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# European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis

## Author

Listed:
• R. E. Caflisch
• G. Gambino
• M. Sammartino
• C. Sgarra

## Abstract

In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.

## Suggested Citation

• R. E. Caflisch & G. Gambino & M. Sammartino & C. Sgarra, 2012. "European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis," Papers 1211.4396, arXiv.org.
• Handle: RePEc:arx:papers:1211.4396
as

File URL: http://arxiv.org/pdf/1211.4396

## References listed on IDEAS

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2. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
3. Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-1222, September.
4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
5. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
6. Hiroaki Kaido & Andres Santos, 2014. "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities," Econometrica, Econometric Society, vol. 82(1), pages 387-413, January.
7. Raj Chetty, 2012. "Bounds on Elasticities With Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply," Econometrica, Econometric Society, vol. 80(3), pages 969-1018, May.
8. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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## Citations

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Cited by:

1. Maxim Bichuch & Ronnie Sircar, 2014. "Optimal Investment with Transaction Costs and Stochastic Volatility," Papers 1401.0562, arXiv.org, revised Aug 2014.

### NEP fields

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