### 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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