How do you calculate:

QUESTION 4 [40]

4.1 You write a call option with X = 45 and buy a call with X = 60. The options are on the same stock and have the same expiration dated. One of the call options sells for R4 (X = 45) and the other for R9 (X = 60).

4.1.1 Determine the payoff and profit for this strategy at the option expiration date.

4.1.2 Draw the payoff graph at expiration for this strategy.

4.1.3 What is the break-even point for this strategy? Indicate whether the investor is bearish or bullish on the stock.

4.2 Use the Black-Scholes formula to find the value of a call option with the following stock:

Time to maturity is 6 months

Standard deviation 50% per year

Exercise price R50

Stock price R50

Annual interest rate 3%

Calculate d1 and d2 to two decimal places.

4.3 You are valuing a call option with an exercise price of R100 and one year to expiration. The underlying stock pays no dividends, its current price is R100 and you believe the stock price has an equal chance to increase by 20% or to decrease by 20%. The risk-free rate of interest is 8%. 4.3.1 Using the binomial option pricing model, draw the binomial tree applicable.

4.3.2 Calculate the call options value using the two-state price model.