6 Options II

We saw in futures ii that you could open a short

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Unformatted text preview: 1- Jan- 09 =date(yyyy,mm,dd) 26 Days to expiration 366.0 =c25- c24 5. The Greek Letters - - Parameters for Hedging Risk with Option Positions: [FYI] {Hull Ch. 17} • Delta Δ = dc/dS (or dp/dS) • Gamma Γ = dΔ/dS • Vega V = dc/dσ (or dp/dσ) • Theta Θ = dc/dt (or dp/dt) - - “time decay parameter” • Rho ρ = dc/drf (or dp/drf) 6. Implied Volatility: {Hull §13.9} a) The BSM model gave fairly accurate predictions of call and put premiums when put to empirical tests, and was quickly in widespread use by options traders. b) Given a belief in the accuracy of the model and faith in the efficiency of financial markets (they quickly and accurately process relevant new information), it is not surprising that people began using the BSM model to determine the underlying stock price volatility σ. 1) For a given stock and recent stock options, the input parameters were entered into the model, and then the value of σ was adjusted so that the model gave the same option premium as that which had been observed in the market. 2) This value of σ is the implied volatility of the stock, and is then put into the BSM model to value new options on the same stock. Ec 174 OPTIONS II p. 17 of 18 7. The VIX and Other Volatility Indexes: {Hull, p. 304; BKM §21.4, pp. 728- 33} a) We learned earlier that there are futures contracts on stock indexes. Similarly, there are also options on stock indexes (S&P 500, DJIA, Nasdaq 100, all traded at the CBOE). 1) For index futures and index options, the underlying asset is the stock index It. 2) As with all options and futures, index futures and index options can be used for both speculation on future moves of the stock market, or for hedging risk. 3) “Portfolio insurance” - - you have a portfolio of equity securities and want to hedge against a decline in the price of your stocks and the value of your portfolio. • We saw in Futures II that you could open a short position in an index futures con- t...
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