Products and Markets: Stocks, Bonds, and Everything in Between

Chapter 1 of Wilmott’s book starts gently. No scary equations yet. Just the basic building blocks of finance that everything else in the book rests on. If you have worked in finance for a while, you know most of this already. But if you are coming from math or engineering background, this is the foundation you need.

Money Has a Price Tag Called Time

The very first concept Wilmott introduces is the time value of money. Simple idea: $1 today is worth more than $1 a year from now. Why? Because you can do things with that dollar in the meantime. Put it in a bank, invest it, lend it to someone.

Banks compete for your money by offering interest rates. If you put $1 in a bank at interest rate r, after one year you have:

$(1 + r)$

After n years with compound interest: $(1 + r)^n$

But in quantitative finance, we almost always use continuously compounded interest. Instead of getting interest once a year, imagine getting it every second. The math works out to:

$e^{rt}$

So $1 invested at continuous rate r for time t gives you $e^{rt}$. This is the formula you will see everywhere in this book. The function e (Euler’s number, approximately 2.718) shows up constantly in finance.

The flip side is also important. If someone promises you $1,000,000 in two years and interest rate is 5%, what is that worth today? You multiply by $e^{-r(T-t)}$. At 5% rate, a million dollars in two years is worth roughly $904,837 today. Future money is always worth less than present money.

Wilmott makes an important aside here: to understand almost all of finance theory, you really only need four mathematical tools: the exponential function e, logarithms, Taylor series, and expectations. That is it. You can build the entire Black-Scholes framework on those four things.

Equities: Owning a Piece of a Company

A stock (or share, or equity) is simply ownership of a small piece of a company. The story is familiar: someone has a business idea, needs money, sells pieces of future profits to investors. Those investors become shareholders.

As a company grows, it might go public, listing shares on a stock exchange where anyone can buy and sell. This is how most of us interact with stocks.

The key point Wilmott emphasizes: stock prices are unpredictable. He shows the Dow Jones Industrial Average from 1950 to 2004 and makes the case that while many people claim to predict prices, nobody has been convincingly right. In this book, we treat prices as having a large element of randomness.

To demonstrate, he does a simple coin-toss experiment. Start with 100 (your stock price). Flip a coin: heads, multiply by 1.01; tails, multiply by 0.99. Plot the results. The random path you get looks surprisingly similar to a real stock chart. That is not a coincidence. It is the foundation of everything that follows.

Dividends and Stock Splits

Stocks also pay dividends, which are periodic cash payments to shareholders. When a stock goes “ex-dividend,” its price typically drops by roughly the dividend amount. There are some tax complications here that smart people exploit.

Stock splits are cosmetic changes. A company with a $900 stock might do a 3-for-1 split: you now hold three shares at $300 each. Same total value, different psychology.

Commodities: Gold, Oil, and Pulp

Commodities are raw materials: precious metals, oil, agricultural products. Their prices show seasonal patterns and depend heavily on scarcity. Most trading happens in the futures market, and most traders never actually take delivery of physical goods. Nobody on Wall Street wants 10,000 barrels of crude oil showing up at their office.

Currencies: The FX World

Exchange rates determine how much of one currency you can swap for another. The foreign exchange market (Forex or FX) is enormous. Some currencies are pegged to each other, some float freely.

There is an important consistency requirement. If you can trade dollars for pounds, and pounds for yen, that implies a specific dollar/yen rate. If that rate is wrong, you can make free money through arbitrage. In practice, traders exploit these tiny mispricings so fast that they rarely last.

Exchange rates are linked to interest rates. If the US raises interest rates while UK rates stay flat, expect the dollar to strengthen against the pound.

Bonds and Fixed Income

When you lend money to a bank, government, or company, you are dealing in the fixed income world. Bonds pay coupons (periodic interest payments) and return your principal at maturity.

Two types of interest payments matter:

• Fixed rate: you know exactly what you will get
• Floating rate: the rate changes over time

Interest rate swaps let people exchange fixed payments for floating ones. Governments and companies issue bonds to borrow money. The less trustworthy the borrower, the higher interest they must pay.

There are also inflation-linked bonds (index-linked in the UK, TIPS in the US). Their coupons and principal adjust with inflation, protecting you from the eroding power of rising prices.

Forwards and Futures: Locking in the Future

A forward contract is a promise to buy an asset at a set price on a future date. No money changes hands until delivery. A futures contract is similar but traded on an exchange with daily settlement.

Both are used for speculation (“I think oil will go up”) and hedging (“I need to lock in an exchange rate for a payment I will receive in six months”).

The No-Arbitrage Principle

This is the big idea of Chapter 1. Wilmott uses forwards to give the first example of no-arbitrage, one of the cornerstones of derivatives theory.

Here is the logic. Suppose a forward contract lets you buy an asset at price F at time T. The asset currently trades at S(t). Can we figure out what F should be?

Yes. Enter the forward contract (costs nothing). Simultaneously sell the asset short (receive S(t)). Put the cash in the bank. At maturity, use the forward to buy back the asset at price F, closing your short position.

Your guaranteed profit is:

$S(t) \cdot e^{r(T-t)} - F$

Since you started with zero and ended with a guaranteed amount, that amount must also be zero. Otherwise you get free money, which markets do not allow (for long). So:

$F = S(t) \cdot e^{r(T-t)}$

The forward price equals the spot price grown at the risk-free interest rate. This is elegant and powerful. The same no-arbitrage logic, applied in more sophisticated ways, is exactly how Black-Scholes pricing works.

The Takeaway

Chapter 1 is a warm-up. The math is simple. The concepts are intuitive. But the no-arbitrage principle introduced at the end is everything. It says: if you can set up a portfolio that eliminates all risk and starts with zero value, it must end with zero value too. Any violation means free money, and free money does not survive long in competitive markets.

Every pricing formula in this book traces back to this idea.

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