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
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The ARBLab relies on
PaR analysis and the Pr/rO ®
software (see other examples in the ARBLab
Samples section, and
- 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.
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).
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
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",
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
For detailed research results on this issue please
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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