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 period S0 = $50, T=12, u=1.03, d=1/1.03, R=1.0025
a. Determine the terminal distribution of the asset price (use binom.dist function in excel)
b. describe the distrubtion (mean, standard deviation, shape)
c. Use the distribution to calculate the premium of a call with strike$55 (10% otm) expiring in 12 months.
- C(k=$55,T=12) 10% out of the money call
- P(k=$55,T=12) put with same parameters
- Draw the payoff diagram (not profit) for buying one call and selling one put
- What is the combined premium? P($55,12) – C($55,12)
d. explain the premium in terms of what you expect to receive for selling and what you expect to spend for purchasing (all on discounted basis)
e. what is the premium of a put with the same strike and time to expiration ?
f. what is the 12 month forward price?