Trading Case
OP7
Case
Objective
To
understand delta hedging in the binomial option pricing model.
Key
Concepts
Binomial
option pricing model; option replication; dynamic trading strategies.
Case
description
This
trading case is identical to OP6 except for the way you earn your trading bonus
(i.e., grade cash). In this case
you are rewarded for managing your position’s exposure to loss from the
underlying price risk. In this case
you will trade American options in a
threeperiod market with price discovery of both the underlying security and the
riskfree bond.
Keywords:
binomial option pricing, American
options, putcall parity, price discovery.
Six
markets are open for three calendar months.
In FTS time a one month trading period will last for x seconds (the
default time for this case is 200 seconds).
The
markets are: a stock market, a bond market, and two option markets (put and
call). In the stock market at
the end of each calendar month either an "uptick" (u) or
"downtick" (d) is realized for the stock price with the probability of
u equal to 0.5. The set of possible
realized paths is depicted below:
At
the end of the second period the stock price will be marked to one of the
following values depending upon
which path is realized from the following four possibilities:
Path 
Marked Value 
uuu 
552 
uud, udu,duu 
351 
udd,dud,ddu 
223 
ddd 
142 
At
the beginning of each trading period you will see information indicating that an up or down tick was realized at the end of the
previous period at the bottom of the market input window. To see this information click once on the stock name (as you
would to buy or sell the stock). At
the bottom of this window you will see information of the type “Per 1, z”
A
"z" discloses that an uptick was realized at the end of the preceding
period. A "y" discloses
that a down tick was realized. The
example “Per 1 z” discloses that an uptick was realized in the preceding
period which was period 1. Similarly,
at the beginning of period 2 you will see “Per 1 z
Per 2 y”. This indicates
that an uptick and then a downtick was realized.
There
is no disclosure at the beginning of period 1.
The
second security market is a riskfree bond that pays $100 at the end of trading
period 3 regardless of which path the stock market takes.
The
third to sixth securities are American options (put, call, put, call) on the
underlying stock. The strike or
exercise price for the first pair of options is $180 and the second pair is
$380. The initial life of each option is 2 months.
The terminal payoffs are defined as:
Terminal
Value:
At
the end of their life options are automatically exercised if they are "in
the money."
To
buy securities you need cash but any residual market cash that you have at the
end of the period in your checking account earns zero interest.
In
this market different traders will have different opening endowments. Your own opening endowment is determined randomly from a
fixed number of endowment types. The
set of types are such that initial positions can be long or short in any
security. However, the stock and
the bond have a positive aggregate supply and options have a zero aggregate
supply,
You
can both make market and/or take market in every market. The
current prices only arise from the market making activities of traders in the
FTS markets. When making
market the FTS market will maintain a book of the best bids and the best asks.
The default depth for the book is 10.
That is, the 10 highest bids and the 10 lowest asks are maintained at any
point in time.
If
one side of the market clears, at any point in time, then the next layer of the
book will automatically appear as the new market quote.
As a market taker you are protected in the sense that if two traders
simultaneously attempt to buy (sell) at the prevailing ask (bid) then the order
is processed on a first come first served basis, and if a new layer of the book
appears then remaining unfilled orders are killed.
For
example, suppose that the current book is:
Bid 
Bid Qty 
Ask 
Ask Qty 
23 
56 
25 
45 
18 
75 
26 
67 
17 
85 
28 
89 
and
two traders approximately at the same time transmit market orders to sell 56
units. The first to be received is
executed at the bid price of 23 and clears the bid side of the market.
Now the prevailing market is:
Bid 
Bid Qty 
Ask 
Ask Qty 
18 
75 
25 
45 
17 
85 
26 
67 


28 
89 
and
the second trader’s market order to sell 56 units at the price of 23 is
automatically killed.
As
a trader in this market you can shortsell
any securities. Thus borrowing and
lending at the riskfree rate is achieved by selling or buying the riskfree
bond. The realized borrowing and
lending rate is determined by the spot bond price at the time of the
transaction.
Your
trading objective is to earn as much grade
cash as possible.
If at the end of any trial you have a closing balance of $30,000 market cash you will earn $4 grade cash. If you have a closing balance of market cash that is lower than $30,000 you will earn zero grade cash. Any amount of market cash that is greater than $30,000 and less than or equal to $100,000 earns grade cash as follows:
Above
$100,000 market cash earns the maximum grade cash equal to $10 with certainty.
© OS Financial Trading System 2001