# Interest rate volatility

My work outside academia includes developing fixed income volatility indexes for Chicago Board Options Exchange (CBOE). I am the co-inventor of the CBOE Interest Rate Swap Volatility Index (CBOE SRVIX)—the first standardized volatility measure in the fixed income market, designed to standardize and simplify interest rate volatility trading much in the spirit of the CBOE-VIX index in the equity space. My work is also at the basis of the first model-free volatility index on both US government debt (CBOE/CBOT TYVIX) and Japanese government debt (S&P/JPX JGB-VIX).

In November 2014, CBOE Future Exchange (CFE) launched futures on TYVIX for multiple months, the first exchange-traded contracts based on these new standardized fixed income volatility gauges. Please visit the following website for market data and other institutional features:

Below are links to white papers, research notes, and historical data since the dissemination of the two CBOE indexes respectively in June 2012 (SRVIX) and May 2013 (TYVIX):

CBOE Interest Rate Swap Volatility Index (SRVIX)

http://www.cboe.com/micro/srvix/default.aspx

CBOE/CBOT 10-year U.S. Treasury Note Volatility Index (TYVIX)

http://www.cboe.com/micro/volatility/TYVIX/default.aspx

Below are links regarding the volatility gauge on Japanese government debt announced in July 2015 (JGB-VIX):

English: http://www.jpx.co.jp/english/news/2040/20150722-1.html

Japanese: http://www.jpx.co.jp/news/2040/20150722-01.html

Some of my work on interest rate volatility is collected below:

[1] “An Interest Rate Swap Volatility Index and Contract” (with Yoshiki Obayashi), June 2012

Technical white paper underlying the CBOE SRVIX Index of Interest Rate Swap Volatility

[2] “Interest Rate Variance Swaps and the Pricing of Fixed Income Volatility” (with Yoshiki Obayashi), **GARP Risk Professional: Quant Perspectives**, March 1-8 (2014)

A succinct presentation of methodology underlying the pricing of variance swaps in the fixed income space

[3] Book: *The Price of Fixed Income Market Volatility* (with Yoshiki Obayashi)

**Springer: Springer Series in Finance**, New York (2015), 250 pages

A book unifying work on security design and related issues arising while pricing and indexing fixed income volatility

Download Preface Springer.com Amazon.com

[4] “Rate Fears Gauges and the Dynamics of Fixed Income and Equity Volatilities” (with Yoshiki Obayashi and Catherine Shalen), **Journal of Banking and Finance** 52, 256-265 (2015)

Compares empirical properties of the CBOE SRVIX Index of Interest Rate Swap volatility with those of the CBOE VIX on equity

[5] “Interest Rate Derivatives and Volatility” (with Yoshiki Obayashi)

**Handbook of Fixed-Income Securities**: Chapter 20, 767-838 (2016)

Handbook Series in Financial Engineering and Econometrics. John Wiley & Sons (Editor Pietro Veronesi)

Surveys interest rate derivatives and their use to hedge against fixed income volatility — a mix of applied and theory pieces

The following working papers contain early work on methodology aimed to reference volatility of government bonds, time deposits and credit markets, i.e., the initial basis for parts of the book [3]:

[6] “The Price of Government Bond Volatility” (with Yoshiki Obayashi), March 2013

[7] “Volatility Indexes and Contracts for Eurodollar and Related Deposits” (with Yoshiki Obayashi), March 2103

[8] “Volatility Indexes and Contracts for Government Bonds and Time Deposits” (with Yoshiki Obayashi), March 2013 (unifying [6] & [7] above)

[9] “Credit Variance Swaps and Volatility Indexes” (with Yoshiki Obayashi), March 2013

The previous work deals with security designs regarding forward-looking measures of fixed income volatility. An important, related but distinct, issue regards the pricing of derivatives written on these measures of fixed income volatility.

The following paper develops a model that prices futures & options referenced to forward looking indexes of government bond volatility. The challenge is the following. Bond volatility cannot be taken to be exogenous as one ordinarily does in the equity case. No-arbitrage restricts bond price volatility to link to the whole yield curve. The paper develops a model that determines the level of forward-looking bond volatility while making sure that the entire yield curve is pinned down without error.

[10] “Pricing Options and Futures on a Government Bond Volatility Index” (with Yoshiki Obayashi and Shihao Yang), May 2015

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