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 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 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 IV. No, because the put-call parity relationship for American options suggests that St - K s ct - Pt < St - K exp(-Ro (T-t)).

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 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 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 IV. No, because the put-call parity relationship for American options suggests that St - K s ct - Pt < St - K exp(-Ro (T-t)).

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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5. Explain and give appropriate use of the following option trading strategies along with their Payoff.: a. Spreads b. Straddles c. Strangles d. Covered Call and Protective Put. State Put-Call Parity theorem for European options. European put and call options with a strike price of Rs. 24 and expiry in 6-months are trading at Rs. 5.09 and Rs. 7.78, respectively. The current stock price is Rs. 20.37 with a risk-free interest rate continuously compounding equal to 7.48%. Is there an arbitrage opportunity? How can it be exploited?
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 ?
You think that there is an arbitrage opportunity on the market. The current stock price of Wesley corp. is $20 per share. A one- year put option on Wesley corp. with a strike price of $18 sells for $3.33, while the identical call sells for $7. The one-year risk- free interest rate is 8%. Assuming that the put option is fairly priced, compute the fair price of the call option and explain what you must do to exploit this arbitrage opportunity and what will be your gain.
3. You have $150,000 for speculating with options and know the market value tendency is falling. Strike = $80 Call = $7 / option Put = $10 / option Probable market values at maturity: 60, 70, 80, 90, 100. Size of contract: one share. Required: a) Show the net results for each market value. b) What would be the maximum loss? c) What would be the equilibrium market value?
Suppose there is also a 1-year European put option on the same stock as in Question 3 with exercise price $30. The current stock price is also $25 and the stock price, in 1 year, will be either $35 (up by 40%) or $20 (down by 20%). The interest rate is 8%. This stock does not pay dividend. What is the value of the put option? Please use risk neutral probability method and assume discrete discounting. (2) What is put-call parity in option pricing? What needs to be true in order for put-call parity to hold?
Which one of the following statements is true? Multiple Choice O O O O A call with a strike price of $25 and a stock price of $23 has positive intrinsic value. A European style option is more valuable than an American style option. An American style out-of-the-money call option can have a positive value. A $40 put option has more intrinsic value than a $50 put option on the same underlying asset. The time value of an option is equal to the intrinsic value minus the option premium.
3
European plain vanilla call options with strikes 30 and 35 on the same non- dividend paying asset with spot price $ 35 are trading for $ 11.50 and $ 7, respectively. Does arbitrage exist, and if so, how do you take advantage of it?
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.
H2. Using the Black-Scholes model (BSOPM), compute the standard deviation that is implied by the following call option data as: the time to the option's maturity is 0.25 years, the price of the underlying option asset is RM30, the continuously compounded risk-free interest rate is 0.12. the exercise or striking price is RM30, and the cost or premium of the call is RM1.90.
What is the rho of a European put option with the following parameters? As a reminder, rho is defined as the first derivative of the option price with respect to the risk free rate. s0 = $40k = $39 r = 10%sigma = 20%T = 0.75 years (required precision 0.01 +/- 0.01) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r
Assume an interest rate of zero. A Call option and a Put option with the same exercise price, X = 100p are priced at 9p for the Call and 4p for the Put.The actual share is priced at S = 110p. Explain how you would exploit thearbitrage opportunity this presents. You must state which securities you would buy or sell. Show that the net cash position is 5p.

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