CLISSOLD INDUSTRIES OPTIONS You are currently working for Clissold Industries. T
ID: 2733947 • Letter: C
Question
CLISSOLD INDUSTRIES OPTIONS
You are currently working for Clissold Industries. The company, which went public five years ago, engages in the design, production, and distribution of lighting equipment and specialty products worldwide. Because of recent events, Mal Clissold, the company president, is con-cerned about the company’s risk, so he asks for your input.
In your discussion with Mal, you explain that the CAPM proposes that the market risk of the company’s stock is the determinant of its expected return. Even though Mal agrees with this, he argues that his portfolio consists entirely of Clissold Industry stock and options, so he is concerned with the total risk, or standard deviation, of the company’s stock. Furthermore, even though he has calculated the standard deviation of the company’s stock for the past five years, he would like an estimate of the stock’s volatility moving forward.
Mal states that you can find the estimated volatility of the stock for future periods by calculating the implied standard deviation of option contracts on the company stock. When you examine the factors that affect the price of an option, all of the factors except the standard deviation of the stock are directly observable in the market. Mal states that because you can observe all of the option factors except the standard deviation, you can simply solve the Black–Scholes model and find the implied standard deviation.
To help you find the implied standard deviation of the company’s stock, Mal has provided you with the following option prices on four call options that expire in six months. The risk-free rate is 4 percent, and the current stock price is $53.
1. How many different volatilities would you expect to see for the stock?
2. Unfortunately, solving for the implied standard deviation is not as easy as Mal suggests. In fact, there is no direct solution for the standard deviation of the stock even if we have all the other variables for the Black–Scholes model. Mal would still like you to estimate theimplied standard deviation of the stock. To do this, set up a spreadsheet using the Solver function in Excel to calculate the implied volatilities for each of the options.
3. Are all of the implied volatilities for the options the same? ( Hint: No.) What are the possible reasons that can cause different volatilities for these options?
4. After you discuss the importance of volatility on option prices, your boss mentions that he has heard of the VIX. What is the VIX and what does it represent? You might need to visit the Chicago Board Options Exchange (CBOE) at www.cboe.com to help with your answer.
5. When you are on the CBOE website, look for the option quotes for the VIX. What does the implied volatility of a VIX option represent?
Explanation / Answer
Answer:1 Since the Black-Scholes model uses the standard deviation of the underlying asset, and there is only one underlying asset no matter how many strike prices are available in theory, we would only expect to see one implied standard deviation.
Answer:2 To find the implied volatility for an option, you can set up a spreadsheet to calculate the option price.The Solver function in Excel will allow you to input the desired price and will solve for the desired unknown variable. We did this (the spreadsheet is available), and the implied standard deviation for each of the options is:
Answer:3 There are two possible explanations. The first is model misspecification. Although the Black-Scholes option pricing model is widely acclaimed, it is possible that the model specifications are incorrect. One potential variable that is incorrectly specified is the assumption of constant volatility. In fact, the volatility of the underlying stock is itself volatile, and will increase or decrease over time. The Black-Scholes model may also ignore important variables. As in any potential arbitrage opportunity, they purchased underpriced assets, in this case warrants on National General stock. Unfortunately, soon after they took this position, American Financial announced a tender offer for National General, which sharply reduced the value of the warrants. The market had already priced the potential tender offer in the warrant price, while this variable was not accounted for in the Black-Scholes model. Parenthetical Note: This explanation is unclear. A tender offer should for National General should increase, not reduce, the value of the warrant.
A second possible explanation is liquidity. At- or near-the-money options tend to be more liquid than deep in-the-money or deep out-of-the-money options. Since options that are not near-the-money are less liquid, the prices of such an options should carry a liquidity discount.This contrasts with at- ornear-the-money options that should carry a liquidity premium.Parenthetical Note:Unfortunately, this observation does not explain the pattern of Implied Standard Deviation, which decline monotonically as the strike price increases.This liquidity explanation implies that the imlied standard deviation should be high for at-the-money options and low for deep in-the-money and out-of-the-money options.
Answer:4 The VIX is a benchmark for stock market volatility. The VIX is based on option prices, which reflect investors' consensus view of future expected stock market volatility. During periods of market turmoil,both option prices and the VIX tend to rise. When the market is calmer, investor fear, option prices, and the VIX decline.
Answer:5 The VIX uses eight different S&P 100 Index (OEX) option series to represent the implied volatility of a hypothetical OEX option with exactly 30 days to expiration.
Strike price Options price Implied standard deviation 30 27.65 144.80% 40 19.45 109.42% 50 11.95 83.16% 55 9.55 78.82%