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Convergence of Jump-Diffusion Modelsto the Black–Scholes Model
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- Authors
- Dowon Hong, In-Suk Wee
- Issue Date
- 2003-03
- Citation
- Stochastic Analysis and Applications, v.21, no.1, pp.141-160
- ISSN
- 0736-2994
- Publisher
- Taylor & Francis
- Language
- English
- Type
- Journal Article
- Abstract
- We consider a jump-diffusion model for asset price which is described as a solution of a linear stochastic differential equation driven by a L챕vy process. Such a market is incomplete and there are many equivalent martingale measures. We price a contingent claim with respect to the minimal martingale measure and construct a hedging strategy for the contingent claim in the locally risk-minimizing sense. We study the problem of convergence of option prices jointly with the costs from the locally risk-minimizing strategies when the jump-diffusion models converge to the Black-Scholes model.
- KSP Keywords
- Black-scholes model, Hedging strategy, Jump-diffusion model, Martingale measure, Stochastic differential equation(SDE)