5. The European call option on Asset Q that expires in one year has strike price $32 and option price $4. The forward price of Asset Q in one year is $36. The annual continuously compounded interest rate is 0.08. Find the price of the put option on Asset Q with strike price of $32.
5. The European call option on Asset Q that expires in one year has strike price $32 and option price $4. The forward price of Asset Q in one year is $36. The annual continuously compounded interest rate is 0.08. Find the price of the put option on Asset Q with strike price of $32.
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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![### European Call and Put Option Pricing
**Problem Statement:**
The European call option on Asset Q that expires in one year has a strike price of $32 and an option price of $4. The forward price of Asset Q in one year is $36. The annual continuously compounded interest rate is 0.08. Find the price of the put option on Asset Q with a strike price of $32.
**Explanation:**
In this problem, you are given:
1. **European Call Option:**
- **Strike Price**: $32
- **Option Price**: $4
2. **Asset Q:**
- **Forward Price in one year**: $36
3. **Interest Rate:**
- **Annual Continuously Compounded Interest Rate**: 0.08
Using the given information, calculate the price of the put option on Asset Q with a strike price of $32.
To find the price of the put option, you may use the Put-Call Parity for European options, which is expressed as:
\[ C - P = S_0 - Ke^{-rt} \]
Where:
- \( C \) is the call option price,
- \( P \) is the put option price,
- \( S_0 \) is the current price of the asset,
- \( K \) is the strike price,
- \( r \) is the continuously compounded risk-free interest rate,
- \( t \) is the time to expiration in years.
Given values can be substituted into the formula to find the required put option price.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e925dc7-1400-40ad-98f3-d1989a82945f%2Ff46f481f-70d3-47fa-a4d6-cb56856e77bd%2Frch56ke.jpeg&w=3840&q=75)
Transcribed Image Text:### European Call and Put Option Pricing
**Problem Statement:**
The European call option on Asset Q that expires in one year has a strike price of $32 and an option price of $4. The forward price of Asset Q in one year is $36. The annual continuously compounded interest rate is 0.08. Find the price of the put option on Asset Q with a strike price of $32.
**Explanation:**
In this problem, you are given:
1. **European Call Option:**
- **Strike Price**: $32
- **Option Price**: $4
2. **Asset Q:**
- **Forward Price in one year**: $36
3. **Interest Rate:**
- **Annual Continuously Compounded Interest Rate**: 0.08
Using the given information, calculate the price of the put option on Asset Q with a strike price of $32.
To find the price of the put option, you may use the Put-Call Parity for European options, which is expressed as:
\[ C - P = S_0 - Ke^{-rt} \]
Where:
- \( C \) is the call option price,
- \( P \) is the put option price,
- \( S_0 \) is the current price of the asset,
- \( K \) is the strike price,
- \( r \) is the continuously compounded risk-free interest rate,
- \( t \) is the time to expiration in years.
Given values can be substituted into the formula to find the required put option price.
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