Lecture 17: Options Markets

What this lecture covers

This lecture introduces options: contracts that give the right, but not the obligation, to buy (a call) or sell (a put) an asset at a fixed strike price. Professor Shiller builds up from everyday analogies, such as an option to buy land, to the formal machinery used to price stock options, ending with a look at implied volatility and the VIX index. It sits within the course's broader treatment of derivatives markets, following earlier lectures on stocks, bonds and futures.

By the end you should be able to explain what makes an option valuable, read an options price table, use put-call parity to check consistency between call and put prices, and follow the logic behind the binomial pricing model and the Black-Scholes formula, without needing to derive Black-Scholes yourself.

Key ideas

• Call and put options: a call gives the right to buy at the strike (exercise) price; a put gives the right to sell at it, both by a set exercise date.
• American vs. European options: American options can be exercised any time up to expiration; European options only on the expiration date itself.
• Theoretical purpose of options: economist Kenneth Arrow argued markets need prices for all possible future states; options, as shown by Stephen Ross, help complete that set of prices.
• Behavioral purpose of options: incentive stock options work partly because they make a company's share price salient to employees, and options resemble insurance, which offers peace of mind.
• Out of the money vs. in the money: a call is out of the money when the stock price is below the strike, and in the money when it is above; the reverse holds for puts.
• Put-call parity: on any date, the stock price equals the call price minus the put price plus the present value of the exercise price (adjusted for expected dividends).
• No-arbitrage pricing: option prices can be derived without knowing the probability of a price move, using a riskless hedged portfolio of the stock and the option.
• Implied volatility and the VIX: inverting the Black-Scholes formula from an observed option price yields the market's implied estimate of future volatility, tracked by the CBOE's VIX index.

Walkthrough

Defining options and everyday examples (0:00)

The lecture opens with the definitions of calls, puts, strike price and exercise date, then the American versus European distinction. Shiller gives non-financial illustrations, such as buying an option on a farmer's land before building a supermarket, and notes that mortgages and dating both have option-like features.

Why options exist (7:11)

Two justifications are offered. The theoretical case, drawing on Kenneth Arrow and Stephen Ross, is that options help complete the set of market prices needed for an efficient economy. The behavioral case ties options to attention and salience: incentive stock options change how employees think about company value, and options resemble insurance in providing peace of mind.

Reading an options price table and the derivatives market (17:11)

Using a Wall Street Journal clipping for America Online (later AOL Time Warner), Shiller shows how strike prices, expiration dates, and call and put prices are quoted. He explains the roles of the option buyer and the "writer" (seller), and how options trading became a large, independent derivatives market after the Chicago Board Options Exchange opened in 1973.

Payoff diagrams and put-call parity (24:54)

On the exercise date, a call's value is max(stock price - strike, 0), a broken straight-line relationship rather than a smooth linear one. Combining a long call and a short put reproduces the stock's own linear payoff, which leads to the put-call parity equation linking the stock price, call price, put price and the present value of the strike price (plus dividends).

Price bounds and the binomial model (39:07)

Before expiration, a call's price sits above the payoff line but below the stock price itself, and gets closer to the payoff line as expiration nears, which is why American call options are rarely exercised early. Shiller then derives a two-state (binomial) pricing formula by constructing a hedge ratio H of shares per option that makes a stock-plus-option portfolio riskless, then setting its return equal to the riskless rate. This no-arbitrage argument prices the option without using the probability of an up or down move.

The Black-Scholes formula (51:02)

The Black-Scholes Option Pricing Formula, developed by Fisher Black and Myron Scholes, extends the same no-arbitrage logic to continuous time. It prices a call using the stock price, strike price, time to maturity, interest rate and sigma, the standard deviation of the stock's price changes, without needing a probability estimate.

Implied volatility and the VIX (55:49)

Inverting Black-Scholes from an observed market price for an option yields the implied volatility, the market's expectation of future price variability; the CBOE publishes this as the VIX. Shiller compares the VIX since 1986 with actual historical volatility, pointing to spikes around the 1987 crash, the Asian financial crisis and the 2008 crisis, and contrasts these calm-punctuated-by-shocks patterns with the unusually volatile Great Depression era.

Options on housing (1:09:33)

The lecture closes with Shiller's own effort to launch options on single-family home prices at the Chicago Mercantile Exchange in 2006, and his continuing view that put options attached to mortgages could help homeowners manage price-decline risk.

Before you watch

• Review the course's earlier lectures on stocks and futures, since options are introduced as a derivative built on those underlying assets.
• Basic familiarity with present value discounting is assumed when the lecture adjusts put-call parity for time and dividends.

Check your understanding

1. What distinguishes an American option from a European option, and why is the American option never worth less than the European one?
2. State the put-call parity relationship and explain why arbitrage should force it to hold.
3. Why does the no-arbitrage pricing of a call option not require knowing the probability of the stock going up or down?
4. What does a high VIX reading tell you about market expectations, and how does implied volatility differ from historical volatility?
5. Why does the lecture argue that exercising an American call option early is usually a mistake?