Implied remaining variance with application to bachelier model

Jian Sun, Qiankun Niu, Shinan Cao, Peter Carr

Research output: Contribution to journalArticle

Abstract

In this article, we propose a way to model vanilla options implied volatility curve in closed form under the Brownian motion assumption for underlying asset. The work is an extension of the recent article by Carr and Sun [2013]. Using Brownian motion to model the financial assets was first proposed by Bachelier one century ago. Even though in the option pricing world, the usual setting is geometric Brownian motion, which guarantees the positiveness of the underlying price, it is becoming common to use the Brownian motion in some other situations as well, in particular for interest rate derivatives due to the environments of super low or even negative rates in JPY, EUR, and USD currencies. We will use our model to calibrate the implied normal volatilities in the swaption market. Calibration results show that the model proposed in this article works very well. Furthermore we will prove that, under certain conditions, our model could be free of arbitrage. The proofs of the main results are left in the appendix.

Original languageEnglish (US)
Pages (from-to)78-95
Number of pages18
JournalJournal of Fixed Income
Volume26
Issue number2
DOIs
StatePublished - Sep 1 2016

Fingerprint

Brownian motion
Guarantee
Swaption
Geometric Brownian motion
Assets
Option pricing
Implied volatility
Currency
Calibration
Financial assets
Interest rate derivatives
Arbitrage

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

Cite this

Implied remaining variance with application to bachelier model. / Sun, Jian; Niu, Qiankun; Cao, Shinan; Carr, Peter.

In: Journal of Fixed Income, Vol. 26, No. 2, 01.09.2016, p. 78-95.

Research output: Contribution to journalArticle

Sun, Jian ; Niu, Qiankun ; Cao, Shinan ; Carr, Peter. / Implied remaining variance with application to bachelier model. In: Journal of Fixed Income. 2016 ; Vol. 26, No. 2. pp. 78-95.
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