5.Use your words or examples to explain why the value of a call option increases as the market interest rate increases, and why the value of a put option increases as the market interest rate decreases. (8 points)

6.6. European options can only be exercised on the expiration date, while American options can be exercised on any date before the expiration. Intuitively, American options should be more popular among investors. However, we rarely see American options being traded on today’s market. Use your words to explain why most of the options on the market are European options. (8 points)

7.7. Black-Scholes model shares common intuitions with risk-neutral option pricing model (also known as the binomial option pricing model). One of the biggest underlying assumptions of risk-neutral (binomial) model is that we live in a risk-neutral world. In a risk-neutral world, all investors only demand risk-free return on all assets. Although the risk-neutral assumption is counterfactual, it is brilliant and desirable because the prices of an option estimated by risk-neutral approach are exactly the same with or without the risk-neutral assumption. Use your words to explain why that is the case, and how risk-neutral assumption greatly simplifies the calculations of risk-neutral option pricing approach. (8 points)