The following questions concern the options on Apple Inc. that are traded at Chicago Board Options Exchange. The ticker symbol for Apple Inc. is AAPL. Hence these options are also known as AAPL options. Attached exhibits (obtained from the CBOE website on 2 July 2015): - Equity Options Product Specifications - APPL Options Chain - All strikes for July 2015 -Near the money for all expiries

Refer to the exhibits and answer the following questions: (a) Describe what the volume and open interest data tell us about the market of AAPL options.

(b) Assuming that the risk-free rate for USD is 0.15% per annum. Find the put options which are struck near the money and expire latest in August with implied volatilities strictly larger than 15% by using the 2-step binomial model. Use ACT/365 in your calculations.

(c) You are a financial advisor and you are required to explain to a client how options may be used to bet that AAPL will be volatile in the coming month. By constructing table(s) and figure(s), explain clearly to your client how this may be done with an option combination and the values of the combination under different scenarios.

Annex Equity options Product Specifications Symbol: The option symbols are the same as for the underlying equity security. Visit the CBOE Symbol Directory for specific symbols. Underlying: Generally, 100 shares of the underlying equity security. Strike Price Intervals: Generally, 2 1/2 points when the strike price is between $5 and $25, 5 points when the strike price is between $25 and $200, and 10 points when the strike price is over $200. Strikes are adjusted for splits, re-capitalizations, etc. Strike (Exercise) Prices: In-, at- and out-of-the-money strike prices are initially listed. New series are generally added when the underlying trades through the highest or lowest strike price available. Premium Quotation: Stated in decimals. One point equals $100. Minimum tick for options trading below 3 is .05 and for all other series, .10. Expiration Date: The third Friday of the expiration month. Expiration Months: Two near-term months plus two additional months from the January, February or March quarterly cycles. Exercise Style: American Equity options generally may be exercised on any business day before the expiration date. Annex Equity options Product Specifications Symbol: The option symbols are the same as for the underlying equity security. Visit the CBOE Symbol Directory for specific symbols. Underlying: Generally, 100 shares of the underlying equity security. Strike Price Intervals: Generally, 2 1/2 points when the strike price is between $5 and $25, 5 points when the strike price is between $25 and $200, and 10 points when the strike price is over $200. Strikes are adjusted for splits, re-capitalizations, etc. Strike (Exercise) Prices: In-, at- and out-of-the-money strike prices are initially listed. New series are generally added when the underlying trades through the highest or lowest strike price available. Premium Quotation: Stated in decimals. One point equals $100. Minimum tick for options trading below 3 is .05 and for all other series, .10. Expiration Date: The third Friday of the expiration month. Expiration Months: Two near-term months plus two additional months from the January, February or March quarterly cycles. Exercise Style: American Equity options generally may be exercised on any business day before the expiration date