APPROXIMATING OPTION PRICES UNDER LARGE CHANGES OF UNDERLYING ASSET PRICES

Jae-Yun Jun and Yves Rakotondratsimba
Additional contact information
Jae-Yun Jun: Applied Mathematics, ECE Paris, 10, rue Sextius Michel, 75015 Paris, France
Yves Rakotondratsimba: Applied Mathematics, ECE Paris, 10, rue Sextius Michel, 75015 Paris, France

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 01, 1-27

Abstract: When one invests in portfolios of derivatives (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the underlying asset price. However, this approximation is locally accepted only for small changes of the underlying asset price. When these changes become large, the option prices estimated by the DGA may significantly differ from those of the market (or those that are estimated using, for instance, the Black–Scholes model), depending mainly on the time-to-maturity, implied volatility, and moneyness. Hence, in practice, before the change of the underlying asset price becomes large, rebalancing operations are demanded to minimize the losses occurred due to the error introduced by the DGA. The frequency of rebalancing may be high when the rate at which the underlying asset price significantly changes. Nonetheless, frequent rebalancing may be unattainable, as there are associated transaction costs. Hence, there is a trade-off between the losses resulting from the inaccurate performance of the DGA and the transaction costs incurring from frequent hedging operations. In the present work, we show two approaches that can outperform the DGA, in this way to increase the accuracy of estimating the option prices with the ultimate goal of reducing the losses due to the estimation error. The first method is similar to the DGA but we change the reference value that the DGA uses (that is, the initial price of the underlying asset) to the underlying asset price forecasted for the time horizon. We coin this method as the extended delta-gamma approximation (EDGA). The second method that we consider in this work is the locally weighted regression (LWR) that locally regresses the option prices from the changes of the underlying asset prices, with the same reference value that is employed in the EDGA method. Finally, we compare the performance of the two methods presented in this work to that of some existing methods.

Keywords: Options; Black–Scholes; delta-gamma; risk (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024923500048
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:26:y:2023:i:01:n:s0219024923500048

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024923500048

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().