1
Solvay Business School
Université Libre de Bruxelles
Ask Agatha[*]
Dear Agatha,
I am worried and I have problems sleeping. My husband, a Russian physicist working in the derivatives department of a large investment bank, is behaving strangely. Some weeks ago (June 25 to be precise), he took me for dinner to celebrate our wedding anniversary in one of the best restaurants downtown. He also offered me lovely earrings. This was marvelous. When asked how he could afford such extravaganza, he replied “By being short on a straddle”. Of course, I didn’t understand his answer but I trusted him.
Since then, Petrov has become very nervous. Every night, we watch CNN and whatever the evolution of the S&P 500, he looks worried (see exhibit 1 for the recent history). He mutters strange things, talks about being exercised and recites the Greek alphabet. As he keeps referring to vega, I am concerned he might be under the influence of a sect.
I found a slip of paper with the following information which, as far as I understand, are the orders he placed on the Chicago Board Options Exchange:
Short 1 call on S&P 500, Maturity December, Strike 1,140
Short 1 put on S&P 500, Maturity December Strike, 1,140
On the web site of the exchange, I found the specifications of the contract (see exhibit.2)
I called a friend who told me I should delta hedge or, even better, delta and gamma hedge. She mentioned that Black and Scholes might help but I don’t know where to reach these persons. They must be important for I found next to Petrov’s computer a printout (exhibit 3) with their names which seems to correspond to the calculation he did before placing his orders.
You are the only one who can help me.
1) What does it mean “being short on a straddle”? Does it have anything to do with horses? Why did Petrov go short on a straddle?
2) What evolution of the S&P 500 did Petrov expected on the day of our wedding anniversary?
3) How much money did he earn by going short on this straddle?
4) Does the recent history of the S&P 500 index explain why Petro became so nervous? Did we loose any money?
5) What should I tell Petrov?
Natacha
Exhibit 1
Source: http://finance.yahoo.com
Exhibit 2
S&P 500 TM Index Options (Symbol: SPX)
Underlying:
The Standard & Poor's 500 Index is a capitalization-weighted index of 500 stocks from a broad range of industries. The component stocks are weighted according to the total market value of their outstanding shares. The impact of a component's price change is proportional to the issue's total market value, which is the share price times the number of shares outstanding. These are summed for all 500 stocks and divided by a predetermined base value. The base value for the S&P 500 Index is adjusted to reflect changes in capitalization resulting from mergers, acquisitions, stock rights, substitutions, etc.
Multiplier:
$100.
Premium Quote:
Stated in decimals. One point equals $100. Minimum tick for options trading below 3.00 is 0.05 ($5.00) and for all other series, 0.10 ($10.00).
Strike Prices:
In-,at- and out-of-the-money strike prices are initially listed. New series are generally added when the underlying trades through the highest or lowest strike price available.
Strike Price Intervals:
Five points. 25-point intervals for far months.
Expiration Months:
Three near-term months followed by three additional months from the March quarterly cycle (March, June, September and December).
Expiration Date:
Saturday following the third Friday of the expiration month.
Exercise Style:
European - SPX options generally may be exercised only on the last business day before expiration.
Last Trading Day:
Trading in SPX options will ordinarily cease on the business day (usually a Thursday) preceding the day on which the exercise-settlement value is calculated.
Settlement of Option Exercise:
The exercise-settlement value, SET, is calculated using the opening (first) reported sales price in the primary market of each component stock on the last business day (usually a Friday) before the expiration date. If a stock in the index does not open on the day on which the exercise & settlement value is determined, the last reported sales price in the primary market will be used in calculating the exercise-settlement value. The exercise-settlement amount is equal to the difference between the exercise- settlement value, SET, and the exercise price of the option, multiplied by $100. Exercise will result in delivery of cash on the business day following expiration.
Position and Exercise Limits:
No position and exercise limits are in effect. Each member (other than a market-maker) or member organization that maintains an end of day position in excess of 100,000 contracts in SPX (10 SPX LEAPS equals 1 SPX full value contract) for its proprietary account or for the account of a customer, shall report certain information to the Department of Market Regulation. The member must report information as to whether such position is hedged and, if so, a description of the hedge employed. A report must be filed when an account initially meets the aforementioned applicable threshold. Thereafter, a report must be filed for each incremental increase of 25,000 contracts. Reductions in an options position do not need to be reported. However, any significant change to the hedge must be reported.
Margin:
Purchases of puts or calls with 9 months or less until expiration must be paid for in full. Writers of uncovered puts or calls must deposit / maintain 100% of the option proceeds* plus 15% of the aggregate contract value (current index level x $100) minus the amount by which the option is out-of-the-money, if any, subject to a minimum for calls of option proceeds* plus 10% of the aggregate contract value and a minimum for puts of option proceeds* plus 10% of the aggregate exercise price amount. (*For calculating maintenance margin, use option current market value instead of option proceeds.) Additional margin may be required pursuant to Exchange Rule 12.10.
Source: http://www.cboe.com
Exhibit
15/11/2004
[*] André Farber prepared this case as a base for class discussion.