An Application of Deep Hedging in Pricing and Hedging Caplets on the Prime Lending Rate

Derivatives in South Africa are traded via an exchange, such as the JSE's derivatives markets, or over-the-counter (OTC). This dissertation focuses on the pricing and hedging of caplets written on the South African prime lending rate. In a complete market, caplets can be continuously hedged with zero risk. However, in the particular case of caplets written on the prime lending rate, market completeness ceases to exist. This is because the prime lending rate is a benchmark for retail lending and is not tradeable, in general. Since parametric models may not be specified and calibrated for such incomplete markets, the aim of this dissertation is to consider the deep hedging approach of Buehler et al. (2019) for pricing and hedging such a derivative. First, a model dependent approach is taken to set a benchmark level of performance. This approach is derived using techniques outlined in West (2008) which rely heavily on interest rate pairs being cointegrated to use the market standard Black (1976) model. Thereafter, the deep hedging approach is considered in which a neural network is set up and used to price and hedge the caplets. The deep hedging approach performs at least as well as the model dependent approach. Furthermore, the deep hedging approach can also be used to recover a volatility skew which is in fact, needed as an input in the model dependent approach. The approach has certain downsides to it: a rich set of historical data is required and it is more time consuming to conduct than the model dependent approach. The deep hedging approach, in this specific implementation, also has a limitation that only one hedge instrument is used. When this limitation is also applied to the model dependent approach, the deep hedging approach performs better in all cases. Therefore, deep hedging proves to be a sufficient alternative to pricing and hedging caplets on the prime lending rate in an incomplete market setting.

Grantor

Department of Finance and Tax

Year dc:date.issued

2022

Author dc:creator

• Patel, Keyur

Advisor dc:contributor.advisor

• Mahomed, Obeid

• Mathematical Finance

Handle dc:identifier.uri

http://hdl.handle.net/11427/37736

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/37736