Parameters:

Company A has a current stock price of $100 per share

There are two options that are outstanding. Both of these are European call options.

Option 1: 3 year maturity with a $120 strike price

Option 2: 2 year maturity with a $90 strike price

Questions:

Base case: What is the theoretical lowest and highest value for Option 1 and 2? Which of these options do you think is more valuable? Please describe your thought process. What model would you use to value these options?

Estimate the fair value of both options using a 30% volatility and a 5% risk free rate. Please use R/Python.

What if the volatility was 50%, would Option 1 or Option 2 increase more (as a percentage of the Base case)?

Case A: Let's assume that Option 2 was modified such that the holder can only exercise if the Company A stock price reaches $150 at the end of the option term - do you expect the value of Option 2 to increase or decrease relative to base case? And why? What methodology would you use to value this option?

Estimate the fair value of both options using a 30% volatility and a 5% risk free rate. Please use R/Python.