文档介绍：Martingales and Measures Chapter 21
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Derivatives Dependent on a Single Underlying Variable
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Forming a Riskless Portfolio
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Market Price of Risk (Page 485)
This shows that (m – r )/s is the same for all derivatives dependent on the same underlying variable, q
We refer to (m – r )/s as the market price of risk for q and denote it by l
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Extension of the Analysis to Several Underlying Variables (Equations and , page 487)
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Martingales (Page 488)
A martingale is a stochastic process with zero drift
A variable following a martingale has the property that its expected future value equals its value today
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Alternative Worlds
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
A Key Result (Page 489)
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Forward Risk Neutrality
We refer to a world where the market price of risk is the volatility of g as a world that is forward risk neutral with respect to g.
If Eg denotes a world that is FRN wrt g
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Aleternative Choices for the Numeraire Security g
Money Market Account
Zero-coupon bond price
Annuity factor
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull