Asymptotic European Option Pricing with Transaction Costs and Stochastic Volatility

Summary

The paper studies valuation and hedging for a European call when volatility is stochastic and trading incurs transaction costs. It analyzes a limiting regime in which transaction costs are small and volatility mean reverts quickly, deriving an asymptotic approximation to the option price. The leading component is the classical Black–Scholes price, with additional terms capturing effects beyond that benchmark.

The stated expansion includes corrections at orders proportional to the square root of the small parameter and to the parameter itself. The paper also derives an explicit optimal hedging strategy within Scott’s stochastic volatility model. This is a model-based asymptotic result rather than a general pricing prescription: its usefulness depends on the assumed volatility dynamics and the small-cost, fast-mean-reversion regime. The supplied summary gives no numerical examples or empirical validation, so it does not indicate how accurate the approximation is outside those conditions.

Key ideas

• The valuation problem combines stochastic volatility with transaction costs for a European call.
• The analysis considers small costs and rapid volatility mean reversion.
• The leading price term matches the Black–Scholes solution.
• Higher-order corrections account for effects of the asymptotic regime.
• An explicit optimal hedge is derived for Scott’s model, with applicability tied to its assumptions.

Tags

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


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









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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.