Trading Case OP5

 

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

OP5 is identical to OP4 except for the way you earn your trading bonus (i.e., grade cash).  You trading bonus is earned by managing the exposure of your position to loss from underlying price risk.  In this case you will trade European options in a two‑period market with price discovery of both the underlying security and the risk-free bond.

 

Concepts:  binomial option pricing, European options, put-call parity, price discovery.

 

Market Environment

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

 

Information

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 up-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 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."

 

Market Cash Account

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.

 

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 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 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 $5 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.