1-A European call option with strike $40 expiring in 6 months is priced at $3.25. The underlying is a dividend paying stock, currently priced at $39.50. The stock is expected to pay dividends of $0.75 in 2 and 5 months. The risk-free rate is 3% per year. What is the price of a 6 month European put option with strike $40?
a) If the market value of a put option on the same underlying, having the same strike and expiring in 6 months is $3.5, what arbitrage opportunities exist?
b) If the market value of a put option on the same underlying and having same strike and expiring in 6 months is $6, what arbitrage opportunities exist?
2-A European put option with strike $35 expiring in 6 months is priced at $4.25. The underlying is a dividend paying stock, currently priced at $34.5. The stock is expected to pay dividends of $0.85 in 3 and 8 months. The risk-free rate is 3% per year. What is the price of a 6 month European call option with strike $35?
a) If the market value of a call option on the same underlying, having the same strike and expiring in 6 months is $5, what arbitrage opportunities exist?
b) If the market value of a call option on the same underlying, having the same strike and expiring in 6 months is $2, what arbitrage opportunities exist?
Please show work and formula used in order to obtain the answer.