# How to price options of differing expiration dates consistently

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When pricing options on a single underlying instrument that share the same expiration date, the simplest way to ensure pricing is consistent in terms of its competitiveness is to compare the vega of the structures being priced. So, it is consistent to make an at-the-money straddle quotation twice as wide as an at-the-money option quotation, since the vega of the former is double that of the latter. Of course there are other factors to account for, such as liquidity or strike risk, but the vega comparison is a ready rule-of-thumb to ensure pricing is consistent in terms of its width. When trading in the Volcube simulation markets, Volcube will measure consistency of pricing in such terms.

However, this rule is less appropriate when comparing pricing across the term structure. In other words, the price of options on the same underlying but with *different* expiration dates ought not to simply be compared by respective vegas alone. One should not, in general, think that the price of one month options with a vega of say 10 ought to be say 20 ticks wide, therefore this is true of all 10 vega options of any duration on the same underlying. The reason for this is quite simply that the vegas of these options are not themselves as comparable as the vegas of options which share the same expiration date. And the reason why the vegas are not so meaningfully compared is that implied volatility across the term structure rarely, if ever, moves identically. In general, fluctuations in implied volatility are greater in the nearer term options than in the back month options. The intuitive reason for this is easy to understand by considering extremes. A sudden profit warning by a company regarding its next quarterly results will have a greater impact on short term realized volatility than on long term realized volatility. It is nearer term options (one, three or even six months) therefore that might expect to see sustained higher actual volatility over the course of their existence rather than longer term options (2 year, 5 year, 10 year etc) in the event of such an announcement. So if implied volatility changes are not identical across the option term structure, (and this is usually the case), then comparing vega directly across the term structure is likewise usually inappropriate. All these effects can be seen when trading in Volcube with multple expirations selected.

How then should pricing compare across the option term structure? There is no single answer to this question as several factors can affect pricing. However, one basic rule-of-thumb is to consider whether options with similar deltas rather than vegas across the term structure should have bid-ask spreads of equal width *in tick terms*. It is not uncommon for one month, two month and three month options to all be quoted an equal number of *ticks* in width, rather than an equal number of *implied* *vols*. So instead of quoting say 1 vol wide in all months (ie making the width of the price equal to the vega of the strategy), the quotes are more consistent if they are always the same number of ticks wide. Often for example the quoted prices of straddles (a measure of implied volatility) are an equal number of ticks wide across durations. Volcube will look to assess a trader’s competitiveness and consistency across durations by noting such factors.

This rule-of-thumb must however be treated with caution. There are several other factors that can and should influence the aggressiveness of pricing across the curve. For example the volatility of the term structure of interest rates. Or the liquidity of each expiration or sections of the skew curve within expirations. Also any dividend risk that pertains to one month but not another. There are several such factors to consider. As always, it is wise to practise trading extensively in the Volcube simulation markets until such skills have been acquired and with the addition of extra expirations from version 2.3 onwards, this opportunity becomes available.

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