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P&L Analysis of Synthetic vs. Outright Curve Options

Please note, as ART Consulting/Research is a fee based service, in the following the results have been "sanitised" to disguise the specific markets, trading factors, strategy parameters and many other essentials.  Of course, all of the analyses is based on real market conditions and real world trading considerations (trans cost, funding, etc).  For access to the "un-sanitised" results, and for analysis tailored to your needs, please submit an email via  Request More Information.

The ARBLab relies on PaR analysis and the  Pr/rO software (see other examples in the ARBLab Samples section, and the TG2RM1st - Chapter 12 provides a detailed introduction to PaR analysis).

Interest rates have fallen dramatically in recent years, and so curves have flattened considerably.  However, curve slope/spread volatility is quite considerable, leading to interesting possibilities in curve/slope options strategies. 


An option on the slope of a curve (e.g. a spread option, say, on the US 30y-10y yield spread) is not the same trade as options on the outright legs of the underlying that "synthetically" replicate the spread, since the outright replication is exposed to both absolute and correlation (rotation) effects, while the spread option is primarily impacted by curve rotation only1.  In the case of extended periods of low yields and flat curves, the outright movements in the individual legs may be sufficiently constrained to permit comparing these two strategies.


A PaR back test analysis of holding period P&L using real market data spanning many years is shown in the image to the right (click to enlarge) for the "outright spread" based position strategy.  Each point in the "cloud" is the net P&L for an entire holding period of this strategy.  The Factor X and Factor Y along the axis represent market measures (e.g. prices, vols, etc), and the "colouring" of the dots represents a third market measure.


This data can be processed to summarise the essential character and "validity" by a combination of various methods which includes the fitting procedure shown to the right (click to enlarge).  This image shows the likelihood of selecting profitable trades based on any one day's market conditions, and then buying/selling the structure/rebalancing strategy as per the values in the image.  For example, the middle right of the image (light blue) suggests market conditions for which this strategy should be sold, and then with an expectation of profiting by 4,000 per "unit of notional" used in this strategy analysis (approx 30% RoC).


A similar analysis for a spread option based strategy produces the image shown to the right.  These results have a different character to those shown above.  This is in part due to two issues:

The data history includes a period during which there was a directional drop in rates, and flattening.

The volatility in the spread has undergone fundamental changes, and option prices reflect the different factors for these different instruments.

However, notice that the "outright spread" strategy "sell condition" discussed above corresponds to a "buy condition" in the "slope option" strategy.  This raises two considerations for trading strategies.  First, under current market conditions, if the outright movements are benign, then the two strategies will have similar risk profiles.  Second, under those market conditions, the one strategy is a buy, and the other is a sell, and so it may represent the possibility of a "near arbitrage" since the combination of buy/sell as suggested here indicated profits on both legs, and has risk cancellation as well.


Even without the "near arbitrage", these conditions may also provide the possibility for other advantages, such as replicating OTC structures with listed products, and that in itself can be quite a considerable saving in transactions cost, "lines", capital/limits, etc.


As usual, caution is required.  The analysis here, though including thousands of trades, and incorporating many real world factors cannot be taken as any perfect predictor of the future, and additional specific analysis may be required for your due diligence.


For detailed research results on this issue please Request More Information and please feel free to indicate specifics of interest to you.


1.  Put differently, an "option on a portfolio" is not the same as a "portfolio of options"



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Last modified: July 25, 2011