Proceedings of the New York State Economics Association

Time-Changed Levy Jump Processes with GARCH model on Reverse Convertibles

Wei Simi and Xiali Wang

vol. 5, October 2012, p. 206-220

For decades, financial institutions have been very motivated in creating structured high-yield financial products, especially in the economic environment of lower interest rates. Reverse Convertible Notes (RCNs) are the type of financial instruments, which in recent years -- first in Europe and then in the U.S. -- have become highly desirable financial structured products. They are complex financial structured products because they are neither plain bonds nor stocks. Instead, they are structured products embedding equity options, which involve a significant amount of asset returns' uncertainty. Given this fact, pricing of Reverse Convertible Notes becomes a really big challenge, where both the general Black-Scholes option pricing model and the Compound Poisson Jump model which are designed to catch large crashes, are not suitable in valuing these kinds of products. In this paper, we propose a new asset-pricing framework for Reverse Convertible Notes by extending the pure Brownian increments to Levy Jump risks for the underlying stock returns movements. Our framework deals with time-changing volatilities of stock options with Levy Jump processes by considering the stocks' infinite-jump possibilities. We then use a discrete-time GARCH with time-changed dynamics Levy Jump processes in order to derive the assets' valuations. The results from our new model are close to the market's valuations, especially with the Normal-Inverse-Gaussian model of the Levy Jump family.

suggested citation:

Wei Simi and Xiali Wang. "Time-Changed Levy Jump Processes with GARCH model on Reverse Convertibles." Proceedings of the New York State Economics Association. vol. 5, October 2012, p. 206-220

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