Hull, J. Options, Futures, and Other Derivatives. Fifth ed. Prentice Hall, Upper Saddle River, NJ, 2003. Home/Search Document Not in Database Summary Related Articles Check |
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Managing Capacity for Telecommunications Networks under.. - d'Halluin, Forsyth.. (2002) (1 citation) (Correct)
....not use it to pay to own the stock when it could be purchased at a lower price on a financial exchange. The field of option pricing is largely concerned with determining the fair price to pay for options. Over the past three decades, this has been a very active area of research in finance (see [8] or [9] for an overview) The related field of real options extends the basic ideas of option pricing to corporate investment decisions. For example, a network planning manager may buy an option on a bundle of dark fiber lines. This gives the manager the right, but not the obligation, to buy this ....
.... (measured in megabits) The different possible paths followed by the demand can be modeled as a stochastic process given by (1) is the drift rate or growth rate, is the volatility and is the increment of a Wiener process (readers unfamiliar with these ideas should consult [8], 2] 9] for a simple introduction) Based on hedging arguments (see [8] 9] and Appendix A) a partial differential equation for the value of an investment is found to be 13 (2) where is the value of the investment in , is the revenue ....
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J. Hull, Options, Futures, and Other Derivatives, Prentice Hall, Inc., Upper Saddle River, NJ, Fourth edition, 2001.
Optimization of Trading Physics Models of Markets - Lester Ingber Lester (2001) (1 citation) (Correct)
.... we can include models based on non equilibrium statistical mechanics [4] fractal geometry [5] turbulence [6] spin glasses and random matrix theory [7] renormalization group [8] and gauge theory [9] Although the very complex nonlinear multivariate character of financial markets is recognized [10], these approaches seem to have had a lesser impact on current quantitative finance practice, although it is becoming increasing clear that this direction can lead to practical trading strategies and models. To bridge the gap between theory and practice, as well as to afford a comparison with ....
J.C. Hull, Options, Futures, and Other Derivatives, 4th Edition, Prentice Hall, Upper Saddle River, NJ, 2000.
A Penalty Method for American Options with Jump Diffusion .. - d'Halluin, Forsyth.. (2003) (Correct)
....For brevity, the details of the derivation of equation (2.2) have been omitted (see [2, 18, 28] Equation (2.2) can be rewritten as Note that if we set # = 0 in (2. 5) then the classical Black Scholes partial di#erential equation for pricing European option contracts is recovered [14, 28]. If we define (2.6) and if V # (S, #) is the payo#, then the American option pricing problem can be stated as V # ) LV = 0) V # = 0) 2.7) where the notation (LV = 0) # = 0) denotes that either (LV = 0) or (V # = 0) at each point in the solution ....
J. Hull. Options, Futures, and Other Derivatives. Prentice Hall, Inc., Upper Saddle River, NJ, 3rd edition, 1997.
Large Sample Properties of Weighted Monte Carlo Estimators - Glasserman, Yu (Correct)
....of the option is E[Y ]with Y = e rT max 0, S K , where the constants T , r,andK are the maturity, interest rate, and strike price. The random variable S is the average level S = j=1 S(t j ) of the underlying asset S over a fixed set of dates 0 t 1 t m = T . See, e.g. Hull [15] for background. We model the dynamics of the underlying asset using geometric Brownian motion. More explicitly, as in, e.g. Hull [15] p.238, we have S(t) S(0) exp [r ]t #W(t) 18) where S(0) is a fixed initial price, # is the asset s volatility, and W is a standard Brownian ....
....The random variable S is the average level S = j=1 S(t j ) of the underlying asset S over a fixed set of dates 0 t 1 t m = T . See, e.g. Hull [15] for background. We model the dynamics of the underlying asset using geometric Brownian motion. More explicitly, as in, e.g. Hull [15], p.238, we have S(t) S(0) exp [r ]t #W(t) 18) where S(0) is a fixed initial price, # is the asset s volatility, and W is a standard Brownian motion. To simulate S, it su#ces to simulate S(t 1 ) S(t m ) and thus to simulate W at times t 1 , t m . This is accomplished by the ....
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Hull, J. (2000) Options, Futures, and Other Derivative Securities, Prentice-Hall, Upper Saddle River, New Jersey.
A Regime-Switching Model for European Option Pricing - David Yao Qing (Correct)
....] t = 0. In addition, we have Psi(t)Q(F (X(t) 1) F (X(t) m) QF (X(t) Delta) ff(t) Hence, Dynkin s formula follows. Finally, the Markov property of (X(t) ff(t) under e P can be established following the same argument as in Ghosh et al. 12] 2 Therefore, in view of Hull [17] and Fouque et al. 11] Omega ; F ; fF t g; e P) defines a risk neutral world. Moreover, e X(t) is a e P martingale. Consider a European style call option with strike price K and expiration date T . Let h(x) x Gamma K) maxfx Gamma K; 0g: The call option premium at time s, ....
....the strike price (K) and the jump rate ( in Fig. 2 (a) As can be observed from Fig. 2 (a) for each fixed 2 Gamma , the implied volatility reaches its minimum at K = 50 (at money) and increases as K moves away from K = 50. This is the well known volatility smile phenomenon in stock options ([17]) In addition, for fixed K 2 Gamma K , implied volatility is increasing in , corresponding to a sooner jump from oe(1) to oe(2) Case (1b) In this case, we take oe(1) 0:3 and fix = 1, and replace the axis in Fig. 2(a) by the volatility jump size oe(2) Gamma oe(1) 2 Gamma oe . As can be ....
J. C. Hull, Options, Futures, and Other Derivatives, 4th Ed., Prentice Hall, Upper Saddle River, NJ, 2000.
Hybrid Stock Models and Parameter Estimation - Yin, Zhang, Yin (Correct)
....are both deterministic. Therefore they are not responsive to the random environment and are not suitable for a longer horizon. It is desirable to modify the model so as to capture the random parameter changes such as random volatility. A host of researchers have made e#ort in this direction, see [3, 4, 10] and the references therein. Built upon the hybrid switching GBM model (HGBM) a number of GBMs modulated by a finite state Markov chain) considered in [15] see also related work [2] we further our understanding in this paper. In order to use the HGBM, a crucial issue is to be able to estimate ....
J.C. Hull, Options, Futures, and Other Derivatives, 3rd Ed., Prentice-Hall, Upper Saddle River, NJ, 1997.
Large Sample Properties of Weighted Monte Carlo Estimators - Glasserman, Yu (2002) (Correct)
....the option is E[Y ]with Y = e rT max 0, S K , where the constants T , r,andK are the maturity, interest rate, and strike price. The random variable S is the average level S = j=1 S(t j ) of the underlying asset S over a fixed set of dates 0 t 1 t m = T . See, e.g. Hull [14] for background. We model the dynamics of the underlying asset using geometric Brownian motion. More explicitly, we have S(t) S(0) exp [r ]t #W(t) 16) where S(0) is a fixed initial price, # is the asset s volatility, and W is a standard Brownian motion. To simulate S, it su#ces ....
....the strikes we 17 use are (K 1 , K 7 ) 0.85, 0.95, 1.05, 1.15) e S(0) 54.57, 60.99, 67.41, 73.83) We take the corresponding implied volatilities to be 0.240, 0.200, 0.182, 0.176. Substituting these values of r, T , S(0) K, and volatility into the Black Scholes formula (e.g. Hull [14]) yields prices for the four options: 13.97, 9.93, 7.07, 5.15. This is how we construct our example; in practice the last step would be reversed: we would observe market prices and their strikes and apply the inverse of the Black Scholes formula to get the implied volatilities. We suppose that ....
Hull, J. (2000) Options, Futures, and Other Derivative Securities, Prentice-Hall, Upper Saddle River, New Jersey.
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John C. Hull. Options, Futures, and Other Derivatives. Prentice Hall, Upper Saddle River, nj, fourth edition, 1999.
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Hull, J.C. (2002). Options, Futures, and Other Derivatives, 5th ed., Prentice Hall, Upper Saddle River, NJ. 32
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