Direction:Please answer following questions with clearly and legibly written final answers. An answer from previous question will be needed to answer the question that follows. You may write down your steps for partial credit, but they are not required. No penalty will be given for attempts. Using powerful mathematical/statistical tool such as financial calculator or Excel spreadsheet is strongly recommended.

Consider following listing of call option on Tesla on Yahoo! Finance (Real quotes used).

Current Price:

$580

Strike Price:

$600

Risk-free Rate:

3.1%

Time to Expiration:

6 months (0.5 year)

Call Premium

$95.06

Dividend Yield

0%

1.What is the implied volatility of above listed call option?

(hint: use the excel file I have uploaded on icollege. Instead of solving the algebraic equation of Black-Scholes, try to manipulate around volatility number to find the volatility that results in the given call price)

2.Above procedure of trying to guess the right number by changing the parameters of an equation is called "numerical approach" of finding an answer. Using this approach, what are the implied volatilities of Tesla using following call options prices?

Strike Price

Call Premium

550

$119.98

650

$78.78

700

$64.40

800

$42.63

900

$29.97

1000

$24.44

3.Plot the calculated implied volatilities on strike price - implied volatility plane and draw a graph by connecting plots. Make the horizontal axis represent "Strike Price" and vertical axis "Implied Volatility". Use points calculated (for strike price 550, 600, 650, 700, 800, 900, 1000).

4.Interpret above graph and explain what the graph may explain about investor's expectations.

(Hint: As implied volatility estimates the volatility of underlying asset's price, if the call premium that investors are willing to pay is correctly priced, the resulting implied volatility numbers should be constant across different strike prices (i.e. flat line). however, such is not the case when real call premium is used to calculate implied volatilities across different strike prices. This phenomenon is known as "Volatility Smile". Look up what this is and explain with respect to what investors believe on what may happen with options that are in the money versus out of the money)