FIN 355 (20) - Introduction to options (module 6).pptx

FIN 355 Principles of Investments Introduction to Options Lecture Preview Big-Picture Motivation: “In total, the average daily turnover of exchange traded options in January 2023 was approximately 20.77 billion U.S. dollars.” -- Statista Research Department “In 2022… total U.S. options volume rea...

FIN 355 Principles of Investments Introduction to Options Lecture Preview Big-Picture Motivation: “In total, the average daily turnover of exchange traded options in January 2023 was approximately 20.77 billion U.S. dollars.” -- Statista Research Department “In 2022… total U.S. options volume reached 10.32 billion contracts, up 4.6% vs. 2021. That total includes 9.6 billion in equity-linked options, 721.2 million in non-equity options, and 55.1 million in options on futures.” -- Investors.com Discussion Outline: • What are option contracts? • Types of listed options • A few common option strategies • Intuition about what factors affect the valuation of option contracts • Put-call parity intuition Call options (right to buy) A call option is a contract that grants the owner the right - but not the obligation - to BUY an underlying asset: • at a specified price (the strike or exercise price) • on or before a specified date (expiration, exercise date, or maturity) By convention, stock options are sold in groups of 100. Important Intuition: The holder of the contract will exercise the call option if the market value of the underlying asset > exercise price. Otherwise the option will be allowed to expire without being exercised. Fincorp’s options Assume Fincorp stock is currently trading at $28.72 per share Strike Price Expiration Call price Put price 27.50 May 07 1.52 0.24 According to this information a person can buy the option to purchase 100 shares of Fincorp stock at $27.50/share before the close of trading on May 7th for $152. The price of Fincorp stock today was $28.72, and the price of the call was $1.52 per share. Put options (right to sell) A put option is a contract that grants the owner the right - but not obligation - to SELL the underlying asset: • at a specified price (strike or exercise price) • on or before a specified date (expiration, exercise date, or maturity) E.g., you can buy the option to sell 100 shares of Fincorp stock for $27.50/share before the close of trading on May 7th. The price of the put was $0.24 per share. Important Intuition: The holder of the contract will exercise the put option if the market value of the underlying asset < exercise price. Otherwise the option will be allowed to expire without being exercised. There are many different types of financial options Examples of options on financial instruments: • • • • • Stocks Foreign currency Stock indices Futures Interest rates Some notation (each of these items affects the option contract value) S = The underlying stock (or asset) price, ST is the underlying asset’s price at expiration S0 is the underlying asset’s price when the option is initiated X = The exercise, or strike, price, at which the asset can be purchased or sold t = The time to expiration, expressed in years; T is the expiration date. = The "volatility" of the underlying asset, equal to the square root of the variance of the asset's annualized rate of return r = The risk-free rate of interest over the life of the option How much is the option worth? (Hint: To answer this question start at the end and work backwards) When a call option expires, its value is never negative. If the stock price exceeds the exercise price, the option is worth the difference. At expiration, therefore, the call value cT is: cT = max [0, ST - X] The way your textbook describes this is with a two-row expression. The Payoff to the call holder: (ST - X) if ST > X 0 if ST < X Profit to call holder: Payoff - Purchase Price (the purchase price is the “premium”) At expiration, whoever “wrote” the call loses the value that the call holder earns. Payoff to call writer: - (ST - X) if ST >X and 0 if ST < X Profit to call writer: Payoff + Premium Fincorp’s options Assume Fincorp stock is currently trading at $28.72 per share Strike Price Expiration Call price Put price 27.50 May 07 1.52 0.24 According to this information a person can buy the option to purchase 100 shares of Fincorp stock at $27.50/share before the close of trading on May 7th for $152. The price of Fincorp stock today was $28.72, and the price of the call was $1.52 per share. A payoff diagram for a call option on a share of stock Value 0 If the stock price ends up being larger than the strike price then there is a positive payoff to the call option. Value X ST 0 X ST Payoff to a call position at expiration Payoff to a short (or written) call position at expiration Note that the payoff is not the same as the profit. These figures don’t account for the initial cost of buying the call (call premium). The payoff diagram for the call writer is the reverse image of the payoff to the call holder. Example – Call option contract on IBM stock Today: June 30 2023 Call option expiration date: Aug 19 2023 Strike price: $150 Premium: $4.10 Would the call be exercised if IBM’s price stays below $150? What will the payoff per share be if IBM’s price goes up to $152? Payoff = 152 – 150 = $2 Profit = 2 – 4.10 = -$2.10 Holding period return = -$2.10/$4.10 = - 51.22% Market and exercise price relationships “In the Money” – immediate exercise of the option would produce a positive payoff Call: exercise price < asset price Put: exercise price > asset price “Out of the Money” – immediate exercise of the option would not have positive payoff Call: asset price < exercise price Put: asset price > exercise price “At the Money” – exercise price = underlying asset price American, European, and Asian Options American - the option can be exercised at any time before expiration. In the U.S., most options are American style except for currency and stock index options. European - the option can only be exercised on the expiration date Asian - (also known as “averaging options”) the option’s payoff depends on the average price of the underlying asset over a certain period of time. The option contract specifies the time period and whether or the average is an arithmetic or geometric average. Typically these options do not allow early exercise but not always. Figure 20.2 Payoff and Profit to Call Option at Expiration The vertical difference between the payoff line and the profit line is the cost of purchasing the option. At what x-axis value does the dotted line cross the horizontal axis? What is the slope of the lines that slope upwards? What would be the slope on the payoff diagram if you invested directly in the stock? Figure 20.3 Payoff and Profit to Call Writers at Expiration How large could the potential loss be for the option writer? What is a “naked option”? What is the slope of the downward? Figure 20.4 Payoff and Profit to Put Option at Expiration How does this payoff and profit diagram compare to a call option payoff diagram at expiration? Consider 3 different portfolios using 100% stock, 100% options for those stocks, or a mix of both. Assume you have $10,000 to invest. Strategy A: Invest entirely in stock. Buy 100 shares, each selling for $100. Strategy B: Invest entirely in at-the-money call options. Buy 1,000 calls, each selling for $10. This would require 10 contracts, each for 100 shares. Strategy C: Purchase 100 call options for $1,000. Invest your remaining $9,000 in 6-month T-bills, to earn 3% interest. The bills will be worth $9,270 at expiration. Payoffs to 3 strategies – remember the original stock price was $100/share Why is the payoff $0 to strategy B if the stock price remains at $100? Why is the payoff $5,000 to strategy B if the stock price goes up to $105? Why is the payoff $9,770 to strategy C if the stock price goes up to $105? What would the return be in the $95 column? What would the return be in the $120 column? Payoffs to 3 strategies – remember the original stock price was $100/share $105 column payoff to strategy C: The 100 call options would be worth $5 each. So the payoff would be 9270 + 500. Why is the payoff $0 to strategy B if the stock price remains at $100? Why is the payoff $5,000 to strategy B if the stock price goes up to $105? Why is the payoff $9,770 to strategy C if the stock price goes up to $105? What would the return be in the $95 column? What would the return be in the $120 column? Payoffs to 3 strategies – remember the original stock price was $100/share Why is the payoff $0 to strategy B if the stock price remains at $100? Why is the payoff $5,000 to strategy B if the stock price goes up to $105? Why is the payoff $9,770 to strategy C if the stock price goes up to $105? What would the return be in the $95 column? What would the return be in the $120 column? Payoffs to 3 strategies – remember the original stock price was $100/share Why is the payoff $0 to strategy B if the stock price remains at $100? $95 column returns: A: (9500 – 10000)/10000 = -5% Why is the payoff $5,000 to strategy B if the stock price goes up to $105? Why is the payoff B: (0 – 10000)/1000 = -100% $9,770 to strategy C if the stock price goes up to $105? C: (9270 – 10000)/10000 = -7.3% What would the return be in the $95 column? What would the(Preturn be0 in the $120 column? 1 – P0)/P Figure 20.5 Plot showing the rate of return to the 3 strategies Why are the upward slopes different for the various strategies? Why do the upward slopes start at S = 100 for both B and C? Protective Put – own the stock and a put option on the stock. Puts can be used as insurance against stock price declines. Figure 20.7 - Protective put vs. stock payoff and profit Table 10.1 – Value of protective put at expiration Covered call – own the underlying stock and write a call against it. The call writer gives up any stock value above X in return for the initial premium Long straddle: Buy call and put with the same exercise price and maturity. The straddle is a bet on volatility. The writer of a straddle is betting the stock price will not change much. Spreads A spread position is a combination of 2 or more calls (or puts) on the same stock with • Differing exercise prices (X1, X2), or • Differing times to maturity. Some options are bought, whereas others are sold, or written. A bullish spread is a way to profit from stock price increases. Table 20.4 – Value of a bullish spread position at expiration: Value of a Bullish Spread Position at Expiration - A bullish spread is a way to profit from stock price increases. Collars A collar is an options strategy that brackets the value of a portfolio between two bounds. • Limit downside risk by selling upside potential • Buy a protective put • Fund put purchase by writing a covered call • Net outlay for options is approximately zero 2 approaches to option valuation • Black Scholes Model • Binomial Lattice Approach Important Intuition: In this class I don’t expect you to calculate the value of options using these approaches. I do expect you to know the general intuition behind these approaches, and the factors that would lead to an increase in option value. The Black-Scholes option pricing formula The value of a call option is: c = S *N (d1) - X *e-rt *N(d2) N(d1) is the cumulative unit normal distribution function evaluated at d1. It is the probability that a draw of a random variable that is normally distributed with mean zero and variance equal to one will be at or below d1. Loosely speaking this tells us the probability that the option will expire in the money. Where The binomial lattice for a four-week option example: Outcome Probability of outcome S = 50, c = 10 .0625 S = 45, c = 5 .25 S = 40, c = 0 .375 S = 35, c = 0 .25 S = 30, c = 0 .0625 Current stock price = 40 Now Week 1 Week 2 Week 3 Week 4 2 approaches to option valuation • Black Scholes Model • Binomial Lattice Approach Important Intuition: • The Black Scholes approach uses a cumulative normal distribution to describe the likely future price outcomes and assesses the probability those outcomes will be in the money or not. • The Binomial Lattice approach uses a lattice with fixed probabilities to describe the likely future price outcomes and assesses the probability those outcomes will be in the money or not. • In both cases, the call option value will increase as t increases or as volatility increases. • In both cases, the call option value will decrease as X increases. The binomial lattice for a four-week option example: Outcome Probability of outcome S = 50, c = 10 .0625 S = 45, c = 5 .25 S = 40, c = 0 .375 S = 35, c = 0 .25 S = 30, c = 0 .0625 Current stock price = 40 Week 1 Week 2 Week 3 Week 4 𝜎 Now Determinants of call option values • For a given exercise price, if S increases then the value of the call increases • Higher volatility in outcomes leads to higher option value. • More time until expiration increases the call value. Put-call parity intuition • You can create the same type of payoff using two different sets of investments: • A call plus bond portfolio • A stock plus put portfolio • The left side of the equation below is the cost to the first approach, the right side is the cost to the second set. If arbitrage can’t exist long term then the value of the left side must (on average) equal the value of the right side. For next time.. Review the concepts and terminology introduced in today’s lecture. Be sure to look at the online schedule for the assigned reading and the upcoming homework assignments. Terminology You should be able to give a 1-2 sentence description of each of these terms. • • • • • • • • • • • Call Put Protective put Covered call “Naked” option writing Strike price Exercise price Maturity date Expiration date Payoff vs profit Callable bonds • American vs European vs Asian options • Straddle vs collar • Put-call parity • Can you combine stock ownership with owning/writing an option to achieve a particular payoff? • Can you see how options are useful for creating hedged positions? (If you don’t know a term you can look in the assigned reading from the textbook or on Investopedia.com) Thank You