Consider an option on a non-dividend-paying stock when the stock price is $28, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Using the Black-Scholes-Merton approach, What is the price of the option if it is a European call? What is the price of the option if it is an American call? What is the price of the option if it is a European put? Show that put–call parity holds.

Consider a European Call Option with a strike of 82. The current price of the underlying asset is 80, and the time to expiry is 5 months. The current market price of the option is 6.22. The risk-free rate is 4.1%. (b) You believe the true volatility is 28.4%. Is the option under-priced or overpriced? Hence what position should you take in option to make money. Explain. (Please provide Screenshots.)

Consider a European call option struck "at-the-money", meaning the strike price equals current stock price. There is one year until expiration and the risk-free annual interest rate is r = 0.06. We define the call option's "delta" as aCE(S,t) A as Is it possible to determine whether or not the call option's delta is greater than or less than 0.5?

Consider the following data (interest rate is per period): S = 100; K = 75;R = 1.20 ; u = 1.5 ; d = .5. 1. What is the binomial price of a European call option with two periods until expiration? What is the price an American option with the same strike price and same time to expiration. Is there ever early exercise? 2. Show that the binomial option price for a European put option with two periods to go until expiration is 3.125. Show that the binomial price for an American put is 6.25. Can you conclude from the difference in prices alone that early exercise may be optimal? When is it optimal? 3. Use your answers to (i) and (ii) to verify that put-call parity holds for European options, but not for American options. Explain all answers in detail or step by step solution.