**Correlation Options Strategies:
Quanto - 1**

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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).

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.

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".

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.

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
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