Mathematical Modeling in Finance with Stochastic Processes
7.6. SENSITIVITY, HEDGING AND THE “GREEKS” 261 The concept of Gamma is important when the hedged portfolio cannot be adjusted co ...
262 CHAPTER 7. THE BLACK-SCHOLES MODEL Given the parametersr, andσ^2 , and any 4 of Θ, ∆, Γ,SandVthe remaining quantity is impli ...
7.6. SENSITIVITY, HEDGING AND THE “GREEKS” 263 formulas presented above. In practice, transaction costs make frequent bal- ancin ...
264 CHAPTER 7. THE BLACK-SCHOLES MODEL (d) Draw the graph of Γ versusSandtfor a European call option withK= 50,r= 0.10,σ= 0.25,T ...
7.7. LIMITATIONS OF THE BLACK-SCHOLES MODEL 265 Section Starter Question We have derived and solved the Black-Scholes equation. ...
266 CHAPTER 7. THE BLACK-SCHOLES MODEL Stochastic volatilitymodels are higher-order mathematical finance models where the volat ...
7.7. LIMITATIONS OF THE BLACK-SCHOLES MODEL 267 modeling, see Brief Remarks on Math Models for the cycle and diagram. A detailed ...
268 CHAPTER 7. THE BLACK-SCHOLES MODEL Figure 7.8: The red distribution has more probability near the mean, and a fatter tail (n ...
7.7. LIMITATIONS OF THE BLACK-SCHOLES MODEL 269 have happened even once in this period is virtually impossible. The popular term ...
270 CHAPTER 7. THE BLACK-SCHOLES MODEL From a scientific point of view, the way to estimate the parameters is statis- tically ev ...
7.7. LIMITATIONS OF THE BLACK-SCHOLES MODEL 271 the problem. Still, changing volatility is an area of active research, both prac ...
272 CHAPTER 7. THE BLACK-SCHOLES MODEL Problems to Work for Understanding A pharmaceutical company has a stock that is currentl ...
Bibliography [1] David Adler. A reliable randomizer, turned on its head. Washington Post, August 2 2009. randomness. [2] Marco A ...
274 BIBLIOGRAPHY [11] James Case. Two theories of relativity, all but identical in substance. SIAM News, page 7 ff, September 20 ...
BIBLIOGRAPHY 275 [24] R. Jarrow and P. Protter. A short history of stochastic integration and mathematical finance: The early ye ...
276 BIBLIOGRAPHY [35] Roger Lowenstein. When Genius Failed: The Rise and Fall of Long- Term Capital Management. Random House, 20 ...
BIBLIOGRAPHY 277 [48] Staff. Over the counter, out of sight. The Economist, pages 93–96, November 14 2009. [49] J. Michael Steel ...
Index American Stock Exchange, 19 AMEX seeAmerican Stock Exchange, 19 approximate Brownian Motion, 172 arbitrage, 13, 32, 33 arb ...
INDEX 279 Liapunov’s Theorem, 139 Central Limit Theorem Lindeberg’s Theorem, 139 Central Limit Theorem, 138 chain rule, 202 Cheb ...
280 INDEX future, 18 futures, 8, 9 Gambler’s Fallacy, 127 gambler’s ruin, 95 Gamma, 261 Gaussian processes, 60 Geometric Brownia ...
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