Turbo warrants under stochastic volatility

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 Google Scholar]) has considered the pricing of turbo warrants under the Black–Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 Google Scholar]), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.