Trading Case
OP3
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
There is one stock, one zero-coupon bond, a put
option and a call option. Both options
are European style options. The market
lasts for three periods. The stock price
is initially 400. The uptick parameter is 1.090513 and the downtick parameter is
0.917. The interest rate each period is
1%. Both options expire at the end of
the third period, and have a strike price of 410. Prices for the stock are fixed at 400
initially, and then follow the binomial process. You are endowed with an initial short
position in one of the two options and a positive amount of cash.
Case Data
The following table shows the cash flows from each
security at the end of period 3 depending on the number of upticks
and downticks that occur. Thus, “udd” in the table means that there was an uptick followed by two downticks. There are no cash flows in intermediate
periods.
|
|
uuu |
uud |
udu |
udd |
duu |
dud |
Ddu |
ddd |
|
Stock |
518.74 |
436.21 |
436.21 |
366.80 |
436.21 |
366.80 |
366.80 |
308.44 |
|
Bond |
103 |
103 |
103 |
103 |
103 |
103 |
103 |
103 |
|
Put |
0 |
0 |
0 |
43.20 |
0 |
43.20 |
43.20 |
101.56 |
|
Call |
108.74 |
26.21 |
26.21 |
0 |
26.21 |
0 |
0 |
0 |
Trading Restrictions
In this trading case you are only permitted to trade
in the Stock and the Bond. You are a
price taker for the stock and as such do not face any liquidity
constraints. You are free to both make
and take market in the bond. That ism,
the trading crowd can discover prices for the bond.
Earning Grade Cash
In the trading period market securities are traded
using market cash. Three trading periods
are equivalent to one trial. If at the end of any trial you have a closing
balance of $5000 market cash then you will earn $8 grade cash. If you have a closing balance of market cash
that is lower than $5000 then you will earn zero grade cash. Any amount of market cash that is greater
than $5000 and less than or equal to $10,000 earns grade cash as follows:
You
trade a number of independent trials and a record of your cumulative grade cash
is maintained.