Growth optimal investment and pricing of derivatives

Physica A: Statistical Mechanics and its Applications

Volumn 280, Issue 3, 2000, Pages 505-521

  Aurell, Erik ^a   Baviera, Roberto ^b   Hammarlid, Ola ^a   Serva, Maurizio ^b   Vulpiani, Angelo ^c  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b INFM   (Italy)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MARKETING; OPTIMIZATION;

PRICE DERIVATIVES;

STATISTICAL MECHANICS;

EID: 0033750071     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(00)00005-4     Document Type: Article

References (47)

1. Black F., Scholes M. The pricing of options and corporate liabilities. J. Political Econ. 3:1973;637.
2. Cox J., Ross S., Rubinstein M. Option pricing: a simplified approach. J. Finance Econ. 7:1979;229-263.
3. Harrison M., Kreps D. Martingales and multiperiod securities markets. J. Econ. Theory. 20:1979;381-408.
4. Cox J., Rubinstein M. Options Markets. 1985;Prentice-Hall, Englewood Cliffs, NJ.
5. Ingersoll J. Theory of Financial Decision Making. 1987;Rowman & Littlefield, New York.
6. Merton R. Continuous-Time Finance. 1990;Blackwell, Oxford.
7. Duffie D. Dynamical Asset Pricing Theory. 1992;Princeton University Press, Princeton, NJ.
8. Hull J.C. Futures, Options and Other Derivative Securities. 1997;Prentice-Hall, Englewood Cliffs, NJ.
9. Black F., Scholes M. The valuation of option contracts and a test of market efficiency. J. Finance. 27:1972;399-417.
10. Black F. Fact and fantasy in the use of options. Financial Analysts J. 31:1975;36-41.
11. Rubinstein M. Implied binomial trees. J. Finance. 49:1994;454-480.
12. Macbeth J.D., Merville L.J. An empirical examination of the Black-Scholes call option pricing model. J. Finance. 34:1979;1172-1186.
13. Rubinstein M. Nonparametric test of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE option classes from August 23, 1976 through August 31, 1978. J. Finance. 40:1978;454-480.
14. Chance D. Empirical tests of the pricing of index call options. Adv. Futures Options Res. A. 1986;141-166.
15. Derman E., Kani I. Riding on the smile, Risk. 7:1994;32-39.
16. E. Derman, I. Kani, Stochastic implied tress: arbitrage pricing with stochastic term and strike structure of volatility, Quantitative Strategies Technical Notes, Goldman Sachs & Co., April 1997, also in Int. J. Theoret. Appl. Finance 1 (1998) 61-110.
17. E. Derman, I. Kani, Stochastic implied tress: arbitrage pricing with stochastic term and strike structure of volatility, Quantitative Strategies Technical Notes, Goldman Sachs & Co., April 1997, also in Int. J. Theoret. Appl. Finance 1 (1998) 61-110.
18. D. Bates, Post-'87 crash fears in S& P 500 futures option Working paper Wharton School, University of Pennsylvania, 1995.
19. D. Bates, Testing option pricing models, Working paper 5129, National Bureau of Economic Research, 1995.
20. E. Aurell, R. Baviera, O. Hammarlid, M. Serva, A. Vulpiani, A general methodology to price and hedge derivatives in incomplete markets, Int. J. Theoret. Appl. Finance 3 (2000) 1.
21. Kelly J.L. Jr. A new interpretation of the information rate. Bell Systems Tech. J. 35:1956;917.
22. Samuelson P. The "fallacy" of maximizing the geometric mean in a long sequence of investing and gambling. Proc. Natl. Acad. Sci. USA. 68:1971;2493-2496.
23. Merton R., Samuelson P. Fallacy of the lognormal approximation to optimal portfolio decision making over many periods. J. Financial Econ. 1:1974;67-94.
24. E. Aurell, R. Baviera, O. Hammarlid, M. Serva, A. Vulpiani, Gambling and pricing of options, Social Science Research Network Electronic Library, (http: // papers.ssrn.com / ).
25. C. Shannon, A mathematical theory of communication, Bell Systems Tech. J. 27 (1948) 379-423, 623-656.
26. Bernoulli D. Exposition of a new theory on the measurement of risk. Econometrica. 22:1738:1954;22-36.
27. Hakanson N., Ziemba W. Capital growth theory. Jarrow R.et al. Handbooks in OR & MS, vol. 9. 1995;Elsevier Science, Amsterdam.
28. E. Aurell, P. Muratore, Financial friction and multiplicative Markov market games, cond-mat / 9908253, (http: // xxx.lanl.gov / ), Int. J. Theoret. Appl. Finance, in press.
29. R. Baviera, Transaction costs: a new point of view, Int. J. Theoret. Appl. Finance, to appear.
30. Serva M. Optimal lag in dynamical investments. Int. J. Theoret. Appl. Finance. 2:1999;471.
31. Samuelson P., Merton R. A complete model of warrant pricing that maximizes utility. Ind. Manage. Rev. 10:1969;17-46.
32. Stutzer M. A simple nonparametric approach to derivative security valuation. J. Finance. 60:1996;1633.
33. Avellaneda M., Friedman C., Holmes R., Samperi S. Calibrating volatility surfaces via relative-entropy minimization. Appl. Math. Finance. 3:1996;21-52.
34. Follmer H., Sondermann D. Hedge of nonredundant contingent claims. Hildenbrand W., Mas-Collel Etaus A. Essays in Honor of G. Debreu. 1986;North-Holland, Amsterdam.
35. Schäl M. On quadratic cost criteria for option hedge. Math. Oper. Res. 19:1994;121-131.
36. Schweizer M. Variance-optimal hedge in discrete time. Math. Oper. Res. 20:1995;1-32.
37. Bouchaud J.-P., Sornette D. The Black-Scholes option pricing problem in mathematical finance; generalization and extensions for a large class of stochastic processes. J. Phys. I (France). 4:1994;863-881.
38. Bouchaud J.-P., Iori G., Sornette D. Real-world options: smile and residual risk. Risk. 9(4):1996;61-65.
39. Wolczyńska G. An explicit formula for option pricing in discrete incomplete markets. Int. J. Theoret. Appl. Finance. 1:1998;283-288.
40. Hammarlid O. On minimizing risk in incomplete markets option pricing models. Int. J. Theoret. Appl. Finance. 1:1998;227-234.
41. Schweizer M. Risky options simplified. Int. J. Theoret. Appl. Finance. 2:1999;59-82.
42. Dybvig P., Ingersoll J. Mean-variance theory in complete markets. J. Bus. 55:1982;233-251.
43. Varadhan S. Large Deviations and Applications. 1984;Society for Industrial and Applied Mathematics, Philadelphia, PA.
44. Efron A., Bradley B. The Jacknife, the Bootstrap and Other Resampling Plans. 1982;Soc. for Industrial and Applied Mathematics, Philadelphia, PA.
45. Press W.H., Flannery B.P., Teukolsky S.A., Vetterling W.T. Numerical Recipes. 1986;Cambridge University Press, Cambridge.
46. G. Demange, J.-C. Rochet, Methods mathematiques de la finance, Economica, 1997.
47. Bachelier L. Théorie de la spéculation. Ann. Sci. École Norm. Sup. 17:1900;21-86.