Trading Case
OP4
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
In
this case you will trade European options
in a two‑period market with price discovery of both the underlying
security and the riskfree bond.
Concepts:
binomial option pricing, European
options, putcall parity, price discovery.
Four
markets are open for two calendar months of actual time.
In FTS time, a one month trading period will lasts for x seconds (the
default time for this case is 240 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 
uu 
155 
ud, du 
90 
dd 
52 
At
the beginning of trading period 2 information as to whether an up or down tick
was realized is disclosed to you 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 such as “Per 1 z”:
A
"z" discloses that an uptick was realized at the end of per 1. A "y" discloses that a down tick was realized.
As a result, “Per 1 z” which discloses that an uptick 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 2 regardless of which path the stock market takes.
The
third and fourth securities are European options (put and call) on the
underlying stock. The strike or
exercise price for each option is $85 and the life of each option, at the
beginning of period 1, is 2 months. The
terminal payoff is defined as:
Terminal
Value:
At
the end of their life options are automatically exercised if they are "in
the money."
To
buy in this market you need cash but any market cash that lies idle in your
market cash (i.e., 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 then all available quantities at the current price
are taken. With market depth this
implies that the next layer of the book will automatically appear as the new
market price/quantity 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.
In
the trading period securities are exchanged using market cash.
Two trading periods are equivalent to one trial. At the end of
any trial you will earn grade cash as follows:
Grade Cash = Ending balance of market cash * 0.0001
Trading is conducted over a number of independent trials and a record of
your cumulative grade cash is maintained.
© OS Financial Trading System 2001