Explanation:
Because there is a pronounced volatility smile, deep out-of-the-money (OTM) calls will have a higher implied volatility than at-the-money (ATM) calls. If the trader used the ATM implied volatility for all options, the short deep OTM calls would be undervalued (i.e., the liability would be understated), artificially inflating the net value of the trader's book and consequently his bonus. To obtain an accurate market value and prevent manipulation, best practice dictates that the book should be marked to market by valuing each option using the implied volatility of the most similar traded option (accounting for strike and maturity), thereby properly incorporating the volatility smile.
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Q.46 A trader wishes to mark to market a book of plain-vanilla stock options in his portfolio. The trader is long at-the-money call options and short deep out-of-the-money call options. Given that the trader’s bonus increases as the value of his book increases, and that there’s a pronounced smile on these options, which of the following approaches should the trader use to mark the book?
A
Use the historical volatility so as to make corrections for pricing mistakes inherent in the option market
B
For each option, use the implied volatility of the most similar option tradable on the market
C
Use the average of the implied volatilities for the traded options for which the trader has data since all options should have the same implied volatility with Black-Scholes
D
Use the implied volatility of at-the-money options since volatility estimation is more reliable