Academic journal article Financial Services Review

Spread Options and Risk Management: Lognormal versus Normal Distribution Approach

Academic journal article Financial Services Review

Spread Options and Risk Management: Lognormal versus Normal Distribution Approach

Article excerpt

(ProQuest: ... denotes formulae omitted.)

1. Introduction

Wealth management firms claim to provide tailor-made solutions to a client's unique financial situations. The assertion is that custom-made financial advice is provided within the context of a client's unique preferences. These assertions and claims, when actual practices are examined, often fall woefully short.

As evidence, consider that neither the client, nor the wealth management firm can articulate the relationship between the behavior of the deployed investment portfolio and the behavior of the client's liabilities. We use the term liabilities here to include both a family's contractual liabilities as well as intended uses for funds (e.g., college tuition, charitable giving, and retirement). We advocate wealth management firms take an asset-liability management approach, an approach successfully used by financial institutions and corporations for decades.

One motivation of this study is to provide better tools for managing the downside risk related to the spread between the asset portfolio and liability portfolio. We seek tools that serve the client better and afford the wealth management firm confidence in their value-added proposition, regardless of financial market behavior. Specifically, we explore managing the spread between assets and liabilities with a particular interest in spread options. Spread options are ideally suited for measuring and managing spread risk exposure. The value of spread options and related risk measures provide useful information regarding the current cost of insuring adverse moves in the spread. Many other authors have sought to connect modern quantitative finance tools and practices to improving individual investor performance. See, for example, Dubil (2004, 2007) and Johnston, Hatem, and Scott (2013). Kyrychenko (2008) sought to incorporate nonfinancial assets into the optimal asset allocation process. We follow a similar strategy, but also include liabilities with a focus on downside risk.

Based on prior academic research, closed form solutions for valuing European-style spread options do not exist when the underlying instruments are lognormally distributed.1 Consequently, numerical techniques and approximations must be used for these option pricing models. Industry practice is to model spread options assuming the spread is normally distributed even when the underlying distributions are known to be non-normal. This assumption is often made because the spread can be and often is negative. For example, when preferred retirement living standards are considered liabilities, then in the context of financial planning, spreads are often negative.

Although assuming the normal distribution is pragmatic, this internal inconsistency creates significant integrity concerns for the risk management systems of many financial institutions. These integrity concerns are especially manifest for risk management of large portfolios and may result in risk measurement errors for individual investors.

For options on underlying instruments other than spreads, current industry practice is to model the underlying instrument options assuming they are lognormally distributed. This assumption is often justified by the fact that the financial instrument prices are non-negative because of limited liability. Continuous time models based on geometric Brownian motion (GBM) imply the terminal distribution of the underlying instrument is lognormal. We refer to the spread option model that assumes both underlying instruments follow the lognormal distribution as the base model for comparison purposes. Industry practice, however, is to model spread options assuming arithmetic Brownian motion (ABM) because the spreads are often negative. These continuous time models based on ABM imply the terminal distribution of the underlying instrument is normal. We refer to spread option pricing models using the normal distribution as the alternate models (to contrast them from the base model). …

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