Harvesting the volatility smile in a large emerging market: A Dynamic Nelson–Siegel approach

• Published date: 01 November 2023
• Author: Sudarshan Kumar,Sobhesh Kumar Agarwalla,Jayanth R. Varma,Vineet Virmani
• Date: 01 November 2023
• DOI: http://doi.org/10.1002/fut.22450

Received: 28 October 2022

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Accepted: 26 June 2023

DOI: 10.1002/fut.22450

RESEARCH ARTICLE

Harvesting the volatility smile in a large emerging market:

A Dynamic Nelson–Siegel approach

Sudarshan Kumar

1

|Sobhesh Kumar Agarwalla

2

|Jayanth R. Varma

2

|

Vineet Virmani

2

1

Indian Institute of Management

Calcutta, Joka, Kolkata, West Bengal,

India

2

Indian Institute of Management

Ahmedabad, Vastrapur, Ahmedabad,

Gujarat, India

Correspondence

Sudarshan Kumar, IIM Calcutta, NAB

302, Kolkata 700104, West Bengal, India.

Email: sudarshank@iimcal.ac.in

Abstract

While there is a large literature on modeling volatility smile in options

markets, most such studies are eventually focused on the forecasting

performance of the model parameters and not on the applicability of the

models in a trading environment. Drawing on the analogy of volatility smile

like a term structure in the context of interest rates in fixed‐income markets,

we evaluate the performance of the Dynamic Nelson–Siegel (DNS) approach

to modeling the dynamics of volatility smile in a trading environment against

competing alternatives. Using model‐based mispricing as our sorting criterion,

and deploying a trading strategy of going long the options in the upper deciles

and going short the options in the lower deciles, we show that dynamic models

consistently outperform their static counterparts, with the worst dynamic

model outperforming the best static model in terms of the percentage of mean

returns from the trading portfolios and the Sharpe ratio. Specifically, we find

that the DNS model consistently outperforms all other competing specifica-

tions on most of our selected criteria.

KEYWORDS

dynamic Nelson–Siegel, equity derivatives, Kalman filter, options market, state‐space

models, volatility smile

JEL CLASSIFICATION

C14, C32, C52, G12, G13

1|INTRODUCTION

There is a growing literature on understanding the behavior of volatility smile in the options markets, the name given

to the commonly observed empirical relationship between implied volatility (IV) and option strike. In the last decade,

using data from economies with liquid option markets, there have been many articles published on the modeling of

volatility smile, as well as on its applications in the larger literature on option pricing, financial engineering, and risk

management (Carr & Wu, 2003; Christoffersen et al., 2009; Cont & Fonseca, 2002; François & Stentoft, 2021a; García‐

Machado & Rybczyński, 2017; GrØborg & Lunde, 2016; Hagan et al., 2002; Jain et al., 2019; Kim et al., 2020; Kim, 2021;

Taylor et al., 2010; Wong & Heaney, 2017).

The importance of having a systematic approach to modeling volatility smile cannot be overemphasized—option

traders are known to quote not option prices but volatility implied by them during trading (Reiswich & Wystup, 2009;

J Futures Markets. 2023;43:1615–1644. wileyonlinelibrary.com/journal/fut © 2023 Wiley Periodicals LLC.

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Wong & Heaney, 2017), making IV an important forward‐looking measure of financial market's view of uncertainty

and risk aversion over the life of an option contract (Jin et al., 2012; Koopman et al., 2005; Park et al., 2019). Options are

traded for various strikes, and each strike provides additional information about the market participant's view of

the prevailing uncertainty and movement of future stock returns and volatility. Given the option price, in terms of the

Black (1976) formula, implied volatility is written as an inverse function:

≡σVFKrτImplied volatility = Option price ( , , , , )

,

IV Black

−1

where

V

FKr,,,

, and

τ

, respectively, denote the option price, price of the futures contract with the same maturity as

the option, strike price, the risk‐free rate, and the time to maturity.

Given the empirically established nature of volatility smile across markets, asset classes, and geographies (for a

survey, see Derman & Miller, 2016; Kearney et al., 2019) a working model for IV becomes important for a variety of

reasons. First, and possibly most importantly, it allows option traders to implement trading strategies, given their view

on the evolution of the volatility smile (Kim et al., 2020). Second, a model for the volatility smile allows for extracting

the market‐implied risk‐neutral probability distribution of future price movements (Hayashi, 2020; Jackwerth, 2004;

Malz, 1997). Finally, the ability to price over‐the‐counter or exotic equity derivatives requires volatility smile as an

input to stochastic volatility models, to ensure that the model‐dependent price of any exotic option and the associated

hedging strategy are consistent with the prices of prevailing plain vanilla option prices (Dupire, 1994; Gatheral

et al., 2020; Rebonato, 2004; Wong & Heaney, 2017).

This study contributes to the stream of literature on modeling volatility smile by showing the superiority of dynamic

models of IV for implementing trading strategies using stock options data from the National Stock Exchange of India

(NSE). The reasons for choosing data from the Indian option markets are threefold: (i) it is one of the few markets

worldwide with a liquid stock options market, consistently ranking among the largest options market globally by

volume (World Federation of Exchanges, 2021b), (ii) a relatively less mature market such as India might bring better

insights in the context of statistical arbitrage, which is the central theme of our study, and finally, although it is more to

do with a methodological expediency, (iii) unlike most developed country options markets, the NSE of India also has

liquid futures contracts simultaneously with liquid options on the same stock, allowing us to directly use the Black

(1976) formula to find IV without needing to estimate stockwise dividend yield (Jain et al., 2019).

We draw on the analogy of volatility smile like a term structure in the context of interest rates in fixed‐income

markets (Derman et al., 1996; Rogers & Tehranchi, 2010), and use a popular approach to dynamically model the term

structure of interest rates called the Dynamic Nelson–Siegel (DNS) model (Diebold & Li, 2006) to similarly model IV as

a function of option delta. We also deploy the extended version of the DNS model to allow for additional flexibility in

possible shapes of the smile on the lines of Svensson's (1994) model. In form, the use of the Diebold and Li (2006)

approach to model the time evolution of volatility is not new. Starting from the work of Chalamandaris and Tsekrekos

(2011), many researchers have used their flexible approach to model volatility surface across markets (Chalamandaris

& Tsekrekos, 2014; Guo et al., 2014) and asset classes (Kearney et al., 2019). All these papers, however, use the Diebold

and Li (2006) specification to only model the time dimension of the volatility surface and not for modeling the dynamics

of the smile itself, which is more important in a trading environment. Also, most of these studies are eventually focused

on the forecasting performance of the model parameters and not on their applicability or use in trading.

There are three main concerns with using static models popular in the literature for fitting the volatility smile. First,

there is no way to ensure that smile evolution is economically reasonable, and because parameters are estimated

separately for each day, the fitted smile can vary wildly over consecutive days. Second, even in liquid option markets,

not all instruments or option strikes are equally liquid (World Federation of Exchanges, 2021b), and therefore the

prices of illiquid options can often be distorted. This is similar to the phenomenon of not all bonds being equally liquid

in fixed‐income markets (Cortazar et al., 2007; Nagy, 2020). Third, and specific to the use of lower‐order polynomials in

fitting volatility smile (Jain et al., 2019), quadratic models assume a symmetry which is at odds with the observed

downward‐sloping relationship between IV and option delta for stock options—a phenomenon referred to as volatility

skew (Zhang & Xiang, 2008).

Our approach of using a dynamic model estimated using a state‐space approach addresses all of these concerns. By

design, the DNS approach estimates the whole panel of observations together by explicitly incorporating the time

dynamics of the underlying factors. This allows for aggregating trading information over a longer period in a

theoretically consistent manner, so the distorted prices pose less of a problem, and the specification is flexible enough

to capture volatility skews at the same time. Finally, with a larger sample of observations available when using a

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KUMAR ET AL.