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Abstract
In this paper, we test the performance of a static hedging strategy for a long-dated European call option and European spread call option in South Africa. The stochastic volatility double jump (SVJJ) model is calibrated to historical FTSE/JSE Top40 returns to generate real-world FTSE/JSE Top40 prices at future dates. The SVJJ model is also calibrated to the FTSE/JSE (Top40) implied volatility surface in order to value the options under the risk-neutral measure. Two static hedging programs are then implemented to test their effectiveness when replicating a long-dated European call option and European spread call option. Our results indicate that static hedging is a simple, yet effective, solution when hedging non-exchange-traded options with vanilla exchange-traded options.
Highlights
This paper is dedicated to product development and considers the sale of vanilla and exotic financial derivatives in South Africa
To determine whether market makers can sell long-dated European call options and European spread call options in South Africa and manage the risks effectively, we propose a simulation-based framework to test the performance of the static hedging program under numerous market conditions
The third subsection presents the static hedging results for a 5-year vanilla European call option written on the FTSE/JSE Top40 index; and, lastly, the fourth subsection shows the static hedging results for an arbitrary 1-year European spread call option
Summary
We focus on the risk management of long-dated European call options and European spread call options for which no liquid market exists. Pricing these options is just one part of the challenge. Institutions wanting to sell long-dated European call options and European spread call options are faced with the challenge of buying assets to cover liabilities. The portfolio manager will buy assets that match the risk sensitivities (the socalled Greeks) of the liabilities. This is seldom the case as many liabilities
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