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.
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- 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.
- 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, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
- 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.
- Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
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