4. Multi Step Binomial Tree: Consider again the European call option with three months left to...
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4. Multi Step Binomial Tree: Consider again the European call option with three months left to maturity written on a non-dividend paying stock. As in exercise 2a, let today's stock price be 100 kr, the stock volatility be 30% and the risk free interest rate be 3%. Construct a five-step Binomial tree for the stock from exercise and calculate today's price of the European call option with strike price K = 105. (b) Compare your valuation results of the European call in exercise 2a and 4a. Are they the same? Why or why not? (c) Same as 4a, except you should price an American call option with strike price K=105. (Hint: a bit of thinking may save a lot of computations.) (d) A long straddle strategy involves buying a European call and put option with the same strike price (and the same underlying stock). Draw the payoff function of a long straddle if the call and put options with strike price K = 105 are used and then compute the price of this straddle using the five step binomial tree from exercise 4a. (Hint: again a bit of thinking may save a lot of computations.) 4. Multi Step Binomial Tree: Consider again the European call option with three months left to maturity written on a non-dividend paying stock. As in exercise 2a, let today's stock price be 100 kr, the stock volatility be 30% and the risk free interest rate be 3%. Construct a five-step Binomial tree for the stock from exercise and calculate today's price of the European call option with strike price K = 105. (b) Compare your valuation results of the European call in exercise 2a and 4a. Are they the same? Why or why not? (c) Same as 4a, except you should price an American call option with strike price K=105. (Hint: a bit of thinking may save a lot of computations.) (d) A long straddle strategy involves buying a European call and put option with the same strike price (and the same underlying stock). Draw the payoff function of a long straddle if the call and put options with strike price K = 105 are used and then compute the price of this straddle using the five step binomial tree from exercise 4a. (Hint: again a bit of thinking may save a lot of computations.)
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