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

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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