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Asia-Pacic Finan Markets (2015) 22:7586 DOI 10.1007/s10690-014-9193-8
Published online: 26 September 2014 Springer Japan 2014
Abstract In this paper, we introduce a new type of barrier options called Lizard Option. The point is that its payoff depends on the stock price jump crossing a given barrier for the rst time. In other words, Lizard Option is jump-dependent. Then, we address the pricing of Lizard Option under the Variance Gamma model, based on the risk neutral modelling.
Keywords Barrier options Lvy processes Variance gamma model WienerHopf
factorization
1 Introduction
A usual one touch knock out option is weak against the price manipulation that aims at breaking its barrier intentionally. That is because once the underlying stock price touches the barrier, the option immediately disappears. This is quite a serious problem, which was revealed about 20 years ago (Wall Street Journal 1995a,b). Since then, in order to overcome this problem, many researchers have invented various improved barrier options, some of which are listed in the following with their knock out conditions (Chesney et al. 1997a,b; Linetsky 1999). St is an underlying stock price process and T is a maturity. A, B and are constants such that A > S0, B < A and 0 < < 1.
Cumulative Parisian Option
K.O. condition: [integraltext] T
0 1[A,)(St) dt [greaterdblequal] T .
Y. Kawanishi (B)
Department of Industrial and Systems Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo, Tokyo, Japane-mail: [email protected]
A New Type of Barrier Options: Lizard Option
Yasuhiro Kawanishi
123
76 Y. Kawanishi
Parisian Option
K.O. condition: max0[lessdblequal]t[lessdblequal]T (t sup{u [lessdblequal] t ; Su = A})1[A,)(St) [greaterdblequal] T .
Simple Parisian Like Option
K.O. condition: inf{t > A ; St [lessdblequal] B} A [greaterdblequal] T ,
where A := inf{t ; St [greaterdblequal] A}.
Meanwhile, geometric Lvy processes have totally become popular as stock price models for dealing with the statistical fact that distributions of stock price returns have the heavy-tailed property and the gain-loss asymmetry (Cont 2001).
With these circumstances in mind, in this paper, we suggest a new type of barrier options called Lizard Option which is proof to some degree against the price manipulation and at the same time, is intrinsic to imcomplete markets with jumps including geometric Lvy models other than the BlackScholes model....