. 15 - Prob. 5CPCh. 15 - Prob. 1WM
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- 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 Profitarrow_forwardAs an option trader, you are constantly looking for opportunities to make an arbitrage transaction (that is, a trade in which you do not need to commit your own capital or take any risk but can still make a profit). Suppose you observe the following prices for options on DRKC Co. stock: $3.18 for a call with an exercise price of $60, and $3.38 for a put with an exercise price of $60. Both options expire in exactly six months, and the price of a six-month T-bill is $97.00 (for face value of $100). a. Using the put-call-spot parity condition, demonstrate graphically how you could synthetically re-create the payoff structure of a share of DRKC stock in six months, using a combination of puts, calls, and T-bills transacted today. b. Given the current market prices for the two options and the T-bill, calculate the no-arbitrage price of a share of DRKC stock. c. If the actual market price of DRKC stock is $60, demonstrate the arbitrage transaction you could create to…arrow_forwardConsider 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…arrow_forward
- Suppose that a European call option to buy a share for $ 90.00 costs a . Under what circumstances will the SELLER of the option make a profit ? \$4.00 and is held until maturity . ( DRAW the GRAPH to show ALL answers ) b . when will the option be exercised ( at what price , show on graph ) ? c . What is the Maximum profit for SELLER and at what stock price ? d . What is the Maximum loss for SELLER and at what stock price ? e . What will be profit / loss for SELLER if St is 150 ?arrow_forwardSuppose that a European call option to buy a share for $100.00 costs $5.00 and is held untilmaturity. Under what circumstances will the holder of the option make a profit? Underwhat circumstances will the option be exercised? Draw a diagram illustrating how the profitfrom a long position in the option depends on the stock price at maturity of the option. Suppose that a European put option to sell a share for $60 costs $8 and is held untilmaturity. Under what circumstances will the seller of the option (the party with the shortposition) make a profit? Under what circumstances will the option be exercised? Draw adiagram illustrating how the profit from a short position in the option depends on thestock price at maturity of the option.arrow_forwardThe hedge ratio of an at-the-money call option on IBM is 0.37. The hedge ratio of an at-the-money put option is −0.63. What is the hedge ratio of an at-the-money straddle position on IBM? Note: Negative answer should be indicated by a minus sign. Round your answer to 2 decimal places.arrow_forward
- Short straddle is an option strategy that involves simultaneously selling a put and a call on the same stock with the same strike price, which is equal to the current stock price. Profit or Loss What is the purpose of this strategy? $400 SO 30 To profit from a large price increase SHORT STRADDLE A To profit from large price deviations from the current price D) To profit from a large price decrease 40 B To profit from the lack of price deviations from the current price 50 Stock Price at Expiration :arrow_forwardTick all those statements on options that are correct (and don't tick those statements that are incorrect). B a. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. b. If interest is compounded continuously then the put-call parity formula is P+ S(0) = C + Ker where T is the expiry time. An American put option should never be exercised before the expiry time. d. In general the equation S(T) +(K-S(T)) = (S(T)-K)+ +K is valid. e. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. C.arrow_forward1. Given that the Asian option is an option where the strike price is equal to the average prices of the underlying stock, what is the strike price if you have the following stock prices? 7.822, 3.026, 9.206, 7.211 2. The asian option is an option where you can exercise the option at any time (True or False) 3. floors can be used to limit the losses for your credit portfolio if you are invested in variable rate bonds (True or False)arrow_forward
- 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.arrow_forwardThe stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option (same maturity and expiration date) is $6. The risk-free interest rate is 8%. Are these prices compatible with the absence of arbitrage opportunities? Why? O I. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-Ro (T-t)) and this is not satisfied in this case. O II. It depends on whether the stock pays dividends or not. O III. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship. O IV. No, because the put-call parity relationship for American options suggests that St - Ks ct - Pt < St - K exp(-RO (T-t)).arrow_forward1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.arrow_forward
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