A risk reserve model for hedging in incomplete markets
This paper presents a new approach to the pricing and hedging problem for contingent claims in incomplete markets. We assume that traders wish to maximize the expected final payoff of the hedging portfolio and the claims, and we avoid the use of utility functions. Instead, we model how traders are punished when taking excessive risks in practice. To do so, we introduce an extra reserve bank account, which earns a smaller rate of return than a standard deposit bank account. The reserve account should always contain a minimal amount of money, which depends on the risk that the trader's portfolio is exposed to. We focus on a specific example which uses option price sensitivities (the 'Greeks') to specify the risk. The resulting optimization problem can then be solved in a rather explicit form, and we show how the solution naturally leads to bid-ask spreads, prices which depend on the trader's current position and implied volatility smiles.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
- Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
- Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
- Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
- Sasha F. Stoikov, 2006. "Pricing Options From The Point Of View Of A Trader," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1245-1266.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:34:y:2010:i:7:p:1233-1247. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.