Financial engineering is a term that refers to the development of pricing
methodologies and hedging techniques underlying financial derivative products.
Black, Scholes and Merton were the first financial engineers in that they
modeled mathematically the pricing of a plain vanilla option, something that
has been around for hundreds of years. We have seen in a previous article that
in developing the mathematics behind the option price, they suggested the way
to hedge the risk. Their construct of the "delta" lies at the heart
of the most basic hedging strategy.
One aspect of financial engineering that leverages the power of derivative
products in a simple, elegant fashion is the combination of existing derivative
products. Let's consider a few of these different combination products that can
contain vanilla products, exotic products, products from different asset
classes or just about any other pairing that one can imagine. In all of the
following examples, I will use foreign exchange as the asset class for the sake
of simplicity. It is just as easy to extend this to equities or fixed income or
commodities. The actual strikes involved are contrived in order to demonstrate
the behavioral characteristics of the products in question.
The Straddle
Let's consider the case where spot USD/JPY (i.e. the number of Japanese Yen
per 1 US dollar) is at 115. The month is February. From our analysis, we have
come to believe that spot USD/JPY is ready for a breakout in the month of
April, following the Japanese fiscal year-end. Or, at least, spot USD/JPY could
be in for some real volatility. This is predicated on the view that Japanese
corporations and investors, having placed money offshore to take advantage of
better investment opportunities abroad, will repatriate these funds for fiscal
year-end only to send them offshore again after closing the books. We also know
that the US trade representative is conducting a review of improvements to
Japanese trading practices and that she will present this report to Congress in
early March. This report is likely to highlight tensions relating to the
burgeoning US trade imbalance with Japan (and the rest of the world). The US
government may seek to "jawbone" the dollar lower in order to improve
the US terms-of-trade.
Spot USD/JPY could follow a roller-coaster over the next few months. Going
much lower before going much higher. If we buy an at-the-money-spot 115 USD
Call/Japanese Yen Put and we simultaneously buy an at-the-money-spot 115 USD
Put/Japanese Yen Call on the same notional amount of $10 million US dollars and
for the same expiry date of May 1, we have purchased a straddle on the USD/JPY.
If spot is volatile with the volatility centered around the strike of 115, we
stand to make a great deal of money by trading the delta (not to mention the
increases in value from hikes in implied volatility) of this combination of
options.
The Strangle
Instead of purchasing options with the same expiry date, notional amount and
strike, we could have varied the strategy by buying two out-of-the-money
options. For example, we could have purchased simultaneously a May 1 130 USD
Call/JPY Put and a May 1 100 USD Put/JPY Call. Compared to the straddle, this
strategy is cheaper, although we have to be careful when we are hedging the
delta around the expiry that we are not left with a cash position that is
unlikely to make money. For example, let us suppose that at expiry, spot is at
122 and from our delta hedging activities we are short US dollars against
Japanese Yen. We must be sure to close out this position as soon as the options
are expired if we do not have a firm view that the US dollar will weaken. Too
often, traders will not be disciplined in managing positions that are created
by their delta-hedging activities.
The Risk Reversal
Consider now the corporation that is hedging their exposure to a move
higher in the US dollar against the Euro. Spot EUR/USD (i.e. the number of US
dollars per 1 unit of the Euro) is quoted at $1.1335. They have a firm
commitment to buy a factory in Germany in three months' time that will cost
them Euro 10 Million. They are exposed to fluctuations in the EUR/USD exchange
rate because they are a US-based company reporting their profits in US dollars.
The first hedge that comes to mind (and the one often chosen to benchmark
risk management performance) is the forward outright. They could buy Euros
against US dollars for delivery on the same date that they need to make the
payment from their account for a rate of $1.1294. However, they think that
there is a possibility that the European Central Bank will not lower interest
rates for at least six months, contrary to market expectations, and so the Euro
could drift higher against the US dollar (i.e. EUR/USD could trade slightly
lower).
Therefore,
they enter into a risk reversal. They buy an out-of-the-money Euro call/USD put
(with a strike of $1.15 against selling an out-of-the-money Euro Put/USD Call
with a strike of $1.11 for zero cost. How does this work at expiry? If spot
settles above $1.15, the corporation will exercise their Euro call and buy
Euros at $1.15. If spot settles below $1.11, they will be exercised on their
Euro put and they will consequently buy Euros at $1.11. Anywhere in between
$1.11 and $1.15 and neither option is exercised, with the corporation buying
their Euros at the market rate in the spot market. This structure is sometimes
called a range forward because it enables the corporation to lock in a range
within which they know with certainty that they will be buying Euros while
giving them the flexibility of gaining from a small movement in their favour in
the currency pair.
Beware of Geeks Bearing Gifts
Banks have made a lot of money from this structure and others like it
because they have encouraged corporations to enter into hedges with no obvious
upfront cost. Many Treasurers believe that there is no reason to buy an option,
that options are products that should only be sold. This has worked to the
advantage of the banks because like every other market, there are times to buy
options and there are times to sell options. When they need to buy options,
corporate Treasurers are flooded with these so-called "zero cost"
alternatives.
Other times, as we shall see, zero cost strategies have costs embedded in
them that are not obviously transparent to the user. Some sophisticated market
participants can discern the true cost nevertheless and still proceed,
believing that these structures are appropriately priced. Of course, not
everyone is a sophisticated market participant. And sophistication like any
other valuable commodity comes with a price.
The Trigger Forward
Consider now a currency pair that is only going in one direction. Think of
the New Zealand dollar against the US dollar during much of the Asian crisis.
This was a "gimme" as far as most market observers were concerned,
bar the odd correction. It was only going to go down. The economy was heavily
dependent upon exporting commodities to mainly Asian countries. And the
Minister of Finance was a man with no experience in monetary or fiscal affairs
who had a known propensity for getting into the newspaper for all of the wrong
reasons.
Again, the simplest strategy might have been to sell NZD/USD (i.e. the
number of US dollars per 1 unit of the New Zealand dollar) on a forward
outright basis. If spot NZD/USD was at 0.6400 and the forward outright was
0.6362 for six months' time, then that meant that holding the period for six
months had a funding cost. If spot NZD/USD stayed at 0.6400, the trader would
be out 0.0038 points on whatever actual amount they traded. Instead they could
have done the following, taking advantage of nervously high NZD/USD implied
volatilities. They could have bought a six month NZD put/USD call struck at
0.6510 which knocked out if 0.6510 traded before the option expired and
simultaneously sold a six month plain vanilla NZD call/USD put struck at
0.6510. The combination of the two options would cost nothing at inception. The
higher the implied volatilities involved the higher the strike would be in
reference to spot because the trader here is net selling volatility.
If NZD/USD went straight down, without touching the knockout option's
trigger at 0.6510, the structure would have made more money for zero cost at
inception than he would have on the forward outright in consideration for
taking the risk of being short a potentially dangerous option without
protection. One can see that structures can be developed that not only address
a given view but also a specific tolerance for risk.
The Range Binary
Finally, let us consider the range binary, a structure that pays out a
lump-sum if spot stays within a specific range without trading at either level
in exchange for the payment of a relatively small upfront premium. Let's say
that we are looking at USD/CAD (i.e. the number of Canadian dollars per 1 unit
of the US dollar). We believe that USD/CAD is stuck in a range between 1.50 and
1.55 for the next two months. How do we take advantage of this view? We could
buy simultaneously a double barrier USD call/CAD put with a strike of 1.50 that
knocks out at either 1.50 or 1.55 and a double barrier USD put/CAD call with a
strike of 1.55 that knocks out at either 1.50 or 1.55. If spot stays in the
range without triggering either 1.50 or 1.55, we will make 0.0500 on the
notional amount of the options. The options themselves are relatively cheap
because they are so likely to be knocked out. The higher the implied
volatility, the more likely they are to get knocked out, the cheaper these
structures.
Summary
We have looked at just some of the different types of combinations of
derivatives that are possible. Indeed, the proliferation of derivative products
means that the tailoring an exposure to a particular view and tolerance for
risk is getting easier all the time.
Article by Chand Sooran, Principal, Victory
Risk Management Consulting, Inc. |