### Option Pricing and Put-Call Parity#### Given Information:1. **Stock Price:** - The current price to buy one share of XYZ stock is $500. The stock does not pay dividends.2. **Interest Rate:** - The risk-free interest rate, compounded continuously, is 6%.3. **European Call Option:** - A European call option on one share of XYZ stock with a strike price of $ K $ that expires in one year costs $66.59.4. **European Put Option:** - A European put option on one share of XYZ stock with a strike price of $ K $ that expires in one year costs $18.64.#### Task:Using put-call parity, determine the strike price, $ K $.#### Explanation:Put-call parity is a principle that defines the relationship between the price of European put and call options of the same class, with the same strike price and expiration date. The formula for put-call parity is:\[ C + K \cdot e^{-rT} = P + S_0 \]Where:- $ C $ is the price of the European call option- $ K $ is the strike price of the options- $ r $ is the risk-free interest rate- $ T $ is the time to maturity (in years)- $ P $ is the price of the European put option- $ S_0 $ is the current stock priceGiven the values:- $ C = \$66.59 $- $ r = 0.06 $- $ T = 1 $- $ P = \$18.64 $- $ S_0 = \$500 $We substitute these values into the put-call parity equation to solve for $ K $:\[ 66.59 + K \cdot e^{-0.06} = 18.64 + 500 \]This equation must be solved for $ K $.#### Detailed Solution:1. Calculate $ e^{-0.06} $, which is the exponential of $-0.06$: \[ e^{-0.06} \approx 0.94176 \]2. Substitute $ e^{-0.06} $ into the equation: \[ 66.59 + K \cdot 0.94176 = 18.64 +

Put call parity is a theorem which determines the relationship between a call option and a put…

You are given the following information: The current price to buy one share of XYZ stock is 500. The stock does not pay dividends. The risk-free interest rate, compounded continuously, is 6%. • A European call option on one share of XYZ stock with a strike price of K that expires in one year costs 66.59. • A European put option on one share of XYZ stock with a strike price of K that expires in one year costs 18.64. Using put-call parity, determine the strike price, K.

You are given the following information: The current price to buy one share of XYZ stock is 500. The stock does not pay dividends. The risk-free interest rate, compounded continuously, is 6%. • A European call option on one share of XYZ stock with a strike price of K that expires in one year costs 66.59. • A European put option on one share of XYZ stock with a strike price of K that expires in one year costs 18.64. Using put-call parity, determine the strike price, K.

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 4P: Put–Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call...

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