A non-dividend paying stock sells for $110. A call on the stock has an exercise price of $105 and expires in 6 months. If the annual interest rate is 11% (0.11) and the annual standard deviation of the stocks returns is 25% (0.25), what is the price of a European put option according to the Black-Scholes-Merton option pricing model.

A call and put expire in 0.41 year and have an exercise price of $100. The underlying stock is worth $90 and has a standard deviation of 0.25. The annual risk-free rate is 11 percent. The annual dividend yield (q) on the stock is 2%. The put option price from the three-period binomial model is: