Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Annals of Finance
Published in: Annals of Finance 2/2018

20-10-2017 | Research Article

Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes

Authors: Vladislav Krasin, Ivan Smirnov, Alexander Melnikov

Published in: Annals of Finance | Issue 2/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper presents a methodology of finding explicit boundaries for some financial quantities via comparison of stochastic processes. The path-wise comparison theorem is used to establish domination of the stock price process by a process with a known distribution that is relatively simple. We demonstrate how the comparison theorem can be applied in the constant elasticity of variance model to derive closed-form expressions for option price bounds, an approximate hedging strategy and a conditional value-at-risk estimate. We also provide numerical examples and compare precision of our method with the distribution-free approach.
previous article Regulation, supervision and deposit insurance for financial cooperatives: an empirical investigation
next article Financial equilibrium with non-linear valuations

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
Barlow, M., Perkins, E.: One dimensional stochastic differential equations involving a singular increasing process. Stochastics 12, 229–249 (1984)CrossRef
Bergenthum, J., Ruschendorf, L.: Comparison of semimartingales and Lèvy processes. Ann Probab 35(1), 228–254 (2007)CrossRef
Black, F., Scholes, M.S.: The pricing of options and corporate liabilities. J Polit Econ 81(3), 637–654 (1973)CrossRef
Carmona, R., Durrleman, V.: Generalizing the Black–Scholes formula to multivariate contingent claims. J Comput Finance 9(2), 43–67 (2006)CrossRef
Cohen, S., Elliott, R., Pearce, C.: A general comparison theorem for backward stochastic differential equations. Adv Appl Probab 42(3), 878–898 (2010)CrossRef
Cont, R., Tankov, P.: Financial Modeling with Jump Processes. Boca Raton: Chapman and Hall/CRC (2004)
Cox, J.C., Ross, S.A.: The valuation of options for alternative stochastic processes. J Financ Econ 3, 145–166 (1976)CrossRef
Ding, X., Wu, R.: A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales. Stoch Process Appl 78(2), 155–171 (1998)CrossRef
Galtchouk, L.I.: A comparison theorem for stochastic equations with integrals with respect to martingales and random measures. Teoriya Veroyatnostei i ee Primeneniya 27(3), 425–433 (1982). (English translation: Theory Probab Appl 27(3), 450–460, 1983)
Hajek, B.: Mean stochastic comparison of diffusions. Probab Theory Relat Fields 68, 315–329 (1985)
Jansen, K., Haezendonck, J., Goovaerts, M.J.: Upper bounds on stop-loss premiums in case of known moments up to the fourth order. Insur Math Econ 5, 315–334 (1986)CrossRef
Jarrow, R., Rudd, A.: Approximate option valuation for arbitrary stochastic processes. J Financ Econ 10, 347–369 (1982)CrossRef
Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations. Applications of Mathematics. Berlin: Springer (1992)
Krasin, V.Y., Melnikov, A.V.: On comparison theorem and its applications to finance. In: Delbaen, F., et al. (eds.) Optimality and Risk: Modern Trends in Mathematical Finance, pp. 171–181. Berlin: Springer (2009)
Lèvy, H.: Upper and lower bounds of put and call option value: stochastic dominance approach. J Finance 40(4), 1197–1217 (1985)CrossRef
MacBeth, J.D., Merville, L.J.: Tests of the Black–Scholes and Cox call option valuation models. J Finance 35(2), 211–219 (1980)CrossRef
Melnikov, A.: On the theory of stochastic equations in components of semimartingales. Matematicheskii Sbornik 110(3), 414–427 (1979a). (English translation: Mathematics of the USSR. Sbornik 38(3), 381–394, 1981)
Melnikov, A.: Strong solutions of stochastic differential equations with non-smooth coefficients. Teoriya Veroyatnostei i ee Primeneniya 24(1), 146–149 (1979b). (English translation: Theory Probab Appl 24(1), 147–150, 1981)
Melnikov, A.: On solutions of stochastic equations with driving semimartingales. In: Proceedings of the Third European Young Statisticians Meeting, pp. 120–124. Leuven: Catholic University (1983)
Peng, S., Zhu, X.: Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations. Stoch Process Appl 116(3), 370–380 (2006)CrossRef
Platen, R., Heath, D.: A Benchmark Approach to Quantitative Finance. Berlin: Springer (2006)
Randal, J.: The Constant Elasticity of Variance Option Pricing Model. Master’s thesis, Victoria University of Wellington, Australia (1998)
Rockafellar, R.T., Uryasev, S.: Conditional value-at-risk for general loss distributions. J Bank Finance 26(7), 1443–1471 (2002)CrossRef
Schepper, A.D., Heijnen, B.: Distribution-free option pricing. Insur Math Econ 40(2), 179–199 (2007)CrossRef
Schroder, M.: Computing the constant elasticity of variance option pricing formula. J Finance 44(1), 211–219 (1989)CrossRef
Skorokhod, A.V.: Studies in the Theory of Random Processes. Kyiv, USSR: Naukova Dumka (1961). (English translation: published by Addison-Wesley, Reading, MA, USA, 1965)
Yamada, T.: On comparison theorem for solutions of stochastic differential equations and its applications. J Math Kyoto Univ 13, 497–512 (1973)CrossRef
Yan, J.-A.: A comparison theorem for semimartingales and its applications. Séminaire de probabilités Strasbourg 20, 349–351 (1986)
Metadata
Title
Approximate option pricing and hedging in the CEV model via path-wise comparison of stochastic processes
Authors
Vladislav Krasin
Ivan Smirnov
Alexander Melnikov
Publication date
20-10-2017
Publisher
Springer Berlin Heidelberg
Published in
Annals of Finance / Issue 2/2018
Print ISSN: 1614-2446
Electronic ISSN: 1614-2454
DOI
https://doi.org/10.1007/s10436-017-0309-9

Other articles of this Issue 2/2018

Annals of Finance 2/2018 Go to the issue

Research Article

On the implied market price of risk under the stochastic numéraire

Research Article

Financial equilibrium with non-linear valuations

Research Article

Asset market equilibrium with liquidity risk

Research Article

Regulation, supervision and deposit insurance for financial cooperatives: an empirical investigation