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Options and Futures Markets: Understanding Call and Put Options, Pricing Models, and Commodity Futures

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This chapter provides an overview of option and futures markets, covering topics such as call and put options, pricing models like Black & Scholes and binomial models, and commodity futures pricing. Learn about the different types of futures contracts and their key features.

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Options and Futures Markets: Understanding Call and Put Options, Pricing Models, and Commodity Futures

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  1. Chapter 4 Option and Futures Markets

  2. A.Option Market • Options • Call option: a contract that allows its holder to purchase a share of stock in the underlying company at a fixed price for a fixed length of time.

  3. A.Option Market • Put option: a contract that allows its holder to sell a share of stock in the underlying company at a fixed price for a fixed length of time.

  4. A.Option Market • 1) Equity as a call option B=S+P-C

  5. A.Option Market • Discrete put-call parity formula • Continuous compound put-call parity

  6. B.Option pricing model (OPM)Black & Scholes (1973) • Binomial model • Assumptions • Stock price follows a binomial generating process u: upward multiplier, u>0 no bound d: downward multiplier, 0≦d<1 • Perfect market Su q S Sd 1-q

  7. B.Option pricing model (OPM) • Model • Hedge ratio in risk-free hedge portfolios In risk-free portfolio, Su-mCu=Sd-mCd Hedge ratio m, Cu=max[0, Su-X] q C Cd=max[0, Sd-X] 1-q Su-mCu q S-mC Sd-mCd 1-q

  8. B.Option pricing model (OPM) • Call premium Hedge Prob. p 1- p

  9. B.Option pricing model (OPM) • B-S Option pricing model • Assumption • Perfect market • Continuous trading opportunity • Stock returns follow a Geometric Brownian Motion Process. Wiener process Instantaneous Expected rate of return Instantaneous S.D. of rate of return

  10. B.Option pricing model (OPM) • Model • Hedge ratio in risk-free hedge portfolio

  11. B.Option pricing model (OPM)

  12. B.Option pricing model (OPM) • Implications

  13. C.Futures Market • Futures • Futures: A contract that its holder was required to deliver or to buy a specified assets at a specified term on a specified expired date. • Types:Long, Short. • Commodities Futures: Corn, metal, etc. Currency Futures:￡,￥, etc. Financial Futures: T.B., T bond, etc. Index Futures: S&P 500, etc. • Date: Contract date • Price, Specification, quality: standardized

  14. C.Futures Market • Futures market: • Participants: Floor Brokers, independents (CBOT) • Rules: • Marked to market

  15. C.Futures Market • Price limit: Minimum price fluctuation limit Maximum daily price fluctuation • Clearing: Clearing house • Margin: Initial margin(3-15%) Maintenance margin(75-80% of Initial Margin) • Open interest • Taxes: Hedgers, speculators

  16. D.Commodity futures pricing • Storage theory • Normal Backwardation: Keynes& Hicks(1924) Compound current spot rate Storage cost Convenience yield

  17. D.Commodity futures pricing • Contango: Hardy(1923) • Unbiased expectation: Hartzmark (1987)

  18. D.Commodity futures pricing 2. Financial futures pricing Equilibrium, Disequilibrium,

  19. D.Commodity futures pricing 3. Synthetic Future Long

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