### Option Pricing and Payoff Analysis#### Problem Statement:Consider a call option on the S&R index with 6 months to expiration and a strike price of $1000. Suppose that the effective rate compounded semiannually is 2% and the premium for this call is $93.81.(a) Draw the payoff and profit graphs for the call option holder.(b) If the S&R index price at expiration is $1100, will the owner exercise this option? What is the profit?(c) If the S&R index price at expiration is $900, will the owner exercise this option? What is the profit?#### Solutions:**(a) Payoff and Profit Graphs:**To draw the payoff and profit graphs, we need to follow these steps:- **Payoff Graph:** - The payoff of a call option at expiration is max(S - K, 0), where S represents the stock price at expiration and K is the strike price. - For a strike price of $1000, the payoff graph will be zero for any stock price below $1000. - For stock prices above $1000, the payoff increases linearly as the stock price increases.- **Profit Graph:** - The profit is the payoff minus the premium paid for the option. - Payoff = max(S - K, 0) - Profit = Payoff - Premium - For this call option, the premium paid is $93.81. - Therefore, the profit graph will start at -$93.81 for stock prices below $1000 (since the option is not exercised and the premium is lost). - For stock prices above $1000, the profit will be max(S - K, 0) - 93.81, increasing linearly after crossing the premium breakeven point.**(b) S&R Index Price at Expiration is $1100:**- If the S&R index price at expiration is $1100, the payoff will be: - Payoff = $1100 - $1000 = $100- The profit will be: - Profit = $100 - $93.81 = $6.19- Therefore, the owner will exercise the option and the profit will be $6.19.**(c) S&R Index Price at Expiration is $900:**- If the S&R index price at expiration

Here is the Payoff and Profit diagram if the call option is shown below:

4. Consider a call option on the S&R index with 6 months to expiration and a strike price of $1000. Suppose that the effective rate compounded semiannually is 2% and the premium for this call is $93.81. (a) Draw the payoff and profit graphs for the call option holder. (b) If the S&R index price at expiration is $1100, will the owner exercise this option? What is the profit? (c) If the S&R index price at expiration is $900, will the owner exercise this option? What is the profit?

4. Consider a call option on the S&R index with 6 months to expiration and a strike price of $1000. Suppose that the effective rate compounded semiannually is 2% and the premium for this call is $93.81. (a) Draw the payoff and profit graphs for the call option holder. (b) If the S&R index price at expiration is $1100, will the owner exercise this option? What is the profit? (c) If the S&R index price at expiration is $900, will the owner exercise this option? What is the profit?

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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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.)
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.
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
Please show step by step how to solve this AMT is currently trading at $110/share. You bought 4 CALL-option contracts on AMT with a strike price of $100 for $26.0 each and sold 4 CALL - option contracts on AMT with a strike price of $130 for $7.0 each. a. What will be your total $ and % gain/loss if AMT price is $115 at the expiration date?b. What will be your total $ and % gain/loss if AMT price is $135 at the expiration date?c. What will be your total $ and % gain/loss if AMT price is $100 at the expiration date?
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
Give typing answer with explanation and conclusion You are considering purchasing a put on a stock with a current price of $33. The exercise price is $35, and the price of the corresponding call option is $3.25. According to the put-call parity theorem, if the risk-free rate of interest is 4% and there are 90 days until expiration, the value of the put should be:
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. What would the price of the call option ‘c’ need to be for put-call parity to hold?
What is the appropriate risk-free rate on May 11, 2022 for an option that expires on Oct 20, 2022 if the T-bill with closest maturity is quoted as 3.65/3.44? a. What is the un-annualized discount rate? Round your answer to two decimals. b. What is the T-bill price? Round your answer to two decimals b . What is the approximate risk-free rate? % Round your answer to two decimals
Consider a call option on one share of BP with a strike price of $70 and exercise time 1 quarter (3 months). Suppose the current stock price for BP is S(0) = $65 per share. Suppose further that A(0) = $100, A(1) = $102 and two possible prices for S(1) are S $74 with probability 0.5, S(1) = $66 with probability 0.5. Evaluate the expected returns E(Ks) and E(Kc) for the stock and the 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.
The speculator buys one put option at a strike price of $70/barrel and expiry date October 2021 for a premium of $1.20/barrel. Consider the following expected payoff chart for buying a put option. What are the names of point A and B? What is the exact value of A? What is the exact value B?
2. What are the prices of a call option and a put option with the following characteristics? Stock price = $74Exercise price = $72Risk-free rate = 2.7% per year, compounded continuouslyMaturity = 4 monthsStandard deviation = 52% per year 3. Draw the payoff picture at expiration for a long position in a call option that has a premium of $1.25 and a strike price of $30. 4. Draw the payoff picture for a short position in the call option given in Problem 2.5. Draw the payoff picture at expiration for a long position in a put option that has a premium of $3.50 and a strike price of $80. 6. Draw the payoff picture for a short position in the put option given in Problem 4.please let me have it by mornin. Thank you.

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