Traditionally, short volatility trading is regarded as a risky investment approach. Even during quiet periods, strategies based on selling naked options can lead to considerable losses. It is no wonder that a financial crisis, accompanied by a sharp rise in historical and implied volatilities, is commonly considered a factor that dramatically raises the risk of substantial losses, right up to the near-bankruptcy level. Scrutinizing the data of the current crisis allows us to judge whether such views are correct.
Three basic issues will be examined: how does the crisis influence the profitability of short option positions, does the crisis change the structure of trading opportunities existing at the option market and is the effectiveness of the criterion used in selection of the most promising trading opportunities affected by the crisis?
Because the timing of trade entry plays a key role in volatility selling strategies, all of these questions will be studied in the context of different time intervals between trade entry and option expiration.
The success of almost any strategy based on selling naked options depends on the selection procedure. This procedure can be based on one or several criteria that may be informal, or have strict mathematical guidelines. A popular metric is profit expectations based on various probability distributions. Here, we’ll examine how the current financial crisis affects the mathematical expectation of profit estimated using lognormal distribution. This is calculated as the integral of the payoff function with respect to the lognormal probability density function.
Two databases were used in this study. The first one, corresponding to the crisis period, covers the time interval from Aug. 1, 2007, to March 30, 2009. The second database corresponds to the period before the crisis (Jan. 2, 2003, to July 31, 2007). Both data arrays contain prices of options corresponding to the shares that make up the S&P 500 index.
Within each database, a series of 60 portfolios was created for each expiration date. These portfolios differed from each other in terms of time to expiration. The most “distant” portfolio was 60 trading days away from the expiration, the next one was 59 days, and so on.
Each portfolio consisted of 500 short straddles related to the stocks forming the S&P 500 index. Each straddle used the strike closest to the current stock price. The quantity of options corresponding to each stock was determined as $1,000,000/x, where x is the price of the stock underlying the straddle.
For all combinations, criterion values were calculated at portfolio creation. Profits were calculated at the expiration date. The sum of mathematical expectations of all straddles in the portfolio gives the criterion value, while the profit is calculated by summing up profits and losses of these combinations.
During calm periods, profit does not depend on the number of days left to expiration, while at the time of crisis, the profitability of short option portfolios falls as the time left to expiration increases (see “Comparing profits” ). Besides, a decrease of average profit is accompanied by a sharp increase in its variability (vertical bars on chart), which can be explained by high market volatility during the crisis. Close to expiration date profits during both crisis and quiet periods are virtually the same, which may be the most important conclusion of this study.