Consider a PUT option for an asset with the following parameters
• Current spot price is $50
• Option expires in 12 months
• Each month the asset could increase in value by 3% or decrease in value by inverse
• The risk free rate is 25 basis points per month
•S0 = $50, T=12, U=1.03, D=1/1.03, R=1.0025
• The strike is $55
1. For which of the 13 possible prices will the owner of the put choose to exercise the option and what is the probability of exercise?
2. Exercising the put involves selling the underlier at the strike price. What is the expected sale price? Hint: use the probability of exercise.
3. What is the expected price of purchase?
4. Use the expected sale price, and the expected purchase price to calculate the premium of the option. Remember to take the present value.
5. An investor purchase the call and sells the put. What do they spend out of pocket and what is the resulting payoff diagram?