EFB344 Risk Management and Derivatives. 100% correct

You are interested in writing a European put option on a stock that is currently trading on $77.83, a strike price of $75, a risk-free rate of 2.647% p.a. (continuously compounded) and 3 months to maturity. The annual volatility (standard deviation) on the stock is 13.5% pa. Find the fair value for this option using each of the following three approaches. a. The Black-Scholes-Merton model b. A one-step binomial tree c. A two-step binomial tree Calculate the price of a three-month European put option on a non-dividend paying stock with a strike price of $50 when the current stock price is $50, the risk free rate is 10% pa and the volatility (standard deviation of returns) is 30% pa. What difference does it make to your calculation in the previous question if a dividend of $1.50 is expected in two months? What is the price of a of a European call option on a non-dividend paying stock when the stock price is $52, strike price of $50, the risk free rate is 12% pa, the volatility is 30%pa and the time to maturity is three months? What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1000 call options be made delta neutral when the delta of each option is 0.7? Calculate the delta of an at-the-money six-month European call option on a non-dividend paying stock when the risk-free rate is 10%p.a. and the stock volatility is 25% p.a. Show that the BSM model formula for a call option gives a price that tends to max(S0 – K, 0) as T goes to 0. Show that the probability that a European call option will be exercised in a risk-neutral world is N(d2). What is an expression for the value of a derivative that pays off $100 if the price of a stock at time T is greater than K?