Question

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)

Answer 1

5.i)Value of a Call Option always increases when the Interest rate increases.An increase in interest helps in saving the outgoing interest to be paid on amount taken as a loan or helps to earn more interest income on other savings accout.Further it can be explained with the help of an example :

Suppose some shares are available at the market @ $150,we can buy 100 shares of the stock outright which could cost to us $ 15,000.Now instead buying Stocks we cought Long an ATM Call Option for $ 10 .So now the total cost would be $ 1,000.Now the left over amount remains as $ 14,000.So this differential amount amount will help in saving the outgoing interest payment on this loaned amount .Alternatively the we could invest the diffrential amount somewhere which will generate an interest income ( assumed interest rate is 6%) of $ 840 in one year.So once the interest interest becomes higher ,the interest income from the investment will be higher & the Option Price also will increase.

ii)Value of a Put Option always increases when the Interest rate decreases.Generally Shorting a stock with a decling price will bring in cash to the Short Seller.The buyer of a Put Option also has the same advantage but it is limited to it's Premium only.So with an increased interest rate Shorting stock is the better option as far as the profit is concerned than the buying put options.So an increased interest rate keeps an adverse effect on Put Price.

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 see European options being traded on today’s market at the most .Some reasons are:

a)The European Options are quite simple & unique than American Options.

b)Anyone will save money on the price of the contract.

c)Extrinsic value is generally less due to fixed exercising date.

d)Less extrinsic value will definitely helps to earn more.

e)Writers of European style will be at less risk as there is no possibilty of exercising it before the expiration date.

f)American Options are more expensive than European Options due taking more risks by the American Traders.

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.Risk-neutral assumption greatly simplifies the calculations of risk-neutral & the probable reasons are :

a) Risk -Neutral Assumption considers the adjusted risks.

b) It helps to ascertain the Expected Asset Value correctly.

c)Risk-Neutral assumptions are used for pricing but not to forecast any asset's future value.