《金融学教学课件》ch.ppt

1,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,1,Chapter 14-15 Forward, Future and Option,Objective Understanding the definitions of forward, future and option Understanding the basic idea of synthetic security,2,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,2,Contents,1 Distinction Between Forward & Futures Contracts 2 Futures Price 3 Financial future,4 Definition of an option 5 How an option works 6 Two-state option-pricing,3,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,3,1 Distinction Between Forward & Futures Contracts,Forward: parties agree to exchange some item in the future at a delivery price specified now the forward price is defined as the delivery price which makes the current market value of the contract zero no money is paid in the present by either party to the other the face value of the contract is the quantity of the item specified in the contract multiplied by the forward price the party who agrees to buy the specified takes the long position, and the party who agrees to sell the item takes the short position,4,Who pays what to whom,If the spot price on the contract maturity date is higher than the forward price, the party who is long makes money. But if the spot price on the contract maturity date is lower than the forward price, the party who is short makes money.,5,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,5,Future: terms,Listing: Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest Mark-to-market at the end of each trading day based on that days settlement price. Margin requirement: the exchange requires that there be enough collateral posted in each account to cover any losses. Margin call: if the collateral in your account falls below a prespecified level, you will receive a margin call from the broker asking you to add money.,6,An illustration,Based on table 13.1. You place an order to take a long position in a July wheat futures contract on June 22, 2006. the broker requires you to deposit money in your account, say $1,500, as margin. On June 23, the future price closes 2.25cents per bushel lower, thus you have lost 1.25*5,000=$112.50 that day. The broker takes that amount out of your account (mark to market). The money is transferred to the exchange, which transfers it to one of the parties who was on the short side of the contract.,7,Daily realization of gains and losses,Such a process minimizes the possibility of contract default. And no matter how great their face value, the market value of future contracts is always 0 at the beginning of each day.,8,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,8,Summarized characteristics for future,standard contracts immune from the credit worthiness of buyer and seller because exchange stands between traders contracts marked to market daily margin requirements,9,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,9,2 Futures Price,Arbitrageurs place an upper bound on futures prices by locking in a sure profit on futures prices if the spread between the futures price and spot price becomes greater than the cost of carry: F - S C the cost of carry varies as a function of time and warehousing organization,10,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,10,3 Financial Futures,We now focus on financial futures standardized contracts for future delivery of stocks, bonds, indices, and foreign currency they have no intrinsic value, but represent claims on future cash flows they have very low storage costs settlement is usually in cash,11,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,11,Financial Futures,With no storage cost, the relationship between the forward and the spot is Any deviation from this will result in an arbitrage opportunity,12,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,12,Financial Futures: Example,Consider shares in Bablonics, Inc, trading at $50 each, ($5,000 for a round lot); assume 6-month T-bills yield 6% (compounded semiannually),13,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,13,Bablonics, Inc (Continued),1 Purchase one round lot of stock at spot This results in a negative cash flow today of $5,000 (out), and will generate a cash flow of 100*Spot6m (in) in six months,14,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,14,Bablonics, Inc (Continued),2 Cover todays negative cash flow by selling short $5,000 worth of 6-month T-bills with a face value of 5000 (1+ 0.06/2)0.5 = $5,150 The cash flow today is $5,000 (in), and the cash flow in six months will be $5,150 (out),15,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,15,Bablonics, Inc (Continued),3 Cover the risk exposure by selling 100 shares forward at the equilibrium price of 5000*(1+0.06/2)0.5 = $5,150 There is no cash flow today, but the value of this forward contract in six months will be $(Spot6m - 5,150),16,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,16,Bablonics, Inc (Continued),-$5,000 (long stock) + $5,000 (short bond) + $0 (short forward) = $0,17,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,17,Bablonics, Inc (Continued),Cash Flow in 6-Months + $Spot6m (settle long stock) - $5,150 (settle short bond) +($5,150 - $Spot6m) (settle forward) = $0,18,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,18,Bablonics, Inc (Conclusion),If your net risk-free investment was zero, and you receive nothing that is what you should expect and you expect to: received positive value with no risk, then the rule of one price has been violated lose value with no risk, then reverse the direction of all transactions, and again you profit with no risk,19,4 Definition of an Option,Recall that an American European call (put) option is the right, but not the obligation to buy (sell) an asset at a specified price any time before its expiration date on its expiration date,20,5 How Options Work,The Language of Options Contingent Claim: Any asset whose future pay-off depends upon the outcome of an uncertain event Call: an option to buy Put: an option to sell Strike or Exercise Price: the fixed price specified in an option contract Expiration or Maturity Date: The date after which an option cant be exercised American Option: an option that can be exercised at any time up to and including maturity date,21,European Option: an option that can only be exercised on the maturity date Tangible Value: The hypothetical value of an option if it were exercised immediately At-the-Money: an option with a strike price equal to the value of the underlying asset Out-of-the-Money: an option thats not at-the-money, but has no tangible value In-the-Money: an option with a tangible value Time Value: the difference between an options market value and its tangible value Exchange-Traded Option: A standardized option that an exchange stands behind in the case of a default Over the Counter Option: An option on a security that is not an exchange-traded option,22,23,24,Investing with Options,The payoff diagram (terminal conditions, boundary conditions) for a call and a put option, each with a strike (exercise price) of $100, is derived next,25,Option Payoff Diagrams,The value of an option at expiration follows immediately from its definition In the case of a call option with strike of $100, if the stock price is $90 ($110), then exercising the option results purchasing the share for $100, which is $10 more expensive ($10 less expensive) than buying it, so you wouldnt (would) exercise your right,26,Call Option Payoff Diagram,27,Put Option Payoff Diagram,28,An example,Suppose you have $100,000 to invest. The riskless interest rate is 5% per year and the stock pays no dividends. Spot stock price is $100 and call premium is $10 Strategies: 1. invest all $100,000 in the stock 2. invest all $100,000 in calls 3.invest $10,000 in calls and the rest in the risk-free asset,29,Payoff Diagrams for Alternative Bullish Stock Strategies,Strategy 2: leverage 10 times (slope 10 times the slope of strategy 1) Strategy 3: minimum portfolio rate of return = -5.5%,30,31,6 Two-State (Binary) Option-Pricing,We are now going to derive a relatively simple model for evaluating options The assumptions will at first appear totally unrealistic, but using some underhand mathematics, the model may be made to price options to any desired level of accuracy The advantage of the method is that it does not require learning stochastic calculus, and yet it illustrates all the key steps necessary to derive any option evaluation model,32,Binary Model Assumptions,Assume: the exercise price is equal to the forward price of the underlying stock option prices then depend only on the volatility and time to maturity, and do not depend on interest rates the put and call have the same price,33,Binary Model Assumptions,More specifically we assume: share price = strike price = $100 time to maturity = 1 year dividend rate = interest rate = 0 stock prices either rise or fall by 20% in the year, and so are either $80 or $120 at yearend,34,Binary Model: Call,Strategy: replicate the call using a portfolio of the underlying stock the riskless bond by the law of one price, the price of the actual call must equal the price of the synthetic call,35,Binary Model: Call,Implementation: the synthetic call, C, is created by buying a fraction x of shares, of the stock, S, and simultaneously selling short risk free bonds with a market value y the fraction x is called the hedge ratio,36,Binary Model: Call,Specification: We have an equation, and given the value of the terminal share price, we know the terminal option value for two cases: By inspection, the solution is x=1/2, y = 40,37,Binary Model: Call,Solution: We now substitute the value of the parameters x=1/2, y = 40 into the equation to obtain:,38,Binary Model: Put,Strategy: replicate the put using a portfolio of the underlying stock and riskless bond by the law of one price, the price of the actual put must equal the price of the synthetic put replicated above Minor changes to the call argument are made in the next few slides for the put,39,Binary Model: Put,Implementation: the synthetic put, P, is created by sell short a fraction x of shares, of the stock, S, and simultaneously buy risk free bonds