The Trading Game: Learning Options by Playing

Chapter 21 is short and completely different from everything else in the book. No equations. No theorems. Instead, Wilmott describes a classroom trading game designed to teach option pricing through actual experience. The game was created by one of his former students, David Epstein, and it is surprisingly brilliant in its simplicity.

Most people reading a 1500-page quant finance textbook have never actually traded an option. They know the Black-Scholes formula. They can calculate Greeks. But they have never felt the tension of putting real money (even play money) on a position and watching it move against them. This chapter fixes that.

How the Game Works

The setup is elegantly simple. One person acts as the game organizer (usually the lecturer). Everyone else is a trader. The game runs over several rounds, and at the end of each round, someone rolls a six-sided die.

The “share price” at the end of the game is the sum of all dice rolls.

That is it. That is the underlying asset. Five rounds, five dice rolls, and the stock price is their total. If you roll 3, 5, 2, 6, 1, the final price is 17.

With a standard six-sided die, each roll averages 3.5. Over five rounds, the expected final price is 17.5, with a possible range from 5 (all ones) to 30 (all sixes).

What You Trade

The organizer decides which contracts are available. For beginners, Wilmott recommends three games with increasing complexity:

Game 1: Forward contracts only. A forward locks in a price to buy the “stock” at the end of the game. If you agree on a forward price of 18 and the final stock price is 21, you make 3 per contract. If the final price is 15, you lose 3. Crucially, forwards cost nothing upfront. You are just agreeing to a future transaction.

This first game teaches the basics of trading. What is a fair price? Should the forward be 17.5 (the expected value)? What happens after a few dice rolls when you have more information?

Game 2: Forward plus a call option with strike 15. Now things get interesting. A call option gives you the right (not obligation) to buy at 15. If the final price is 21, the call is worth 6. If the final price is 12, the call expires worthless.

But unlike the forward, the call costs money upfront. How much should you pay? That is the whole point. Players discover option pricing through haggling, intuition, and eventually, pain.

Game 3: Forward, call, and put option with strike 15. The put gives you the right to sell at 15. Now traders can express views on both directions. They can also discover put-call parity by accident. If they notice that buying a call and selling a put at the same strike recreates a forward, they have just derived one of the most fundamental relationships in options theory without any math.

Each game runs five rounds, five minutes per round. Plenty of time for negotiation and regret.

The Trading Process

During each round, players shout out bids and offers. “I’ll sell you a forward at 19!” “I’ll buy a call at 15 strike for $2!” If someone accepts, both parties record the transaction on their trading sheets.

Each trade records:

• For forwards: the forward price and quantity
• For options: type (call/put), exercise price, cost per contract, and quantity

When nobody wants to trade, the organizer acts as market maker to keep things moving. “Anyone want to buy shares? At what price?” Sometimes you need to push people into the deep end.

After each round, the die is rolled and everyone sees the result. Now the math changes. After three rounds with rolls of 4, 6, and 2, you know the running total is 12 with two rounds left. The expected final price shifts. The fair value of every contract shifts. And suddenly the quiet student in the corner realizes their forward at 16 is looking really good.

What Players Actually Learn

Here is why this game is so much better than a lecture:

Bid-offer spreads emerge naturally. Nobody will sell a forward at exactly 17.5. The seller wants 18. The buyer wants 17. The spread between bid and offer is real and meaningful. It is how market makers survive.

Liquidity matters. In a room of 20 students, you might find nobody wants to trade with you. Your position is “illiquid.” You know it is worth something, but you cannot exit. This is a lesson that no equation teaches.

Information changes everything. After each dice roll, the expected final price shifts. Contracts that seemed fairly priced suddenly look expensive or cheap. Players learn to update their views in real time.

Arbitrage becomes intuitive. If someone sells a call too cheap while someone else sells a put too expensive, a sharp player can lock in a guaranteed profit. No formula needed. Just common sense about what these contracts are worth relative to each other.

Risk feels different when it is your money. Buying ten calls at $2 each costs $20 of play money. If those calls expire worthless, you have lost $20. The math said it was a reasonable bet. Your stomach says otherwise. That emotional experience is irreplaceable.

The Trading Sheet

Each player keeps a paper trading sheet. During the game, you fill in your contracts, whether you bought or sold, and the cost per contract. At the end of the game, when the final stock price is known, you fill in the settlement value and calculate your profit or loss.

Wilmott gives a worked example. A player does three trades in a round:

• Buy 10 calls (strike 20) at $2 each
• Sell 1 put (strike 15) at $1
• Buy 5 forwards (forward price 19)

Final stock price comes in at 21. The calls at strike 20 are worth $1 each (bought for $2, so loss of $1 each, times 10 = -$10). The put at strike 15 expires worthless (the seller keeps the $1 premium, profit = +$1). The forwards at 19 are worth 21 - 19 = $2 each, times 5 = +$10.

Total: -10 + 1 + 10 = +$1. A small win.

That $1 profit feels earned in a way that solving a textbook problem never does.

Advanced Variations

For students who have mastered the basics, Wilmott suggests cranking up the complexity:

• More rounds. More dice rolls means a wider range of outcomes and more opportunity for trading.
• Shorter rounds. Less time to think means faster, more instinctive decisions. Closer to real trading.
• Multiple strike prices. Instead of just one call at strike 15, offer calls at 10, 15, 20, and 25. Now players must think about the relationship between options at different strikes.
• Exotic options. Throw in an Asian option (payoff based on the average stock price across all rounds, not just the final price). Or a barrier option (option dies if the stock hits a certain level during the game). These teach path dependence in a visceral way.
• Second die. A second die creates a second “stock.” Now players can trade options on two different underlyings. Correlation between them is zero (they are independent dice), which itself is an important lesson.
• Futures with margin. Instead of forwards (settled at the end), introduce futures that are marked to market after each round. Players must pay or receive margin. If you run out of cash, you are bankrupt. This teaches why leverage kills.

Why This Chapter Matters

This is the shortest chapter in the book. No formulas, no proofs, no Greeks. Some readers probably skip it. That would be a mistake.

The entire first part of Wilmott’s book has been building mathematical machinery: random walks, Ito’s lemma, Black-Scholes, hedging strategies. All essential. But the trading game connects that theory to human behavior. You discover that fair value means nothing if nobody will trade with you. That being right about direction does not help if your timing is wrong. That risk management is not about avoiding losses but about surviving the bad days long enough to benefit from the good ones.

Wilmott designed his Certificate in Quantitative Finance (CQF) program around the idea that quants need practical understanding, not just mathematical skill. This chapter is a small example of that philosophy.

If you have a group of friends interested in finance, try this game. A couple of dice, some paper, an hour of time. You will learn more about options in that hour than in a week of reading.

The goal, after all, is simple: make more money than your opponents. Everything else is just theory.

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