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 equity even if we have all other variables for the Black–Scholes model. Mal would still like you to estimate the implied standard deviation of the share.

To do this, set up a spreadsheet using the Solver function in Excel to calculate the implied volatilities for each of the 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 speciality products worldwide. Because of recent events, Mal Clissold, the company president, is concerned 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 equity is the determinant of its expected return. Even though Mal agrees with this, he argues that his portfolio consists entirely of Clissold Industry shares and options, so he is concerned with the total risk, or standard deviation, of the company’s equity. Furthermore, even though he has calculated the standard deviation of the company’s equity for the past five years, he would like an estimate of the share’s volatility moving forward.
Mal states that you can find the estimated volatility of the share for future periods by calculating the implied standard deviation of option contracts on the company equity. When you examine the factors that affect the price of an option, all of the factors except the standard deviation of the shares are directly observable in the market. You can also observe the option price as well. 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 equity, Mal has provided you with the following option prices on four call options that expire in six months. The risk-free rate is 6 per cent, and the current share price is £50.
Strike Price (£) Option Price (£)
30 23.00 40 16.05 50 9.75 55 7.95