# Bài giảng Financial Markets - Lecture 22: Other Derivatives

Option Parameters Delta: Partial derivative of option price with respect to underlying price: ∂C/∂S Gamma: Second partial derivative of option price with respect to underlying: ∂2C/∂S2 Theta: Partial derivative of option price with respect to time ∂C/∂T. (Equals minus the partial derivative with respect to time remaining until exercise) Vega: Partial derivative of option price with respect to volatility ∂C/∂σ

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Lecture 22: Other DerivativesOption ParametersDelta: Partial derivative of option price with respect to underlying price: ∂C/∂SGamma: Second partial derivative of option price with respect to underlying: ∂2C/∂S2Theta: Partial derivative of option price with respect to time ∂C/∂T. (Equals minus the partial derivative with respect to time remaining until exercise)Vega: Partial derivative of option price with respect to volatility ∂C/∂σOption DeltaOption delta is derivative of option price with respect to stock priceFor calls, if stock price is way below exercise price, delta is nearly zeroFor calls, if option is at the money, delta is roughly a half, but price of option may be way below half the price of the stock.For calls, if stock price is way above the exercise price, delta is nearly one and one pays approximately stock price minus pdv of exercise price, like buying stock with credit pdv(E)Call Delta ∂C/∂S∂log(C)/∂log(S)Call Gamma ∂2C/∂S2Call Theta ∂C/∂TBehavioral Aspects of Options DemandThaler’s mental categories theoryWriting an out-of-the-money call on a stock one holds, appears to be a win-win situation (Shefrin)Buying an option is a way of attaining a more leveraged, risky positionLottery principle in psychology, people inordinately attracted to small probabilities of winning bigMargin requirements are circumvented by optionsSwaps and Risk ManagementSwaps are simple exchanges between parties of one risk for anotherStarted in 1981, now in trillions of dollars worldwidePrecursor to Swaps: Parallel Loan AgreementsBreakdown of Bretton Woods fixed exchange rates in 1973 led to new ways to manage exchange rate risksUS firm with UK subsidiary lends dollars to a UK firm with US subsidiary. They lend pounds to US firm.Hedges exchange rate riskLong-term, to terms of parties, hence better than futures market hedgingProblems with Parallel Loan AgreementsDefault Risk: loans are independent instruments, so default by one party does not release other from obligated paymentsBalance sheet impact: parallel loans will inflate the balance sheet, which leads to possible problems with financial covenants, with public perception of safety of their stockEfforts to Stabilize EarningsCurrency swings caused major changes in income statements of firms.Zeckhauser and Patel show that firms rarely lose earnings, truncated distribution of earnings changeGE showed steadily growing earnings for last 20 yearsSwaps as Parallel Loan Agreements “Stapled Together”First privately arranged swaps occurred in mid 1970sFirst public introduction of a currency swap between IBM and World Bank 1981.Interest Rate SwapsSwap fixed for floatingA bank with a lot of long-term investments and short-term deposits may swap the short-term deposits for long-termSwaps on Telerate Screen Treasury-LIBOR Swap2 Yr. T+70 T+743 Yr. T+74 T+774 Yr. T+74 T+785 Yr. T+74 T+797 Yr. T+73 T+7910 Yr. T+73 T+78 SpidersMITTs: Market Index Target Term SecuritiesTraded on AMEX, often issued by Merrill Lynch“What if I told you there’s an investment that will give you no downside but an unlimited upside?”Example: Five-year MITTs issued in 1992 for \$10 pay promise to pay the \$10(1+x*1.15) back in five years, where x is percentage increase in the S&P if positive, otherwise zero.Downsides: You get no dividends, your floor of \$10 is pretty low given that interest rates were around 5% a year in 1992Futures OptionsWhy Options on Futures?Futures market more liquid, up-to-date, than spot marketEasier to hedge an options position in futures market than in spot marketFutures on REITsAugust 1998 Chicago Mercantile Exchange announced plan for futures on the S&P Real Estate Trust Composite IndexScreen-traded rather than open-outcry
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