Impact of Negative Rates on Derivatives Valuations & Risk Calculations

A Case Study Focusing On Japan

The Bank of Japan recently adopted negative interest rates following the lead of several European central banks. Enacted to help stimulate their economies, these rates present big challenges to derivatives valuation and risk assessment in terms of curve construction, volatility quotation, volatility cube construction, and model calibration. Because assumptions as few as five years ago for many derivatives models didn’t allow for sub-zero rates, much of the industry has been left scrambling to adapt to the prolonged and increasingly negative rate environment.

Although there are several proposed approaches on the market to help alleviate the problems (from crude shifts to more flexible adaptations), the potential solutions can have quantitative effects on PnL and Greek calculations. These potential unknowns present challenges to banks who require a consistent modeling framework to properly capture negative rates and have accurate PnLs and risk assessment. And practitioners can’t help but wonder – how will my models react if rates continue to become even more negative?

On Wednesday, April 20th featured speaker Dr. Dan Li Senior Vice President and Global Head of Financial Engineering at Numerix presented a case study on the impact of negative rates for derivative practitioners. It was specifically focused on the Japanese derivative markets since the Bank of Japan pushed rates below zero. He delved into the current modeling challenges in dealing with these rates along with additional pricing and risk implications for financial institutions.

Dr. Li addressed the impact of negative interest rates on:

  • Curve construction
  • Volatility quotations
    • Normal
    • Shifted lognormal (displaced diffusion lognormal)
  • Volatility interpolations
    • Shifted SABR
    • Free-boundary SABR
  • Model calibration
  • Valuations and risk sensitivities

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