Final answer:
To estimate the values of derivatives using Binomial Trees, we can use the characteristics of the underlying assets and apply appropriate models. The values of European and American options with IBM stock as the underlying asset can be calculated considering the stock prices, volatility, and other factors. If the dividend yield is 0, the options pricing would not be affected by dividend payments. Additionally, we can estimate the price of a derivative with the highest payoff by incorporating another asset, Microsoft stock, using the Margrabe model.
Step-by-step explanation:
For European and American call options, we can estimate their values using Binomial Trees with 20 steps. Let's use IBM stock as the underlying asset with a current price of $60, a strike price of $59, a risk-free rate of 6%, a dividend yield of 4%, and a time to maturity of 1 year. Using the actual stock prices to calculate the stock volatility, we can notice that the values of the options will differ depending on whether they are European or American options. European options can only be exercised at expiration, while American options can be exercised at any time before expiration.
If the dividend yield (d) is 0, we would observe that the pricing of the options would not be affected by dividend payments, as there would be no dividends to factor into the calculation.
For part b, we have an additional asset, Microsoft stock, with a current value of $70, a dividend yield of 5%, and a standard deviation of 20%. With these two underlying assets, we can estimate the price of a derivative with the highest payoff using the Margrabe model (Margrabe 1978).