Question: Consider a call 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. Determine the terminal distribution of the asset price (hint: use binom.dist function in excel)
2. Describe the distribution (mean, standard deviation, shape, ...). Remember to use the probabilities to calculate mean, variance, and std. deviation.
3. What do you expect to spend to buy the underlier (assume $0 if not exercised) and what is the present value?
4. What do you expect to receive from selling the underlier (assume $0 if not exercised) and what is the present value?
5. Combine your answers to questions 3 and 4 to calculate the premium (value ) of a call option with strike $55 (10% otm) expiring in 12 months