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FUTURES AND OPTIONS Chapter 16

FUTURES AND OPTIONS Chapter 16. Futures and Options Relations Futures Option Contracts. Put-Call-Futures Parity. Conversion: Long in futures at fo Long in put Short in call At expiration the value of the position will be X-fo regardless of the price of the underlying asset.

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FUTURES AND OPTIONS Chapter 16

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  1. FUTURES AND OPTIONSChapter 16 Futures and Options Relations Futures Option Contracts

  2. Put-Call-Futures Parity Conversion: • Long in futures at fo • Long in put • Short in call At expiration the value of the position will be X-fo regardless of the price of the underlying asset.

  3. Put-Call-Futures Parity

  4. Put-Call-Futures Parity • Note: If the carrying-Cost Model holds and the futures and option expire at the same time, then put-call-futures parity and put-call parity are the same. • Proof:

  5. BOPM Defined in Terms of Futures Contracts • The replicating portfolio underlying the BOPM can be defined in terms of futures positions instead of the spot • Consider the example for the single-period BOPM for currency options presented in Chapter 15: • u = 1.1, d = .95, Rus = .05, RF = .03, X = $1.50, Eo = $1.50, and Co = $0.066. • Suppose there is a futures contract on the currency that expires in one period and assume that the carrying-cost model (IRPT) holds.

  6. BOPM Defined in Terms of Futures Contracts

  7. BOPM Defined in Terms of Futures Contracts • Replicating Portfolio: • Go long in Ho futures contracts and borrow Bo dollars.

  8. BOPM Defined in Terms of Futures Contracts • Solve for Ho and Bo where: • Solution:

  9. BOPM Defined in Terms of Futures Contracts • Equilibrium Price • The same price obtained with a replicating portfolio using the spot position.

  10. BOPM Defined in Terms of Futures Contracts • If the call is mispriced, then the arbitrage can be defined in terms of the futures position. For example, if the market price of the currency call were $0.075, an arbitrageur would sell the call at $0.75, go long in Ho = .6667 currency futures at Ef = $1.529, and invest $0.066 in a risk-free security. This would yield an initial CF of .009 and no liabilities at T (see Table 16.3-1). • This is a much simpler arbitrage strategy than the one using a spot position.

  11. Futures Options • Futures options give the holder the right to take a futures position: • Futures Call Option gives the holder the right to go long. When the holder exercises, she obtains a long position in the futures at the current price, ft, and the assigned writer takes the short position and pays the holder ft - X. • Futures Put Option gives the holder the right to go short. When the holder exercises, she obtains a short position at the current futures price, ft, and the assigned writer takes the long position and pays the put holder X - ft. • Futures options on Treasuries, stock indices, currency, and commodities.

  12. Futures Options Call on S&P 500 Futures: • X = 1250 • C = 10, Multiplier = 500 • Futures and options futures have same expiration.

  13. Futures Options • Put on SP 500 Futures • X = 1250 • P =10, multiplier = 500 • Futures and options futures have same expiration.

  14. Put-Call Parity • Put-call parity for futures options is formed with a conversion: Long in futures at fo, long in put, and Short in call. • At expiration the value of the position will be X-fo regardless of the price of the underlying futures. • If the futures option, spot option, and futures expire at the same time and the carrying-cost model holds, then put-call-futures, put-call spot and put-call on futures option are thesame.

  15. BOPM for Futures Option • BOPM for a futures option is the same as the BOPM for a spot if the futures and option expire at the same time and if the carrying cost model holds. • If the futures and futures option do not expire at the same time, then the BOPM for futures option will differ.

  16. BOPM for Futures Option

  17. BOPM for Futures Options • Replicating Portfolio: • Go long in Ho futures contract and borrow Bo dollars.

  18. BOPM for Futures Options • Solve for Ho and Bo where: • Solution:

  19. BOPM for Futures Options • Equilibrium Price

  20. Black Model for Futures Options • Equilibrium Price • Black Model includes fo instead of So and there is no interest rate. • If the carrying-cost model holds and the futures and futures option expire at the same time, then the Black futures option model is the same as the B-S OPM for spot.

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