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 three-period market with price discovery of both the underlying security and the risk-free bond.

 

Keywords:  binomial option pricing, American options, put-call parity, price discovery.

 

Market Environment

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

 

Information

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 up-tick 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 up-tick and then a down-tick was realized.

 

There is no disclosure at the beginning of period 1.

 

Other Financial Contracts

The second security market is a risk-free 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."

 

Market Cash (i.e., checking) Account

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.

 

Endowments

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,

 

Market Actions

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 risk-free rate is achieved by selling or buying the risk-free bond.  The realized borrowing and lending rate is determined by the spot bond price at the time of the transaction.

 

Trading Objective

Your trading objective is to earn as much grade cash as possible.

 

Earning Grade Cash

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.

 

Trading is conducted over a number of independent trials and a record of your cumulative grade cash is maintained.

 

 

 

© OS Financial Trading System 2001