Interest rate risk in long‐dated commodity options positions: To hedge or not to hedge?

• DOI: http://doi.org/10.1002/fut.21954
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 5 February 2018

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Revised: 13 June 2018

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Accepted: 13 June 2018

DOI: 10.1002/fut.21954

RESEARCH ARTICLE

Interest rate risk in long‐dated commodity options

positions: To hedge or not to hedge?

Benjamin Cheng

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Christina Sklibosios Nikitopoulos

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Erik Schlögl

Finance Discipline Group, UTS Business

School, University of Technology Sydney,

Broadway, NSW, Australia

Correspondence

Christina Sklibosios Nikitopoulos,

Finance Discipline Group, UTS Business

School, University of Technology Sydney,

PO Box 123, Broadway, NSW 2007,

Australia.

Email: christina.nikitopoulos@uts.edu.au

Funding information

Australian Research Council, Grant/

Award Number: DP 130103315;

Australian Government Research

Training Program Scholarship

Abstract

We empirically assess hedging interest rate risk beyond the conventional delta,

gamma, and vega hedges in long‐dated crude oil options positions. Using factor

hedging in a model featuring stochastic interest rates and stochastic volatility,

interest rate hedges consistently provide an improvement beyond delta, gamma,

and vega hedges. Under high interest rate volatility and/or when a rolling hedge

is used, combining interest rate and delta hedging improves performance by up

to four percentage points over the common hedges of gamma and/or vega.

Thus, contrary to common practice, hedging interest rate risk should have

priority over these “second‐order”hedges.

KEYWORDS

delta hedge, interest rate hedge, long‐dated crude oil options, stochastic interest rates

JEL CLASSIFICATION

C13, C60, G13, Q40

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INTRODUCTION

Motivated by the importance of managing longer‐term exposures to commodity market risk, this paper aims to gauge

the impact of interest rate risk on the hedging of commodity futures options. While it is intuitively clear that hedging

interest rate risk is relatively more important for longer‐dated options and during periods of high interest rate volatility,

it is not obvious what practical significance should be accorded to interest rate hedges compared to the “second‐order”

hedges, which are more commonly put in place in addition to the core delta hedge, that is, gamma and/or vega hedges.

Answering this question requires careful empirical analysis on market data of hedging efficacy in the context of a

comprehensive model integrating stochastic volatility, commodity, and interest rate risk. This setup then also allows us

to consider another issue of practical importance: Due to the higher liquidity of shorter maturity contracts, these are

often used to construct “rolling”hedges

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for longer‐dated options—this raises the question whether this maturity

mismatch increases the practical necessity to hedge the resulting basis risk, and whether an interest rate hedge can help

to mitigate this risk.

The literature on hedging long‐dated commodity commitments is relatively sparse and with few exceptions does not

explicitly model interest rate risk, see for instance Schwartz (1997), Brennan and Crew (1997), Bühler, Korn, and

Schöbel (2004), Veld‐Merkoulova and De Roon (2003), Dempster, Medova, and Tang (2008), Lautier and Galli (2010),

J Futures Markets. 2019;39:109–127. wileyonlinelibrary.com/journal/fut © 2018 Wiley Periodicals, Inc.

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When hedging positions in long‐dated derivatives, the available hedging instruments may have shorter maturities than the hedging time horizon, typically due to liquidity constraints. When the

hedging instruments approach their maturity, thehedge is rolled forward by closing out the hedge position and entering into a new hedge in the next set of available hedging instruments. The maturity

mismatch between the hedge instruments and the hedging time horizon introduces basis risk in the hedge. This is a form of “time”basis (in contrast to the “grade”basis introduced by hedging across

different—but highly correlated—assets). Due to the time value of money, the “time”basis is closely related to interest rate risk. Thus, one may expect that the basis risk in rolling hedges may be

mitigated by interest rate hedges.

and Shiraya and Takahashi (2012).

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There is somewhat more emphasis in the literature on hedging short‐maturity

commodity derivative contracts (Chiarella, Kang, Nikitopoulos, & Tô, 2013; Trolle & Schwartz, 2009) or spot

commodity prices (Hilliard & Huang, 2005; Liu, Chng, & Xu, 2014). Trolle and Schwartz (2009) demonstrated that the

crude oil futures volatility is unspanned, since adding options to the set of hedging instruments (as opposed to using

only futures) significantly improves hedging of volatility trades, such as straddles. This finding in particular motivates

our choice to include stochastic volatility in the model used in the empirical analysis of the paper, and makes it all the

more remarkable (though not contradictory to their findings) that for long‐dated commodity options, in some situations

hedging interest rate risk is more important than vega for the performance of the hedge. Chiarella et al. (2013)

empirically demonstrate that hump‐shaped volatility specifications reduce the hedging error of crude oil volatility

trades (straddles) compared to exponential volatility specifications. However, these latter papers assume deterministic

interest rates and do not address the question to what extent these models can provide adequate hedges for long‐dated

options positions.

This paper conducts an extensive empirical study using crude oil derivatives, arguably the most important and most

liquid commodity derivatives market.

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To this end, the futures pricing model by Cheng, Nikitopoulos, and Schlögl

(2017) is used, since it integrates commodity, volatility, and interest rate risk, making it well suited to compute hedge

ratios for these risks. In contrast, most of the literature is restricted to spot price models, which cannot fit well the term

structure of the futures curve and/or cannot accommodate all these dimensions of risk.

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Cheng et al. (2017) have

empirically demonstrated that this stochastic volatility–stochastic interest rate model improves pricing performance on

long‐dated crude oil derivative prices, and thus provides a “good”fit to market data. Alexander and Kaeck (2012)

provide empirical evidence on the importance of the model calibration for hedging performance of stochastic volatility

models in FTSE 100 options. This motivates the choice of a multidimensional model, which can directly describe the

entire term structure of futures prices, allows for a full correlation structure and leads to affine representations of

futures prices and quasi-analytical option prices, and thus is well suited for model estimation or calibration for the

purpose of hedging applications.

The model parameters and the resulting hedge ratios are estimated from historical crude oil futures and futures

options prices and Treasury yields. Delta, vega, gamma, and interest rate hedges for futures options positions are

simultaneously constructed and compared, and their performance over 2006–2011

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is empirically tested under

scenarios representing different levels of exposure to basis risk. To confirm the necessity of models with stochastic

interest rates, their hedging performance is also compared with deterministic interest rate specifications fitted to a

Nelson and Siegel (1987) curve. We found that stochastic interest rate models consistently improve hedging

performance (compared to deterministic interest rate models) for all hedging schemes and for any level of exposure to

basis risk, with the improvement being stronger over volatile periods.

Furthermore, the efficacy of the factor‐hedging methodology is empirically assessed. Factor hedging is well suited for

hedging with general multidimensional models (Chiarella et al., 2013; Clewlow & Strickland, 2000) and allows

simultaneous hedging of multiple risk factors impacting the entire term structure of the forward curve of commodities,

and their derivatives. Theoretical self‐financing replicating hedge strategies are predicated on rebalancing in continuous

time (see, e.g., Barrieu & El Karoui, 2008; Tebaldi, 2005), while in practice hedges can only be rebalanced discretely—

this is another reason why factor hedging is the more suitable approach, as it better caters for the fact that a perfectly

self‐financing replicating hedge in continuous time is not implementable in practice.

Finally, we add to the existing literature that underscores the importance of hedging basis risk in derivatives

positions and provide strong evidence for the need to consider basis risk resulting from rolling hedges for long‐

dated options positions. Motivated by the increasing importance of the issue to risk management in insurance

(Ankirchner, Schneider, & Schweizer, 2014), investments (Zhang, Tan, & Weng, 2017) and commodity markets

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Veld‐Merkoulova and De Roon (2003) propose a term structure model of futures convenience yields and develop a strategy that minimises both spot price risk and basis risk. They show that it

outperforms the simple stack‐and‐roll hedge substantially. Similarly, Shiraya and Takahashi (2012) propose a mean reverting Gaussian model of commodity spot prices and empirically demonstrate

that their Gaussian model outperforms a stack‐and‐roll model.

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See D’Ecclesia, Magrini, Montalbano, and Triulzi (2014).

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It has been shown that interest rate risk is relevant to equity derivativeswith longer maturities and models with stochastic interest rates tend to improvepricing and hedging of such contracts (Bakshi,

Cao, & Chen, 2000). A representative literature on spot option pricing models with stochastic interest rates includes Rabinovitch (1989), Amin and Jarrow (1992), Scott (1997), Kim and Kunitomo

(1999), and van Haastrecht and Pelsser (2011). Fabozzi, Paletta, Stanescu, and Tunaru (2016) propose a quasianalytic method for pricing and hedging long‐dated equity options. However, it is limited

to deterministic interest rates.

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This spans periods before, during, and after the Global Financial Crisis (GFC), yielding three qualitatively different financial market environments. Since December 2011, the interest rate

environment has remained very benign, and thus interest rate hedges have remained relatively unimportant for the time being (until such a time that interest rate volatility, perhaps inevitably, picks

up again).

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