I got into options trading straight out of college. In 2000, the option exchanges were bustling. The Amex in NYC (where I was based), the PHLX, the P-Coast, and of course the CBOE. As a trainee, your day consisted of assisting the option market makers and specialists. Building spreadsheets, running risk reports (hitting a macro, then killing some trees), and the worst part of the job — the pre-open routine of reconciling positions and breaks. Hopefully, you’d finish before your trader sauntered into the office hungover.
During the actual trading day, your duties were pretty limited. I remember going to Cafe World at the corner of Trinity and Rector with a diagram of where my trader wanted each dish from the buffet arranged on his plate. Although you aren’t paid much you are still a liability for your first 6-12 months.
Your main purpose in the cocoon phase is to learn. After the market close, you’d attend “mock” which was short for mock-trading. Mock would be led by senior traders. “Senior” basically meant a market-maker that was now “on a badge” the credential you needed to trade on the floor. You were getting taught by people that ranged from 1 to 5 years older than you which should tell you a) how start-uppy the culture and b) how much every day’s hundreds of trades added up to valuable experience quickly.
At my firm, mock was basically hunger games. You’d stand around for an hour shoulder to shoulder with 15 guys (yes it was mostly guys) in front of a dry erase board as 3 or 4 senior traders posed as brokers barking out orders and moving the stock and option prices around setting up opportunities for the trainees to spot arbitrages.
You’d have to hedge your trades (nothing like selling one of your teacher’s some puts as another teacher announced the stock bid was now 25 cents lower), lean markets based on what prevailing bids or offers were “resting” on the exchange book, read body language, remember all the verbally announced orders that might have been announced but were not in play until the stock moved. Memory, pattern recognition, and extremely fast mental math. In fact, everyone in the room would play a timed put/call parity computer game during the day to prepare (I actually trained during the tail end of the fractions era).
So for fun, I thought I’d share an example of what mock trading would be like.
Spot The Edge
Requirements and assumptions:
- Stay delta-neutral. If you want to buy or sell the stock you must cross the spread.
- Options markets are all 500 up, meaning the bids and offers have 500 contracts on them.
- Cost of carry = 0%
- 90 days until expiration
- You will need to know Put/Call Parity
Call = (Stock Price – Strike Price) + Put + Cost of Carry
Since there’s no cost of carry let’s restate this more simply:
Call = Intrinsic + Put
Ok, here’s the option’s board:
A broker walks into the pit and announces:
I have 200 XYZ 55 straddles offered at $4.15!
I’ll get you started with a hint. Be the first person to yell: “Buy em!”
Now go figure out why.
Here are the exercises you can do with the information above.
- Compute the implied volatility.
- Find the arbitrages or best series of trades in conjunction with the broker orders that are being shouted into the pit.
- Report your remaining position and at what average price it was established.
Extra credit: Compute your P/L. You may reference an option model after the mock trading session ends.
It’s all spoilers ahead so if you actually want to do this, don’t scroll further until you are done.
- Compute the implied volatility
The approximation for the ATM straddle is given by the expression1 :
Straddle = .8Sσ√T
where S = stock price
σ = implied volatility
T = time to expiry (in years)
Let’s use mid-market of the 55 put and put/call parity to get the call price.
C = Intrinsic + P
C = 0 + $2.10 = $2.10
Since the straddle is just C + P we get $4.20 for the straddle. Plugging into the approximation:
$4.20 = .8 x $55 x σ x √.25
Solving for σ we get an implied volatility of 19%
- What series of trades do we do?
1. Buy 200 55 straddles for $4.15
2. Sell 200 55 calls at $2.15
3. Sell 400 60 calls at $1.05
4. Buy 400 65 calls for $.05
5. Sell 200 65 puts at $10.10
6. Sell 3,000 shares of stock for $54.95
Whoa. That’s a lot of trading. Because of put/call parity, traders can collapse their thinking and position by strike. A call is a put and a put is a call. You can always convert one into the other by taking the opposing delta in the underlying.
Let’s summarize these trades by strike.
Buy 400 65 calls for $.05
Sell 200 65 puts at $10.10
1. Buy 200 65 calls for $.05 and sell 200 65 puts at $10.10. Buying a call and selling a put on the same strike is known as a combo. It is the same thing as synthetically buying the stock. Why? Think about it, no matter what happens you will be buying the stock for $65 at expiration. You’ll either exercise the call or be assigned on the put. But you collected $10.05 today to make that commitment so you effectively bought the stock for $65 – $10.05 today or $54.95. Sweet.
So this can be summarized simply as buying 20,000 shares for $54.95
2. You also bought 200 extra 65 calls for .05
Sell 400 60 calls at $1.05
Buy 200 55 straddles for $4.15
Sell 200 55 calls at $2.15
Since you bought 200 straddles, you bought 200 calls and 200 puts. The calls cancel out and you are left long 200 puts at a net price of $2.00 (spent $4.15 200x in straddle premia and collected $2.15 200x in call premia).
Now remember we synthetically bought 20,000 shares for $54.95 via the 65 strike combos.
Back to put/call parity.
C = (S-K) + P
C = ($54.95 – $55) + $2.00
C = $1.95
So the combo plus these 200 55 puts means you legged buying 200 55 calls for $1.95
- What is our residual position and at what average price?
Let’s do what option traders do and show the net position by strike. That’s how we see what we actually have on. It allows us to make sense of the complexity at a glance.
1. First, we can see the 200/-400/200 pattern on equidistant strikes (ie they are each $5 apart). That is a butterfly. A relatively low-risk distributional trade that has very little vega, gamma, and theta with several months until expiration.
What price did we leg it for?
1. We bought 55 strike call synthetically for $1.95
2. We sold 2x as many 60 calls at $1.05
3. We bought the 65 calls for $.05
Adding up, $1.95 + (2 x -$1.05) + $.05 = -$.10
Negative 10 cents?
Correct. You just legged buying a structure that can never be worth less than zero for a credit. Arbitrage.
What is the delta of our total position?
Option traders want to stay delta-neutral. So estimating the deltas (or having Black Scholes spit them out) we compute the delta contribution of each strike and find we must sell or short 3,000 shares to be delta neutral.
- Extra Credit: What’s the P/L?
Using a flat 19% implied vol I get a Black Scholes value of $.93 for the butterfly. We actually got paid $.10 to own it. So our theoretical profit or edge is $1.03 times 200 contracts.
$1.03 x 200 contracts x 100 multiplier = $20,600 profit
Combo or Synthetic Stock P/L
We bought 20,000 shares of stock synthetically for $54.95 via the 200 65 strike combos. If the stock is marked at mid or $55.025 then we made $.075 on 20,000 shares or $1,500.
We did need to sell 3,000 shares at $55.00 (the bid) to hedge 3,000 shares or deltas. If the stock is marked at mid or $55.025 then we lost $.025 on 3,000 shares or $75
Total profit: $20,600 + $1,500 – $75 or $22,025!
Back in those olden days, we’d play this game after market hours but you can imagine multiple brokers shouting orders at the same time and more months than just a single expiry. We studied many different types of arbitrage relationships so we could spot mispricings from many angles.
You’d take what you learned from these games and apply it during the trading day. You’d watch how market makers and brokers in the pits reacted to different orders as you start to piece the matrix together. At my firm, the people who performed best were sent to a Philly suburb for 3 months. This was known as “class” and it was held 4 times a year. “Class” was theory and option nerd stuff until lunch then mock for the rest of the afternoon. Mock had a simulation environment with electronic overhead screens just like the exchanges and everyone held a tablet PC with stock trading software and a proper option model. This is where you started going beyond mock and getting into more game theory and real-life trading scenarios.
The faster you got into a “class” cohort the faster you got your own “badge”, P/L, and risk budget (not to mention enough comp to rent a 400 sq ft studio without a roommate).
Times have changed. The game isn’t about mental math and yelling loud and having the best memory. But this was how my intuition was built up and the lessons still permeate how I think about trading today.
- Technically, this approximation is for the at-the-forward strike not the ATM strike. The ATF strike is the strike where the call and put are equal because it is the carry-adjusted spot price. For a complete derivation see https://brilliant.org/wiki/straddle-approximation-formula/