4) The premium of a call option with a strike price of $50 is equal to $5.5 and the premium of a call option with a strike price of $55 is equal to $4. The premium of a put option with a strike price of $50 is equal to $3.5. The risk-free rate of interest is 9%. In the absence of arbitrage opportunities, what should be the premium of a put option with a strike price of $55? All these options have a time to maturity of 6 months. (You are not allowed to use the put-call parity to solve this problem)

4) The premium of a call option with a strike price of $50 is equal to $5.5 and the premium of a call option with a strike price of $55 is equal to $4. The premium of a put option with a strike price of $50 is equal to $3.5. The risk-free rate of interest is 9%. In the absence of arbitrage opportunities, what should be the premium of a put option with a strike price of $55? All these options have a time to maturity of 6 months. (You are not allowed to use the put-call parity to solve this problem)

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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A trader buys (long) a call option with a strike price of $120 andsells (short) a put option with a strike price of $100. Both options have the same maturity.The call costs $20 and the price of put is $10. What is the portfolio payoff at expiry ifthe security price at expiry is $70? Draw a diagram showing the variation of the trader’sprofit with the security price at expiry.
Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. A. Using the Black model, calculate the price of a call option on a forward contract. B. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset. Should this pricing be any different from the one calculated in letter A? Explain your answer. C. Using the Black model, calculate the price of a put option on a forward contract. D. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset. Should this pricing be any different from the one calculated in letter C? Explain your answer.
If, for a $1000 premium, you buy a $100,000 put option on bond futures with a strike price of 110. At the same time, for a $1000 premium, you buy a $100,000 call option on bond futures with a strike price of 110. On the expiration date, the contract price is 106. Your total profit is $______ (negative if it is a loss).
Suppose you buy one SPX call option contract with a strike of 2200. At maturity, the S&P 500 index is at 2218. What is your net gain or loss if the premium you paid was $14? (Input the amount as a positive value.)
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?
Using put-call parity, if the price of an At-the-Money Call option maturing in 1 day is $3.14, what is the price of an of an At-the-Money Put option maturing in 1 day (give an approximation)? A. $0.95 B. $2.86 C. $3.14 D.$3.26
Suppose you combine two option contracts as follows. You buy a call option on a stock with an exercise price of $65 for a premium of 9$. At the same time you sell a call option on the same stock with an exercise price of $75 for a premium of $4. Both calls expire at the same time. The stock sells currently at $72. Answer the following questions about this investment strategy: 1. Determinethevalueatexpiration(thepayoffs)andtheprofitunderthefollowingoutcomes: a. The price of the stock at expiration is $78b. The price of the stock at expiration is $69c. Thepriceofthestockatexpirationis$62 2. Determine the following:a. The maximum profit b. The maximum loss 3. Determinethebreakevenstockpriceatexpiration(thestockpriceforwhichyourstrategydeliversno profit and no loss). 4. Depictthepayoffandprofitdiagramsofyourinvestmentstrategy.
Assume interest rate is zero. In a shout call option the strike price is $30. The holder shouts when the asset price is $40. What is the payoﬀ from the option if the ﬁnal asset price is $35? A. $0 B. $5 C. $10 D. $15
Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent. Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent.
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.
The premium on a call option is primarily a function of the difference in spot price S relative to the strike price X, the length of time until expiration T, and the volatility of the currency o. C = f(S-X, T, o) For each characteristic of a call option, use the table to indicate whether that would lead to a higher call option premium or a low call option premium (all else equal). Characteristic A lower spot price relative to the strike price A shorter time before expiration A higher level of volatility for the currency Higher Call Option Premium O Lower Call Option Premium When using a call option to hedge payables in an international currency, a U.S. based MNC can lock in the to obtain the needed foreign currency. maximum minimum amount of dollars needed
Consider the following information: Put Premium: $0.46 Strike Price: $32.82 Price of the underlying at initiation: $35.00 Calculate the breakeven price on a protective put option strategy (The breakeven price is the price of the underlying that would lead to a profit of $0).

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