Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
Need to know
- We extend the exact theoretical spanning relation in Carr and Wu (2014) to include options not restricted to a common short maturity.
- Discretize the spanning relation using a Gaussian Quadrature algorithm for practical application of our method to construct hedge portfolios with a finite number of options over multiple short maturities.
- We perform a comparative analysis of the performance of our method with the one in Carr and Wu (2014) in each of the cases when the number of quadrature points, the short maturities, and the strike intervals are varied for the Black-Scholes model and Merton Jump Diffusion models.
- The performance of our method and the method in Carr and Wu (2014) are studied in comparison to a Delta Hedging algorithm, throughout the duration of the hedge, using simulated stock paths, in both the Black-Scholes and Merton Jump Diffusion models.
Abstract
We consider the hedging of European options when the price of the underlying asset follows a single-factor Markovian framework. By working in such a setting, in 2014 Carr and Wu derived a spanning relation between a given option and a continuum of shorter-term options written on the same asset. We extend their approach to simultaneously include options over multiple short maturities. We then demonstrate a practical implementation of this extension with a finite set of shorter-term options to determine the hedging error using a Gaussian quadrature method. A wide range of experiments are performed for both the Black–Scholes model and the Merton jump-diffusion model, illustrating the comparative performance of the two methods.
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