×

Turbo warrants under stochastic volatility. (English) Zbl 1154.91486

Summary: 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. J. Eriksson [Explicit pricing formulas for turbo warrants. Dissertation, Uppsala (2005)] 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 [loc. cit.], 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.

MSC:

91B28 Finance etc. (MSC2000)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1111/1540-6261.00454
[2] DOI: 10.2307/2327490
[3] DOI: 10.1111/j.0960-1627.2004.00188.x · Zbl 1124.91331
[4] Cox J, J. Portfol. Mgmt 2 pp 15– (1996)
[5] DOI: 10.1287/mnsc.47.7.949.9804 · Zbl 1232.91659
[6] DOI: 10.2469/faj.v52.n4.2008
[7] Dupire B, Risk 7 pp 18– (1994)
[8] DOI: 10.2307/2330906
[9] Eriksson J, Uppsala Dissertation in Mathematics 45 (2005)
[10] DOI: 10.1088/1469-7688/3/5/301
[11] Fouque JP, Derivatives in Financial Markets with Stochastic Volatility (2000) · Zbl 0954.91025
[12] DOI: 10.1137/030600291 · Zbl 1074.91015
[13] DOI: 10.1080/13504860600563127 · Zbl 1142.91523
[14] DOI: 10.1093/rfs/6.2.327 · Zbl 1384.35131
[15] DOI: 10.2307/2328253
[16] DOI: 10.1137/S0036139902420043 · Zbl 1099.91062
[17] Kwok YK, Mathematical Models of Financial Derivatives (1998)
[18] DOI: 10.1080/14697680600895021 · Zbl 1278.91164
[19] DOI: 10.1016/j.insmatheco.2006.05.006 · Zbl 1183.91173
[20] DOI: 10.1088/1469-7688/4/3/006
[21] DOI: 10.1023/A:1027377228682 · Zbl 1059.91049
[22] DOI: 10.1002/fut.20306
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.