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Correlation Options Strategies: Quanto - 1

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.

There are many different common options and structures that aim to exploit opportunities or provide protection against multi-component correlated market dynamics.  One common method for providing FX protection is via options known as "quantos".  The simplest and most common flavour of quanto options is the the "classic quanto" which offers to provide FX protection against foreign denominated investments that have an unknown future value.

The classic quanto may be most easily illustrated with the following position.  Suppose a UK based investor wishes to purchase foreign denominated equity index option, e.g. an option against the S&P Index (SPX), but wishes the pay-out to be in GBP.  The market maker does not know in advance how well the USD SPX option will do, and so does not know in advance how much notional of GBP/USD forward to use to hedge the position.  Instead, the market maker requires a "quantity adjusted option" or "quanto" to provide the required USD SPX option payout in GBP.

Structuring and position keeping a quanto may be accomplished by running dynamic replication processes in both the SPX index and the GBP/USD forwards.  This means that the quanto is being replicated by simultaneous synthetic replication in two assets, and so any correlation between these assets will affect the market maker's P&L.

An approach to position keeping

The market maker has many strategies available for such replication.  For example it  is possible to run purely delta/delta rebalancing both SPX and GBP/USD.  It is also possible to use vanilla options in one or both underlying assets to further improve the hedge effectiveness by matching curvature risk.  In addition to the large number of permutations of such strategies, there are also many parameterisation questions such as what is the "best" rebalancing frequency (this can be time-based, standard deviation based, etc), and so forth.

But which is profitable, and which has the best holding period risk-adjusted P&L?

The PaR approach in combination with the Pr/rO software has been shown in other examples to be a useful technique in selecting P&L optimal trading strategies (e.g. see any of the  ARBLab analysis, such as Optimal P&L Options Rebalancing Strategies - 1, while all of TG2RM1st - Chapter 12 is dedicated to the introduction of PaR analysis .  Here a similar holding period P&L/strategy analysis is performed for position keeping a quanto,  using different models for the rebalancing calculations (with a variety of rebalancing strategies/structures).  The analysis is repeated many times for many market conditions, over many market periods, using back-testing methodologies and real market conditions/data (e.g. market prices, transactions cost, liquidity constraints, etc).

Quanto Net P&L 1.jpg (234047 bytes)Consider for example the net-P&L's from a particular rebalancing strategy.  The figure to the right (just click on to ENLARGE it) shows 2882 points.  Each point is a net-P&L for the stated conditions.  If the market pricing convention was truly arbitrage free, then the points in this graph should be distributed evenly in "three space".  The "trading factors" Fact1 and Fact2 are real world trading parameters as might be used by any trader but have disguised for the purposes of this discussion.  Notice that this strategy has quite a high variation in holding net-P&L.  Moreover, under certain market conditions, the strategies has "loss bias", meaning that under those conditions the strategy always looses money (this implies that the opposite strategy would, net of transactions and relate costs, be biased to always make money.

Quanto Net P&L 1 Max Min Surf.jpg (177986 bytes)The pattern in the "dots" can be more easily seen with a surface fitting approach as seen to the right.  This result implies that for the given market conditions, the person trading on the model prices as and rebalance formulation will be loosing money consistently if they are "this way around on this structure".

Quanto Net P&L 2.jpg (230389 bytes)By comparison, consider the P&L results with another trading strategy.  In fact, there can be many other strategies, but here one particular strategy has been chosen to accomplish two things.  First, the basic P&L character of the position is maintained, except that the actual P&L variations are very much smaller.  Second, some of the "loss-bias" has been  removed, implying a more efficient rebalancing strategy under those conditions. 

Quanto Net P&L 2 Max Min Surf.jpg (168444 bytes)Again, a surface fit may be used to better illustrate the trends.  In this case there are two surfaces showing the "upper-" and "lower-envelope" that defines the space filled by the net-P&L points.  Here again, it is clear that the bias is very much reduced, and so implies a better strategy.

 

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.

  

If you are interested in obtaining research results on this issue please Request More Information and please feel free to indicate a few specifics of interest to you.

 

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Last modified: July 25, 2011