A multiscale extension of the Margrabe formula under stochastic volatility

Jeong Hoon Kim, Chang Rae Park

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The pricing of financial derivatives based on stochastic volatility models has been a popular subject in computational finance. Although exact or approximate closed form formulas of the prices of many options under stochastic volatility have been obtained so that the option prices can be easily computed, such formulas for exchange options leave much to be desired. In this paper, we consider two different risky assets with two different scales of mean-reversion rate of volatility and use asymptotic analysis to extend the classical Margrabe formula, which corresponds to a geometric Brownian motion model, and obtain a pricing formula under a stochastic volatility. The resultant formula can be computed easily, simply by taking derivatives of the Margrabe price itself. Based on the formula, we show how the stochastic volatility corrects the Margrabe price behavior depending on the moneyness and the correlation coefficient between the two asset prices.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
JournalChaos, Solitons and Fractals
Publication statusPublished - 2017 Apr 1

Bibliographical note

Funding Information:
We thank anonymous referees for comments that greatly improved the manuscript. The research of J.-H. Kim was supported by the National Research Foundation of Korea NRF-2016K2A9A1A01951934.

Publisher Copyright:
© 2017 Elsevier Ltd

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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