Trading Case
XR2
Case Objectives
To understand using options and futures to manage
currency risk; to understand options trading strategies in an environment in
which exchange rate crises exist. Finally,
to gain experience working with a derivative trading support system.
Key Concepts
Currency option and futures pricing; option hedge
parameters; implied volatility shifts.
Case
description
Currency markets can
experience very volatile periods. For
example, in the 1992 European currency crisis the implied volatility for sterling/dollars and dm/dollars jumped from
the 11-12% range in August 1992 to in excess of 20% by October 1992 and then
fell back sharply to above historic levels.
A study by a
In this trading case you
will face the problem of managing exchange rate risk in a currency crisis.
That is, during each trading trial a currency crisis will occur at some
point in time which is marked by a sharp increase in volatility. Although, the timing and the duration of the
crisis is random, prices in the options markets will only provide signals that
volatility is expected to increase near the time of the realized increase.
You will compete against
other traders in the FTS markets by earning grade
cash with respect to a conversion scheme that is designed to both reward
you for seeking out higher returns but penalize you for dropping below an
acceptable floor.
The operational details
of this trading case are the same as for XR1.
The major difference is that a significant shift in volatility will
occur at some time during the trading year (trial).
Trading
Screen
Each trader's screen will
monitor eight markets: the exchange rate, a risk-free bond (strip) with 104
weeks remaining to maturity at the beginning of the period, European call and
put options on the exchange for two different strike prices with a remaining
life of 52 weeks, an exchange rate future contract, and a cash money market.
Definition of A Trading Trial
One trial in this case is
almost 12 months, but time is condensed so that two weeks is equal to “n”
seconds. That is, throughout the trial
trading is continuous but prices will change in discrete time, two week steps
every “n” seconds of FTS time. That is,
in calendar time the markets are open for FTS traders on the first trading day
of every two weeks.
Note: In the
default form of the case “n” seconds equals 20.
The following table
describes price changes in this market:
|
Calendar Time |
Real-time |
|
|
|
|
Day 1, Week 1 |
Time 0-20 seconds |
|
Day 1, Week 3 |
Time 21-40 seconds |
|
Day 1, Week 5 |
Time 41-60 seconds |
|
....................... |
............................... |
New prices are realized
for each trading Day (20 second interval).
Prices reflect the underlying difference in calendar time. That is, the Treasury Strip appreciates
toward its face value over time, and option prices reflect the time left to
maturity etc.
At the end of the year ( = one trading trial), your currency position is
marked-to-market at the prevailing rate.
Market Environment
The first market is the
exchange rate. This is the value of 500 units
of the basket of currencies (bfx) in units of $US. Analyst research has indicated that the
statistical process that approximately describes the behavior of this exchange
rate is a geometric Wiener process with the following properties:
|
Projected |
14%-16% per annum |
|
Spot Index Value (Bid/Ask) |
Near 300 |
|
Projected Drift () |
0.0% per annum |
|
Unit of Time |
2 week (20 seconds) |
|
Eurodollar rate US |
0.03 |
|
Euromark rate |
0.07 |
The projected volatility
is a little above historical averages for volatility but
well below the heights reached in the European currency crisis in 1992.
Securities
And Trading Restrictions
|
Financial Markets |
|
Spot x-rate (500 bfx) in $US (S) |
|
US Treasury Strip (maturity 104 weeks) |
|
52 week call on spot x-rate, Strike 290 |
|
52 week Put on spot x-rate, Strike 290 |
|
52 week Call on spot x-rate, Strike 310 |
|
52 week Put on spot x-rate, Strike 310 |
|
X-rate Future (500 bfx / 52 weeks) |
|
Money market (3% p.a.) |
The
currency crisis is not interest rate related, so you can assume that the
interest rates remain constant.
Trading
Objective
Your trading objective is
to earn as much grade cash as possible subject to the constraints imposed by
your firm upon your trading activities.
Earning
Grade Cash
Securities are exchanged
using market cash in a trading period that lasts for 52 weeks. Each 52 weeks is
referred to as one trading trial. Multiple independent trials will be
conducted.
That is, at the start of
a trial your initial endowment is either Type A or Type B, and an independent
exchange rate path (starting from the spot lot price of around 300).
If
at the end of any trial you have a closing balance of $4,500,000 market cash
you will earn $20 grade cash. If you
have a closing balance of market cash that is lower than $4,500,00
you will earn $0 grade cash. Any amount
of market cash that is greater than $4,500,000 and less than or equal to $100,000,000
earns grade cash as follows:
Above
$100,000,000 market cash earns the maximum of $402 grade cash for one trial.
Trading
is conducted over a number of independent trials and a record of your
cumulative grade cash is maintained.
Linking to the
Trading Support Spreadsheet for Trading Case XR2
Download the trading support spreadsheet for XR2
(just below the ftsTrader link) from the Virtual
Classroom page and open it in Excel.
Note: Read
carefully the appropriate Excel settings from the Virtual Classroom section
where you download the XR2 support spreadsheet from.
Launch the FTS Trader and link to the market. In FTS Trader click on the File menu and
select Excel Link from the sub menu items.
The following screen will pop up.
Select the spreadsheet titled XR2TradSupport and be sure to select Sheet
1 as the Market Data Sheet and Sheet 2 as the Trading History Sheet as depicted
below:
Click OK and the spreadsheet is automatically linked
to the market. By giving focus to the
spreadsheet (i.e., resize so it is on the same screen as your trading window),
you can see your position greeks
update in real time. The spreadsheet
support is illustrated below:
Corresponding
Trading Screen in the FTS Trader
Appendix
Trading Tips for Trading XR2
In
trading case XR2 you are a short term “news trader.” You have information that lets you form a
“market view” about the short term price behavior of the underlying exchange
rate. In XR2 the price of the underlying
exchange follows the geometric Brownian motion process assumed by Black and Scholes with one important difference. During the trading period at least one
significant economic news event will occur that will result in the price of the
exchange rate taking a jump. However,
you do not know when the jump will take place or it’s
magnitude and direction. In addition,
there may be more than one significant jump (but there will be at least
one). Unlike the real world you do not
face any liquidity or capital constraints.
You
have an initial position in an option that you cannot trade, but you can trade
the remaining derivatives (option and futures).
As a result, your task is to manage your trading strategy so that it
makes money if your view of the market is correct. At any time if you want to lock in your
trading gains you can also manage the delta of your position. By linking to the XR2 support spreadsheet
(you can download this from the Virtual Classroom page immediately below where
you download the FTS Trader from).
Why Delta?
Delta
is a measure of the dollar sensitivity of your position to changes in the
underlying (i.e., the exchange rate).
Formally, the delta of a derivative security is the partial derivative
(i.e., calculus) of the derivative security’s price w.r.t.
a change in the underlying asset price.
The delta of each security and your position’s delta are provided in the
support spreadsheet in real time.
Excel Note for FTS Trader: If Excel is set
to Automatic Calculate (Tools, Options, Calculations, Automatic) and you link
FTS Trader to this spreadsheet, it will automatically recalculate your position
delta whenever the exchange rate changes in XR2.
By
trading the options and futures you can manage your position delta to be
approximately zero, positive or negative.
For the case of a zero position delta your position’s value will be
relatively insensitive to shifts in the underlying exchange rate. If you assume a large positive position delta
your position will be very sensitive to shifts in the price of the underlying
(with increasing sensitivity the larger your position delta is). That is, if the underlying exchange rate
increases so does your position’s value and if the underlying exchange rate
decreases your position value will decline.
Finally, if you assume a large negative position delta then the value of
your position responds in the opposite way to the change in the exchange
rate. That is, if the exchange rate
increases your position’s value decreases and vice versa.
Finer points: Your position
gamma is a measure of how sensitivity your position delta is to changes in the
underlying. Formally, gamma is the
partial derivative (in calculus) of the derivative security’s delta w.r.t. the underlying asset price (i.e., the second partial
derivative w.r.t. the underlying asset price). In the field, suppose a dealer is hedging the
exchange rate risk by maintaining an approximate delta neutral exposure (i.e.,
position delta equals 0). If a dealer
maintains a gamma sensitive (i.e., large position gamma) position they must
adjust delta frequently and by larger amounts to maintain a zero position
delta. If a dealer maintains a gamma
insensitive position (i.e., approximately zero position gamma) then this
reduces the frequency and size of delta adjustments that need to be made to
maintain a zero position delta. In practice
by reducing the size and frequency of having to adjust your position’s delta
results in a source of significant transaction cost savings.
Finally,
your position Vega is a measure of how sensitive your position is to
volatility.
Inferring Information from Implied
Volatility Estimates: You should monitor the implied volatility in
your spreadsheet because prior to a crisis you will observe in this trading
case that implied volatility makes a significant initial jump. After the first jump it will then jump again
and so you should think about how you can adjust your trading strategies to
exploit this information.