In this paper, the valuation problem of a European call option in the 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 is shown to be the classical Black and Scholes solution, the correction terms appear at O(ε1/2) and O(ε). The optimal hedging strategy is then explicitly obtained for Scott's model.
Caflisch, R.E., Gambino, G., Sammartino, M., Sgarra, C. (2015). European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis. IMA JOURNAL OF APPLIED MATHEMATICS, 80(4), 981-1008 [10.1093/imamat/hxu033].
European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis
GAMBINO, Gaetana;SAMMARTINO, Marco Maria Luigi;
2015-01-01
Abstract
In this paper, the valuation problem of a European call option in the 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 is shown to be the classical Black and Scholes solution, the correction terms appear at O(ε1/2) and O(ε). The optimal hedging strategy is then explicitly obtained for Scott's model.
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