The Zero Lower Bound and Economic Determinants of the Volatility Surface in the Interest Cap Markets

• DOI: http://doi.org/10.1002/fut.21829
• Published date: 01 June 2017
• Date: 01 June 2017

The Zero Lower Bound and Economic

Determinants of the Volatility Surface in

the Interest Cap Markets

Myeong-Hyeon Kim, Changki Kim, and Injun Hwang*

Weaddress an important yet unanswered question: what would be the economic determinants

of the implied volatility during the zero lower bound periods? To answer this question, we

examine time variations of the cap market implied volatility and investigate economic deter-

minants on slopes and curvatures of the implied volatility curves. We find that unexpected

unemployment and inflation shocks play an important role in explaining implied volatility

curves for different maturities. Weassociate negative jumps in the volatility dynamics (Jarrow,

Li, & Zhao, 2007) with two unexpected macroeconomic shocks. Our results provide an impor-

tant implication for practitioners who prepare future exit strategies. ©2016 Wiley Periodicals,

Inc. Jrl Fut Mark 37:578–598, 2017

1. INTRODUCTION

As the federal funds rate hit the zero lower bound1(hereafter, ZLB) in 2009, this unorthodox

condition has created major challenges in many fields of research. Such challenges are

mainly discussed from the monetary policy perspective, and little academic attention has

been paid to the interest rate options market, despite its important practical implications

for hedging and pricing. One possible concern is that the price of a zero strike floor should

be equal to zero according to the Black model (1976), while current market quotes have

positive values during ZLB periods. Under this unorthodox condition, when some of the

fixed-income security markets enter the zone of zero nominal rates or even negative rates,

studies of financial instruments embedded with option features, such as caps, floors, and

swaptions, face herculean tasks in improving pricing mechanisms and understanding interest

rate options markets. Our primary interest is in examining the implied dynamics of interest

Myeong-Hyeon Kim is at the Korea Housing & Urban Guarantee Corporation (KHUG), BIFC40, Busan,

Republic of Korea and Asian Institute of Corporate Governance (AICG) at Korea University. Changki Kim

and Injun Hwang are at the Korea University Business School, Anam-dong, Seongbuk-Gu, Seoul 136-701,

Republic of Korea. This work was supported by the National Research Foundation of Korea Grant funded

by the Korean Government (NRF-2014S1A3A2036037), and this research was partially supported by IBRE

Award granted by Korea University Business School. We thank Robbert I. Webb, Baeho Kim, Lingxia Sun,

FergusBevin-McCrimmon, and participants at the 2016 Derivatives Markets Conference at Auckland Centre

for Financial Research for their helpful comments.

JEL Classification: G10, G12, G13

*Correspondence author,Korea University Business School, Anam-dong, Seongbuk-Gu, Seoul 136-701, Republic

of Korea. Tel: 82-2-3290-1307, Fax:82-2-922-7220, e-mail:hwangi@korea.ac.kr

Received September 2016; Accepted October 2016

1For recent discussion on the zero lower bound, refer to Blinder (2012), Hamilton and Wu (2012), Swanson and

Williams (2014), and Wu and Xia (2016).

The Journal of Futures Markets, Vol. 37, No.6, 578–598 (2017)

©2016 Wiley Periodicals, Inc.

Published online 19 December 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21829

The Zero Lower Bound and Economic Determinants 579

rate options markets, focusing on the ZLB period. Specifically, we examine time variations

of the implied volatility surface of the cap market and investigate economic determinants of

volatility slopes and curvatures.

Volatility smiles or smirks are omnipresent yet puzzling phenomenon in the equity and

currency options markets. The majority of studies on the patterns of the volatility surface

has been focused on explaining the dynamics of the patterns by imposing some relaxations

on the Black–Scholes–Merton assumptions. Dumas, Fleming, and Whaley (1998), Hull and

White (1987), and Heston (1993) introduce stochastic volatility by relaxing deterministic

volatility assumption and Bates (1991), Das and Sundaram (1999), Merton (1976), and

Rubinstein (1994) apply random jumps using Levy process. From the modeling perspective,

these models, with the help of liquidity effects or market frictions, have achieved a level of

success in explaining the behavior of the observed implied volatility.2Interestingly, Bakshi,

Cao, and Chen (1997) find that employing stochastic interest rates or stochastic volatility

with random jumps does not fully explain the implied volatility dynamics. Proposed infer-

ences on the portions unexplained are due to the existence of liquidity issues, default risks,

and leverage effects from asymmetric volatility responses.

Unlike much of the literature on equity options, research on the volatility smile patterns

in interest rate options markets is remarkably sparse and does not directly examine the

economic determinants. At-the-money (ATM) and the strikes around ATMoptions have been

the central issue among most academic studies, whereas virtually no attention has been paid

to the economic determinants of volatility smiles and skews in the interest rate options and no

study has been done on determining economic factors of the volatility surface during the ZLB

periods. Fan, Gupta, and Ritchken (2007), Gupta and Subrahmanyam (2005), and Jarrow,

Li, and Zhao (2007) study the patterns of volatility smiles/skews in interest rate options

markets from the modeling perspective. Two exceptions are the papers of Deuskar, Gupta,

and Subrahmanyam (2008) and Pe˜

na, Rubio, and Serna (1999). Pe˜

na et al. (1999) examine

the determinants of the implied volatility function in the Spanish equity index options market

and Deuskar et al. (2008) investigate economic determinants on the implied volatility in the

U.S. interest rate options markets. Deuskar et al. (2008) explore potential factors and find

evidence that factors outside yield curves, such as liquidity and default risk measures, are

necessary to explain smiles in the cap market. In the same vein, Li and Zhao (2009) find

that employing the factors outside yield curves helps explain the prevailing patterns of the

cap implied volatility. Their finding is based on the estimation results of the LIBOR rates

distribution under the T-forwardmeasures and the state-price densities of market cap quotes.

In this paper, we investigate U.S. interest rate options market by characterizing the time-

series dynamics of the implied volatility and examining its economic determinants.

In spite of many similarities among options markets, note that the conclusions of equity

options markets are not mechanically transferable to those of interest rate options because

the implied dynamics of interest rate derivatives present some distinctive observed features.

Two representative instances are the inverse relationship between the underlying interest

rates and the humped or decreasing shape of their term structure (see Brigo and Mercurio

(2002) and Rebonato (2002) for stylized facts). These distinctions mainly arise from struc-

tural differences between the two markets. One of these structural differences is discussed

in terms of market participants. In the interest rate options market, institutional investors

with access to homogeneous information set trade interest rate options via over-the-counter

2For detailed literature, refer to Bollen and Whaley (2004), Dennis and Mayhew (2009), Longstaff (1995), Mayhew

(2002), and Pe˜

na et al. (1999). As alternative channels of smiles/skews, Pe˜

na et al. (1999) suggest transaction costs

matter,Bollen and Whaley (2004) point out the net buying pressure and limits to arbitrage, and Dennis and Mayhew

(2009) raise a question on tick size of market quotes.