Topic 4 Option Basics and Put_Ca by benbenzhou

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									                    Overview of the Options Market
              No Arbitrage Bounds on Option Prices
                                     Put-Call Parity
                 Early Exercise of American Options




         Topic 4: Option Basics and Put-Call Parity
                                 Finance 353: Derivatives


                                              Hengjie Ai

                       The Fuqua School of Business, Duke University


                                     Daytime MBA 2009




1 / 23                                  Finance 353    Topic 4: Option Basics
                       Overview of the Options Market
                 No Arbitrage Bounds on Option Prices
                                        Put-Call Parity
                    Early Exercise of American Options



Outline of the Lecture



         Overview of the Options Market
         No Arbitrage Bounds on Option Prices
         Put-Call Parity
         Optimal Exercise of American Options
         Required Reading Before Class:
             Section 9.1, 9.2, 9.3 of textbook




2 / 23                                     Finance 353    Topic 4: Option Basics
Some Market Statistics
Option Trading Volume by Type of Contracts and by Exchange
Some Market Statistics
Option Trading Volume by Type of Contracts and by Exchange
Some Market Statistics
Equity Option Trading Volume and Index Option Trading Volume
Some Market Statistics
Equity Option Trading Volume and Index Option Trading Volume
Some Market Statistics
Futures Option Trading Volume
                      Overview of the Options Market
                                                         Some Market Statistics
                No Arbitrage Bounds on Option Prices
                                                         Reading Newspaper Quotes
                                       Put-Call Parity
                                                         Floor-Based Trading and Electronic Trading
                   Early Exercise of American Options



Reading Newspaper Quotes




         Quote from WSJ




6 / 23                                    Finance 353    Topic 4: Option Basics
                        Overview of the Options Market
                                                           Some Market Statistics
                  No Arbitrage Bounds on Option Prices
                                                           Reading Newspaper Quotes
                                         Put-Call Parity
                                                           Floor-Based Trading and Electronic Trading
                     Early Exercise of American Options



Floor-Based Trading and Electronic Trading



         Floor-based trading
             Market makers
             Floor brokers
             Order book o¢ cials and exchange o¢ cials
             Margin Requirements
         Electronic Trading
             The primary market maker
             The competitive market maker
             The electronic access member




7 / 23                                      Finance 353    Topic 4: Option Basics
                        Overview of the Options Market
                                                           Some Market Statistics
                  No Arbitrage Bounds on Option Prices
                                                           Reading Newspaper Quotes
                                         Put-Call Parity
                                                           Floor-Based Trading and Electronic Trading
                     Early Exercise of American Options



Floor-Based Trading and Electronic Trading



         Floor-based trading
             Market makers
             Floor brokers
             Order book o¢ cials and exchange o¢ cials
             Margin Requirements
         Electronic Trading
             The primary market maker
             The competitive market maker
             The electronic access member




7 / 23                                      Finance 353    Topic 4: Option Basics
                          Overview of the Options Market
                                                                 Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                                 Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                                 Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Upper Bounds on the Value of Call and Put Options
An Upper Bound on the Price of Call Options


          Price of a call must be less than the current price of the stock:

                                                             c     S0

               Intuition: A call allows you to buy the stock, however, at a cost
               (strike price).
          A no arbitrage argument: How would you make an arbitrage if
          c > S0 ?

               Portfolio Strategy                  Cash Flow                  Cash Flow @ Date T
                                                    @ Date 0                    ITM       OTM
                   Long Stock                           S0                       ST        ST
                    Sell Call                          c                       ST + K       0
                     Total                           c S0                        K         ST

8 / 23                                        Finance 353        Topic 4: Option Basics
                          Overview of the Options Market
                                                                 Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                                 Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                                 Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Upper Bounds on the Value of Call and Put Options
An Upper Bound on the Price of Call Options


          Price of a call must be less than the current price of the stock:

                                                             c     S0

               Intuition: A call allows you to buy the stock, however, at a cost
               (strike price).
          A no arbitrage argument: How would you make an arbitrage if
          c > S0 ?

               Portfolio Strategy                  Cash Flow                  Cash Flow @ Date T
                                                    @ Date 0                    ITM       OTM
                   Long Stock                           S0                       ST        ST
                    Sell Call                          c                       ST + K       0
                     Total                           c S0                        K         ST

8 / 23                                        Finance 353        Topic 4: Option Basics
                          Overview of the Options Market
                                                             Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                             Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                             Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Upper Bounds on the Value of Call and Put Options
An Upper Bound on the Price of Put Options



          Price of a put is never higher than the strike price
                                                                 rT
                                                       p     e        K

               Intuition: With a put option, in order to obtain the strike price, you
               must give up the stock, which is of positive value.
          A no arbitrage argument: How would you make an arbitrage if
          p > e rT K ?
               Answer: Write the put and invest the money
          The upper bounds for option prices derived here are very general
               It does not depend on whether the option is European or American
               It does not depend on the dividend policy of the stock


9 / 23                                        Finance 353    Topic 4: Option Basics
                          Overview of the Options Market
                                                                 Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                                 Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                                 Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Lower Bounds for the Price of Put Options
A Lower Bound for Put Options on Non-Dividend Paying Stocks


          For non-dividend-paying stocks:
                                                                 rT
                                                  p          e        K     S0

          A no arbitrage proof:

              Portfolio Strategy                 Date 0 Cash Flow                     Date T Cash Flow
              C     Long 1 put                           p                              max fK , ST g
                   Long 1 stock                          S0
              D Invest Ke rT                           Ke rT                                        K

          Conclusion:
               Portfolio C has higher payo¤ than D, therefore must have higher
               cost.
               In general, [PV (ST ) + p ] PV (K )

10 / 23                                       Finance 353        Topic 4: Option Basics
                          Overview of the Options Market
                                                                  Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                                  Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                                  Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Lower Bounds for the Price of Put Options
A Lower Bound on Put Options on Stocks with Dividend

          For stocks with continuous dividend:
                                                             rT               δT
                                              p      e            K     e          S0

          A no arbitrage proof:

               Portfolio Strategy                    Date 0 Cash Flow                       Date T Cash Flow
            C0       Long 1 put                              p                                max fK , ST g
                  Long e δT stock                         e δ T S0
            D0      Invest Ke rT                           Ke rT                                         K

          Similarly, for stocks with discrete dividends:
                                                                                                 !
                                                                             n
                                 p        e    rT
                                                    K             S0        ∑e        rti
                                                                                            Di
                                                                            i =1

11 / 23                                       Finance 353         Topic 4: Option Basics
                          Overview of the Options Market
                                                                  Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                                  Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                                  Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Lower Bounds for the Price of Call Options
Non-Dividend Paying Stocks


          For Non-dividend Paying Stocks:
                                                                          rT
                                                 c0          S0       e        K

          A no arbitrage proof:

                Portfolio Strategy                           Date 0 Cash Flow                   Date T Cash Flow
           A          Long 1 call                                    c                            max fK , ST g
                Invest Ke rT in bond                               e rT K
           B         Long 1 stock                                    S0                                       ST

          Conclusion:
               There cannot be an asset that always beats the stock.
               In general, c + PV (K ) PV (ST )

12 / 23                                       Finance 353         Topic 4: Option Basics
                          Overview of the Options Market
                                                                  Upper Bounds on the Value of Call and Put Options
                    No Arbitrage Bounds on Option Prices
                                                                  Lower Bounds for the Price of Put Options
                                           Put-Call Parity
                                                                  Lower Bounds for the Price of Call Options
                       Early Exercise of American Options



Lower Bounds for the Price of Call Options
Dividend Paying Stocks

          For stocks with continuous dividend:
                                                             δT                rT
                                             c       e            S0       e        K

          A no arbitrage argument:

                 Portfolio Strategy                           Date 0 Cash Flow                      Date T Cash Flow
            A0         Long 1 call                                    c                               max fK , ST g
                 Invest Ke rT in bond                               e rT K
            B0     Long e δT stock                                 e δ T S0                                    ST

          Similarly, for stocks with discrete dividends:
                                                    !
                                                          n
                                 c            S0         ∑e         rti
                                                                          Di         e     rT
                                                                                                K
                                                         i =1

13 / 23                                       Finance 353         Topic 4: Option Basics
                          Overview of the Options Market
                                                               Put-Call Parity for Stock Options
                    No Arbitrage Bounds on Option Prices
                                                               An Alternative Formulation of the Put-Call Parity
                                           Put-Call Parity
                                                               Put-Call Parity for Other Options
                       Early Exercise of American Options



Put-Call Parity for Stock Options
Non-Dividend Paying Stocks


          For non-dividend paying stocks:
                                                                           rT
                                              c       p = S0          e         K

          A no arbitrage argument:

                Portfolio Strategy                           Date 0 Cash Flow                  Date T Cash Flow
           A          Long 1 call                                    c                           max fK , ST g
                Invest Ke rT in bond                               e rT K
           C          Long 1 put                                     p                              max fK , ST g
                     Long 1 stock                                    S0

          Conclusion: law of one price implies portfolio A and B must have the
          same price at date 0: c + e rT K = p + S0

14 / 23                                       Finance 353      Topic 4: Option Basics
                          Overview of the Options Market
                                                                  Put-Call Parity for Stock Options
                    No Arbitrage Bounds on Option Prices
                                                                  An Alternative Formulation of the Put-Call Parity
                                           Put-Call Parity
                                                                  Put-Call Parity for Other Options
                       Early Exercise of American Options



Put-Call Parity for Stock Options
Dividend Paying Stocks



          For stocks with continuous dividend at annual rate δ:
                                                               δT                   rT
                                         c       p=e                S0         e         K

               Proof: compare portfolio A 0 and C 0
          For stocks with (known) discrete dividend payments:
                                                   !
                                                              n
                              c      p=          S0          ∑e         rti
                                                                              Di           e   rT
                                                                                                    K
                                                             i =1

          where the dividend payments D1 , D2 ,                                    , Dn are scheduled at t1 ,
          t2 ,  , tn .


15 / 23                                       Finance 353         Topic 4: Option Basics
                         Overview of the Options Market
                                                               Put-Call Parity for Stock Options
                   No Arbitrage Bounds on Option Prices
                                                               An Alternative Formulation of the Put-Call Parity
                                          Put-Call Parity
                                                               Put-Call Parity for Other Options
                      Early Exercise of American Options



An Alternative Version of the Put-Call Parity


          An alternative version:

                         c      p = PV (stock )                   PV (Exercise Price )

          This encompasses the formula developed above. Verify it.
          Implications of the Put-Call Parity
              If we can price a call, we will be able to price a put, and vice versa.
              We can create synthetic options, synthetic stocks, and synthetic
              T-bills using the formula:

                                             Call           Put = Stock            TBill

              It does NOT apply to American options




16 / 23                                      Finance 353       Topic 4: Option Basics
                         Overview of the Options Market
                                                             Put-Call Parity for Stock Options
                   No Arbitrage Bounds on Option Prices
                                                             An Alternative Formulation of the Put-Call Parity
                                          Put-Call Parity
                                                             Put-Call Parity for Other Options
                      Early Exercise of American Options



Put-Call Parity for Other Options


          Consider European call and put options on the Euro:
               with strike price K ($/e) and maturity date T .
               Current exchange rate is x0 ($/e).
               The continuously compounded interest rate for $ is r , and r for e.
          The put-call parity is:
                                                            r T                rT
                                       c       p=e                x0     e          K

          Put-Call Parity for Stock Exchange Options

                                                                           strike
                                 c       p = PV (ST )                  PV ST




17 / 23                                      Finance 353     Topic 4: Option Basics
                        Overview of the Options Market
                                                           Why is it important?
                  No Arbitrage Bounds on Option Prices
                                                           American Call on Dividend Paying Stocks (Optional Reading)
                                         Put-Call Parity
                                                           Early Exercise of Put Options (Optional Reading)
                     Early Exercise of American Options



Why is it important?




          Question: Should an American option have a higher price than a
          European option with the same strike price and maturity?
          Answer: It depends.
          We cannot understand the valuation of an American option without
          understanding how to exercise it.
          When is early exercise optimal?




18 / 23                                     Finance 353    Topic 4: Option Basics
                         Overview of the Options Market
                                                            Why is it important?
                   No Arbitrage Bounds on Option Prices
                                                            American Call on Dividend Paying Stocks (Optional Reading)
                                          Put-Call Parity
                                                            Early Exercise of Put Options (Optional Reading)
                      Early Exercise of American Options



American Call on Non-Dividend Paying Stock (I)
The Short Answer




          It is NEVER optimal to exercise before maturity. Why?
          The short answer: You make more money by selling the option than
          exercising it
              cAmerican c St e r (T t ) K > St K
              If you exercise it, the payo¤ is St K .
              If the option is out of the money, then you do not want to exercise
              either.




19 / 23                                      Finance 353    Topic 4: Option Basics
                           Overview of the Options Market
                                                               Why is it important?
                     No Arbitrage Bounds on Option Prices
                                                               American Call on Dividend Paying Stocks (Optional Reading)
                                            Put-Call Parity
                                                               Early Exercise of Put Options (Optional Reading)
                        Early Exercise of American Options



American Call on Non-Dividend Paying Stock (II)
The Long Answer




          What if you cannot sell the option?
          Compare the two strategies:
              Strategy A: Exercise now, and sell the stock at time T
              Strategy B: Delay exercise until maturity

                  Strategy         Date t                               Date T Cash Flow
                                  Cash Flow                   In The Money         Out of the Money
                     A                 K                             ST                     ST
                     B                0                           ST K                       0
                                       K                        e r (T t ) K i
                                                                h                      e r (T t ) K
                   Total                   K             S T + e r (T      t)      1 K           e r (T    t)K    > ST




20 / 23                                        Finance 353     Topic 4: Option Basics
                            Overview of the Options Market
                                                                    Why is it important?
                      No Arbitrage Bounds on Option Prices
                                                                    American Call on Dividend Paying Stocks (Optional Reading)
                                             Put-Call Parity
                                                                    Early Exercise of Put Options (Optional Reading)
                         Early Exercise of American Options



American Call on Non-Dividend Paying Stock (III)
What if you expect the stock price will fall?



           You will short the stock, in stead of exercise the call
           Compare the two strategies:
                 Strategy A: Exercise at time t, and sell the stock immediately
                 Strategy B: Delay exercise until maturity, short the stock at time t
                 Assume interest rate is 0 for simplicity

                    Strategy          Date t                               Date T Cash Flow
                                     Cash Flow                  In The Money       Out of the Money
                       A              St K                              0                    0
                       B                 0                         ST K                      0
                                          K                       e r (T t ) K         e r (T t ) K
                                        St                     h        ST i                 ST
                     Total              St      K               e r (T   t)     1 K          e r (T   t)K        ST > 0



21 / 23                                         Finance 353         Topic 4: Option Basics
                         Overview of the Options Market
                                                            Why is it important?
                   No Arbitrage Bounds on Option Prices
                                                            American Call on Dividend Paying Stocks (Optional Reading)
                                          Put-Call Parity
                                                            Early Exercise of Put Options (Optional Reading)
                      Early Exercise of American Options



American Call on Dividend Paying Stocks
          Lessons from the last example
              If you have an opinion about the underlying asset and want to
                                                                         t
              speculate on that opinion, trade that asset directly. Don’ do it by
              exercising the option.
              Even if you cannot trade the asset directly, sell the option rather
              than exercise it.
          Advantages of delaying exercise of American calls
              You pay the strike price K at a later date (time value of money)
              You can decide later on after uncertainty is resolved
          However, if the stock pays dividend, you lose the dividend payment
          if you delay exercise.
          Conclusion:
              If dividend payment is small, then late exercise is probably optimal
              It might be optimal to exercise early if dividend is large, especially
              when you are anticipating a large dividend payment.
22 / 23                                      Finance 353    Topic 4: Option Basics
                         Overview of the Options Market
                                                            Why is it important?
                   No Arbitrage Bounds on Option Prices
                                                            American Call on Dividend Paying Stocks (Optional Reading)
                                          Put-Call Parity
                                                            Early Exercise of Put Options (Optional Reading)
                      Early Exercise of American Options



Early Exercise of Put Options


          Disadvantages:
              By exercising early, we sell the stock for $K today, yet the stock
              price might go down in the future (optionality)
              By exercising early, we lose the dividend payment
          Advantages
              We receive $K early (time value of money)
          Conclusion:
              The only reason to exercise early is the time value of money
              Not optimal to exercise early if the dividend payment is large, or if
              stock price is volatile




23 / 23                                      Finance 353    Topic 4: Option Basics

								
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