Option Pricing with a General Marked Point Process

References

• Aase K. Contingent claims valuation when the security price is a combinaison of an Ito process and a random point process. Stochastic Processes Appl. (1988) 28:185–220Crossref, Google Scholar
• Ansel J. P., Stricker C. Unicité et existence de la loi minimale. Sem. Probab. Lecture Notes in Math. XXVII (1993) 1557:22–29Crossref, Google Scholar
• Ansel J. P. Lois de martingale, densités et décomposition de Föllmer Schweizer. Ann. Inst. Henri Poincaré (1992) 28:375–392Google Scholar
• Bardhan I., Chao X. Pricing options on securities with discontinuous returns. Stochastic Processes Appl. (1993) 48:123–137Crossref, Google Scholar
• Bellamy N., Jeanblanc M. Incompleteness of markets driven by a mixed diffusion. Finance Stochastics (2000) 4(2):209–222Crossref, Google Scholar
• Bibby B. M., Sorensen M. A Hyperbolic diffusion model for stock prices. Finance Stochastics (1997) 1:25–41Crossref, Google Scholar
• Björk T., Kabanov Y., Runggaldier W. Bond market structure in the presence of marked point processes. Math. Finance (1997) 7:211–240Crossref, Google Scholar
• Bremaud P.Point Processes and Queues: Martingale Dynamics (1981) (Springer Verlag, Berlin, Germany) Crossref, Google Scholar
• Buhlman H., Delbaen F., Embrecht P., Shiryaev A. No-arbitrage, change of measure and conditional Esscher transforms in a semimartingale model of stock processes. CWI Quart. (1996) 9:291–317Google Scholar
• Chan T. Pricing contingent claims on stocks driven by Levy processes. Ann. App. Probab. (1999) 9:504–528Crossref, Google Scholar
• Chou C. S., Meyer P. A. Sur la représentation des martingales comme intégrales stochastiques dans les processus ponctuels. Sém. Probab. IX, Lecture Notes Math. (1975) 226–236Google Scholar
• Clark P. K. A subordinated stochastic process model with finite variance for speculative prices. Econometrica (1973) 41:135–155Crossref, Google Scholar
• Colwell D. B., Elliott R. J. Discontinuous asset prices and non-attainable contingent claims. Math. Finance (1993) 3:295–308Crossref, Google Scholar
• Cox J. C., Ross S. A., Rubinstein M. Option pricing: a simplified approach. J. Financial Econom. (1979) 7:229–263Crossref, Google Scholar
• Duffie D. Stochastic equilibria: existence, spanning number, and the no expected financial gain from trade hypothesis. Econometrica (1986) 54:1161–1183Crossref, Google Scholar
• Eberlein E., Jacod J. On the range of options prices. Finance and Stochastics (1997) 1:131–140Crossref, Google Scholar
• Engle R. F., Russel J. Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica (1998) 66:1127–1162Crossref, Google Scholar
• Föllmer H., Schweizer M., Davis M. H. A., Elliott R. J. Hedging of contingent claims under incomplete information. Applied Stochastic Analysis, Stochastics Monographs (1991) 5(Gordon and Breach, London/New York) 389–414Google Scholar
• Frey R., Runggaldier W. J. A Nonlinear Filtering Approach to Volatility Estimation with a view Towards High Frequency Data. (1999) . Preprint, Swiss Banking Institute, University of Zürich, SwitzerlandGoogle Scholar
• Fritelli M.On Minimal Martingale Measure (1999) (University of Milan, Milan, Italy) . ForthcomingGoogle Scholar
• Geman H., El Karoui N., Rochet J. C. Changes of numeraire, changes of probability measure and option pricing. J. Appl. Probab. (1995) 32:443–458Crossref, Google Scholar
• Geman H., Madan D., Yor M.Asset Prices are Brownian Motion: Only in Business Time (1998) (University of Maryland, College Park, MD) Google Scholar
• Gourieroux C., Jasiak J., Lefol G. Intra-day Market Activity. (1996) . Working paper, CREST No 9633, Paris, FranceGoogle Scholar
• Harrison J. M., Kreps D. Martingales and arbitrage in multiperiod securities Markets. J. Econom. Theory (1979) 20:381–408Crossref, Google Scholar
• Harrison J. M., Pliska S. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes Appl. (1981) 11:215–260Crossref, Google Scholar
• Jacod J. A general theorem of representation for martingales. Proc. Sympos. Pure Math. (1977) 31:37–53Crossref, Google Scholar
• Jacod J. Multivariate point process: Predictable projection, radon-nikodym derivatives, representation of martingales. Z. Wahrsch. Verw. Geb. (1975) 31:235–253Crossref, Google Scholar
• Jacod J., Shiryaev A. N.Limit Theorems for Stochastic Processes (1987) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Jarrow R., Madan D. Option pricing using the term structure of interest rates to hedge systematic discontinuities in asset returns. Math. Finance (1995) 5:311–336Crossref, Google Scholar
• Jeanblanc M., Pontier M. Optimal portfolio for a small investor in a market model with discontinuous prices. Appl. Math. Optim. (1992) 22:287–310Crossref, Google Scholar
• Karr A. F.Point Processes and their Statistical Inference (1991) (Marcel Dekker, New York) Google Scholar
• Last G., Brandt A.Marked Point Processes on the Real Line (1995) (Springer-Verlag, Berlin, Germany) Google Scholar
• Leblanc B., Yor M. Lévy processes in finance: a remedy to the non-stationnarity of continuous martingales. Finance Stochastics (1998) 2:399–408Crossref, Google Scholar
• Leblanc B.Quelques applications des processus à accroissements indépendants en mathématiques financières (1996) (Laboratoire de Probabilités Université Paris VI, Paris, France) Google Scholar
• Lepingle D., Mémin J. Sur l'intégrabilité uniforme des martingales exponentielles. Z. Wahrsch. Verw. Geb. (1978) 42:175–203Crossref, Google Scholar
• Lesne J. P., Prigent J. L. A General Subordinated Stochastic Process for the Derivatives Pricing. Proc. 1996 Stable and jumps processes in Finance Evry. Internat. J. Theoret. Appl. Finance (2001) 4(1):121–146Google Scholar
• Lesne J. P., Prigent J. L., Scaillet O. Convergence of discrete time options pricing models under stochastic interest rates. Finance Stochastics (1998) 4(1):81–93Crossref, Google Scholar
• Madan D. B., Milne F. Option pricing with V. G. Martingale Components. Math. Finance (1991) 14:39–55Crossref, Google Scholar
• Mandelbrot B., Taylor H. M. On the distribution of stock price differences. Oper. Res. (1967) 11:1057–1062Link, Google Scholar
• Merton R. Option pricing when underlying stock returns are discontinuous. J. Financial Econom. (1976) 3:125–144Crossref, Google Scholar
• Pham H. Optimal stopping, free boundary and American option in a jump diffusion model. Appl. Math. Optim. (1997) 35:145–164Crossref, Google Scholar
• Pham H. Pricing and Hedging of an European Option in a Jump-Diffusion Model. (1994) . Working paper, Crest. ENSAE, Paris, FranceGoogle Scholar
• Prigent J. L. Incomplete markets: convergence of options values under the minimal martingale measure. Adv. Appl. Probab. (1999) 31(4):1058–1077Crossref, Google Scholar
• Protter P.Stochastic Integration and Differential Equations (1992) (Springer Verlag, New York) Google Scholar
• Rogers L. C. G., Zane O.Designing Models for high frequency data (1998) . ForthcomingGoogle Scholar
• Schweizer M. Variance-optimal hedging in discrete time. Math. Oper. Res. (1993) 20:1–32Link, Google Scholar
• Schweizer M. Mean-variance hedging for general claims. Ann. Appl. Probab. (1992) 2:171–179Crossref, Google Scholar
• Schweizer M. Option hedging for semimartingales. Stochastic Processes their Appl. (1991) 37:339–363Crossref, Google Scholar
• Shiryaev A.Essentials of stochastic finance (1999) (World Scientific)Crossref, Google Scholar