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, , .03, /1.03, .00251. Determine the terminal distribution of the asset price (hint: use binom.dist function in excel)
2. Use the distribution to calculate the discounted expected value of each of the following cash flows a) C(k=$55,) 10% out of the money call
b) P(k=$55,) put with same parameters
c) Draw the payoff diagram (not profit) for buying one call and selling one put
d) What is the combined premium? P($55,12) - C($55,12)
3. Use the distribution to calculate the discounted expected value of each of the following cash flows a) A cash flow exactly equal to the value of the share at time 12
b) A constant cash flow of $55
4. Use the binomial probabilities to calculate each of the following assuming rational behavior in exercising the call option
a) expected sale price and discounted expected sale price
b) probability of exercise and the purchase price if exercised
c) expected purchase price (multiply by probability) and discounted expected purchase price
Consider a call option with the following parameters
• Current spot price is $50
• Option expires in 1 year
• The annualized volatility is 11.5%
• The interest rate is 3% per year
• The strike is $55
5. Use the Black-Scholes formula to determine
a) discounted expected sale price
b) probability of exercise and the purchase price if exercised
c) expected purchase price (multiply by probability) and discounted expected purchase price