A multiscale correction to the Black-Scholes formula

Jeong Hoon Kim, Jungwoo Lee, Song Ping Zhu, Seok Hyon Yu

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Based on a new multiscale hybrid structure of the volatility of the underlying asset price, we study the pricing of a European option in such a way that the resultant option price has a desirable correction to the Black-Scholes formula. The correction effects are obtained by asymptotic analysis based upon the Ornstein-Uhlenbeck diffusion that decorrelates rapidly while fluctuating on a fast time-scale. The subsequent implied volatilities demonstrate a smile effect (right geometry), which overcomes the major drawback of the Black-Scholes model as well as local volatility models, and move to a right direction as the underlying asset price increases (right dynamics), which fits the observed market behavior and removes the possible instability of hedging that the local volatility models may cope with. Further, we demonstrate that our correction brings significant improvement in terms of fitting to the implied volatility surface through a calibration exercise.

Original languageEnglish
Pages (from-to)753-765
Number of pages13
JournalApplied Stochastic Models in Business and Industry
Volume30
Issue number6
DOIs
Publication statusPublished - 2014 Nov 1

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Business, Management and Accounting(all)
  • Management Science and Operations Research

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