Exploring the difference between implied volatilities of options embedded in convertible bonds and exchange‐traded options and its contributing factors

• Author: Supawut Sinthawat,Narapong Srivisal,Tanawit Sae‐Sue
• Date: 01 January 2020
• Published date: 01 January 2020
• DOI: http://doi.org/10.1002/jcaf.22429

BLIND PEER REVIEW

Exploring the difference between implied volatilities

of options embedded in convertible bonds and

exchange-traded options and its contributing factors

Tanawit Sae-Sue

1,2

| Supawut Sinthawat

1

| Narapong Srivisal

1

1

Department of Banking and Finance,

Faculty of Commerce and Accountancy,

Chulalongkorn University, Bangkok,

Thailand

2

Environment, Health and Social Data

Analytics Research Group, Chulalongkorn

University, Bangkok, Thailand

Correspondence

Tanawit Sae-Sue, 254 Payathai Rd, Wang

Mai, Pathumwan, Bangkok 10330,

Thailand.

Email: tanawit@cbs.chula.ac.th

Funding information

Chulalongkorn University;

Ratchadapiseksomphot Endowment

Fund; Grants of Development of New

Faculty and Staff

Abstract

The convertible feature attached to a newly issued bond represents an embed-

ded option whose value is determined by firm. The embedded option's implied

volatility reflects the firm's view of its stock price risk which may differ from

that of the market reflected in the exchange-traded option. If such a gap in

implied volatilities exists, it may create arbitrage opportunity for investors.

Hence, we determined the gap between the implied volatilities extracted from

the U.S. exchange-traded option and embedded option and investigated its

potential contributing factors, including corporate variables (price-to-book,

market capitalization, cost of debt, debt-to-equity) and bond variables (matu-

rity, default probability). The result showed that, during 2014–2016, the differ-

ence existed and was attributed to the firm's market capitalization. Our finding

suggests the potential arbitrage opportunity in the debt, equity, and convertible

instruments of small market capitalization firms.

KEYWORDS

convertible bond, embedded option, implied volatility

1|INTRODUCTION

Implied volatility is an important deciding factor in

option pricing, which is a financial instrument that

allows the holder to buy or sell an asset for a specific

price at a predetermined time. Option pricing is often

performed using modeling, especially the famous Black–

Scholes–Merton model, whose important input parame-

ters include implied volatility. Implied volatility indicates

the market's views and estimates future volatility, based

on probability. Because the implied volatility is forward-

looking, it provides investors with the sentiment about a

stock or the market's volatility, and therefore helping

them determine trading strategy. Nevertheless, implied

volatility does not predict the direction in which the stock

is headed. It is based solely on option prices and sensitive

to unexpected factors, such as news events.

Implied volatility is traditionally extracted from actively

traded options in the market, thus reflecting the market

participants' view of volatility. However, another non-

traditional approach for obtaining implied volatility is to

extractitfromconvertiblebondsattheirissuancedate.

Because the convertible bond's features, such as price, cou-

pon, yield, conversion ratio, are set by the underlying firm

through the underwriting process, the implied volatility

obtained from convertible bonds at issuance should reflect

the firm's view of its share price's volatility.

Convertible bond can be converted to a certain

amount of stocks before maturity, thus naturally viewed

as a financial product consisting of a straight bond and a

call option. Under the perfect market assumption, it can

Correction added on December 19, 2019, after first online publication:

Article categoryupdated from “Editorial Review”to “Blind PeerReview.”

Received: 24 October 2019 Revised: 2 November 2019 Accepted: 9 November 2019

DOI: 10.1002/jcaf.22429

J Corp Acct Fin. 2020;31:125–133. wileyonlinelibrary.com/journal/jcaf © 2019 Wiley Periodicals, Inc. 125