Valuation and Optimal Exercise of the Wild Card Option in the Treasury Bond Futures Market

The Chicago Board of Trade Treasury Bond Futures Contract allows the short position several delivery options as to when and with which bond the contract will be settled. The timing option allows the short position to choose any business day in the delivery month to make delivery. In addition, the contract settlement price is locked in at 2:00 p .m . when the futures market closes, despite the facts that the short position need not declare an intent to settle the contract until 8:00 p .m . and that trading in Treasury bonds can occur all day in dealer markets. If bond prices change significantly between 2:00 and 8:00 p .m ., the short has the option of settling the contract at a favorable 2:00 p .m . price. This phenomenon, which recurs on every trading day of the delivery month, creates a sequence of 6-hour put options for the short position which has been dubbed the “wild card option.” This paper presents a valuation model for the wild card option and computes estimates of the value of that option, as well as rules for its optimal exercise.     

The rationality of early exercise decisions: evidence from the S&P 100 index options market

This study provides a comprehensive empirical analysis of theearly exercise history of S&P 100 put and call option. Eventhough the S&P 100 index option market is generally consideredto be the most efficient options market in the world, we showthat many exercise decisions are inefficient because they occurwhen recorded bids are greater than exercise values. Due tomarket imperfections, some of the cases of inefficient exerciseare still rational, but we show that a substantial number ofthese decisions are clearly irrational since it would have beenpossible to realize a larger riskless net cash flow by selling.Unlike previous studies of early exercise, our tests of efficiencyand the rational decisions that presumably lead to efficientmarkets are model independent. We also provide evidence concerningthe relative significance of dividends and the wild card toindex option pricing models, and introduce and document theimportance of the option to exercise and avoid the indirectcosts of the spread. We also find evidence of a significantday-of the-week exercise effect, and present some likely explanationsfor that effect.     

Over-the-Counter Option Market Dividend Protection and “Biases” in the Black-Scholes Model: A Note

Most options are traded over-the-counter (OTC) and are dividend “protected;” the exercise price decreases on the ex date by an amount equal to the dividend. This protection completely inhibits the early exercise of American call options. Nevertheless, OTC-protected options have market values which differ systematically from Black-Scholes values for European options on non-dividend paying stocks. The pricing difference is related to both the variance of the underlying stock return and to time until expiration of the option, but it is quite small in dollar amount.     

Options on the Spot and Options on Futures

This paper analyzes and compares the valuation of two types of options that relate to the same asset: options on the asset itself and options on the futures on the asset. The early exercise privilege plays a central role in explaining the differences between the values of the two options. It is shown that in the case of a cash instrument that does not make interim payments, such as gold, the value of a call option on the spot is smaller than the call option on the futures contract; the opposite is true for put options. The early exercise boundaries, which characterize when it pays to exercise, are also compared and analyzed.     

Biases in option prices : Evidence from the foreign currency option market

This paper examines a European call model of option pricing over a data set which does not suffer from the early exercise problems that have plagued earlier studies of call options on common stocks. We specifically examine a data set of American call prices on spot foreign exchange for which it is plausible to apply an adjusted version of the Garman-Kohlhagen (1983) and Grabbe (1983) European call option model. We make adjustments for interest rate risk and find that the model is nearly unbiased in the valuation of foreign currency options. We conclude that the Geske-Roll (1984) conjecture about dividend uncertainty creating biases in stock option prices holds analogously in the foreign currency option market. Interest rate differential risk (analogous to risky dividends) thus appears to be an important element in the valuation of foreign currency options.     

THE PROPOSED INTRODUCTION OF FUTURES‐STYLE MARGINING IN THE UNITED STATES: AN AUSTRALIAN COMPARISON

We extend the quadratic approximation method to examine American‐style options traded using futures‐style margining and show that an early exercise premium can exist when the cost of carry is negative. Empirical results based on a reduced form of the model using futures‐style call options traded on the Australian All Ordinaries Share Price Index are consistent with previous research: call option early exercise premiums are economically zero. Full option prices are examined by comparing observed futures‐style with theoretical stock‐style values. We find futures‐style values exceed stock‐style values and argue that the increase results from improvements in liquidity. The findings are particularly relevant given the pending decision at the Commodity Futures Trading Commission to introduce a futures‐style system in the United States. JEL classification: G13, C13     

Brealey,Myers, and Allen on Real Options

Real options are valuable sources of flexibility that are either inherent in, or can be built into, corporate assets. The value of such options are generally not captured by the standard discounted cash flow (DCF) approach, but can be estimated using a variant of financial option pricing techniques. This article provides an overview of the basics of real option valuation by examining four important kinds of real options:

• 1 The option to make follow‐on investments. Companies often cite “strategic” value when taking on negative‐NPV projects. A close look at the payoffs from such projects reveals call options on follow‐on projects in addition to the immediate cash flows from the projects. Today's investments can generate tomorrow's opportunities.
• 2 The option to wait (and learn) before investing. This is equivalent to owning a call option on the investment project. The call is exercised when the firm commits to the project. But often it's better to defer a positive‐NPV project in order to keep the call alive. Deferral is most attractive when uncertainty is great and immediate project cash flows—which are lost or postponed by waiting—are small.
• 3 The option to abandon. The option to abandon a project provides partial insurance against failure. This is a put option; the put's exercise price is the value of the project's assets if sold or shifted to a more valuable use.
• 4 The option to vary the firm's output or its production methods. Companies often build flexibility into their production facilities so that they can use the cheapest raw materials or produce the most valuable set of outputs. In this case they effectively acquire the option to exchange one asset for another.

The authors also make the point that, in most applications, real‐option valuation methods are a complement to, not a substitute for, the DCF method. Indeed DCF, which is best suited to and usually sufficient for safe investments and “cash cow” assets, is typically the starting point for real‐option analyses. In such cases, DCF is used to generate the values of the “underlying assets”—that is, the projects when viewed without their options or sources of flexibility.     

THE EFFECT OF TRADED OPTION INTRODUCTION ON SHAREHOLDER WEALTH

Several authors suggest that the opening of a market in traded options constitutes a “feasibility-expanding” change. In this paper evidence on changes in the price of underlying stocks at the time of option listing is examined to determine whether option listing constitutes such a change. Evidence supports the hypothesis that call option listing is feasibility expanding, that put option listing is not feasibility expanding, and that call listings closer to the initiation of organized option trading have a larger impact relative to later listings.     

An empirical analysis of common stock call exercise: A note

This study tests the hypothesis that common stock call options are exercised rationally and in accordance with the commonly used frictionless markets boundary conditions. Using two years of historical early exercise data for common stock call options, the results show that contrary to the frictionless markets boundary conditions, approximately 20 percent of the early call exercise occurs at times other than ex-dividend dates. While most of the non-dividend related early exercise may be explained by transactions costs, a significant number of contracts appear to be exercised irrationally. These results suggest that failure to incorporate market frictions in option pricing models is likely to lead to specification error.     

CONVERTIBLE BONDS: MATCHING FINANCIAL AND REAL OPTIONS

For companies whose value consists in large part of “real options”‐ growth opportunities that may (or may not) materialize‐convertible bonds may offer the ideal financing vehicle because of the matching financial options built into the securities. This paper proposes that convertible debt can be a key element in a financing strategy that aims not only to fund current activities, but to give companies access to low‐cost capital if and when their real investment options turn out to be valuable. In this sense, convertibles can be seen as the most cost‐effective solution to a sequential financing problem‐how to fund not only today's activities, but also tomorrow's growth opportunities (some of them not yet even foreseeable). For companies with real options, the ability of convertibles to match capital inflows with corporate outlays adds value by minimizing two sets of costs: those associated with having too much (particularly equity) capital (known as “agency costs of free cash flow”) and those associated with having too little (“new issue” costs). The key to the cost‐effectiveness of convertibles in funding real options is the call provision. Provided the stock price is “in the money” (and the call protection period is over), the call gives managers the option to force conversion of the bonds into equity. If and when the company's investment opportunity materializes, exercise of the call feature gives the firm an infusion of new equity (while eliminating the debt service burden associated with the convertible) that enables it to carry out its new investment plan. Consistent with this argument, the author's recent study of the investment and financing activities of 289 companies around the time of convertible calls reports significant increases in capital expenditures starting in the year of the call and extending three years after. The companies also showed increased financing activity following the call, mainly new long‐term debt issues (many of them also convertibles) in the year of the call.     

The Value of Wildcard Options

Wildcard options are embedded in many derivative contracts. They arise when the settlement price of the contract is established before the time at which the wildcard option holder must declare his intention to make or accept delivery and the exercise of the wildcard option closes out the underlying asset position. This paper provides a simple method for valuing wildcard options and illustrates the technique by valuing the sequence of wildcard options embedded in the S&P 100 index (OEX) option contract. The results show that wildcard options can account for an economically significant fraction of OEX option value.     

Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model

We analyze American put options in a hyper-exponential jump-diffusion model. Our contribution is threefold. Firstly, by following a maturity randomization approach, we solve the partial integro-differential equation and obtain a tight lower bound for the American option price. Secondly, our method allows to disentangle the contributions of jumps and diffusion for the early exercise premium. Finally, using American-style options on the S&P 100 index from January 2007 until December 2012, we estimate various hyper-exponential specifications and investigate the implications for option pricing and jump-diffusion disentanglement. We find that jump risk accounts for a large part of the early exercise premium.     

A P.D.E. approach to Asian options: analytical and numerical evidence

We first derive a one-state-variable partial differential equation, easy to implement, which characterizes the price of a European type Asian option. This result is explained and related to previous literature. We then derive new results on the hedging of an Asian option and propose analytical and numerical analysis on the comparison between Asian and European options. Our methodology which applies to “fixed-strike” Asian options as well as to “floating-strike” Asian options completes and clarifies various results in the literature. In this paper we focus on “backward-starting” Asian options. Our approach is quite general however, and we explain how to adapt our main results to the case of “forward-starting” Asian options.     

Overreactions in the Options Market

This paper examines the “term structure” of options' implied volatilities, using data on S&P 100 index options. Because implied volatility is strongly mean reverting, the implied volatility on a longer maturity option should move by less than one percent in response to a one percent move in the implied volatility of a shorter maturity option. Empirically, this elasticity turns out to be larger than suggested by rational expectations theory—long-maturity options tend to “overreact” to changes in the implied volatility of short-maturity options.     

An empirical analysis of implicit delivery options in the treasury bond futures contract

Assuming perfect, frictionless and efficient markets, this paper develops a framework to estimate the composite value of the quality, wild card and end-of-month options implicit in the T-bond futures contract. The value of delivery options is shown to be the excess of forward price of the cheapest bond over its conversion factor times the exercise price of futures contract. Empirical results indicate that the option values over the last quarter of the nearby contract are on average less than 0.5 percent of the mean futures price, which is substantially lower than the value reported by previous studies. Further scrutiny reveals that although the empirical estimates are contaminated by non-synchronous bond data, they are consistent with certain known theoretical properties of option values.     

OPTION PRICING THEORY AND ASSET EXPECTATIONS: A Review and Discussion in Tribute to James Boness

James Boness shared with other early option theorists the hope that options could be used to infer investor expectations revealed in observed market prices. His research unfortunately pre-dated theoretical tools that might have helped that hope become a reality. Moreover, the modern option theory of Black and Scholes, Merton, Rubinstein, and others appeared to have “doomed to failure” any attempt to pursue the original “expectations intuition,” since expectations terms are not explicit terms in their option pricing equations. A subsequent theoretical advance by O'Brien, following Brennan, along with some observations by Figlewski, have furthered the possibility that obtaining implied expectations from observed option prices can become a reality. This review discussion of the literature is in honor of James Boness. The review is confined to the fundamental theory of valuing dividend-protected European “equity” options.     

Commodity Spread Option with Cointegration

We derive the valuation formula of a European call option on the spread of two cointegrated commodity futures prices, based on the Gibson–Schwartz with cointegration (GSC) model. We also analyze the American commodity spread option including the early exercise premium representation and an analytical approximation valuation formulae with cointegration. In the numerical analysis, we compare the spread option values calculated by the GSC model and the Gibson–Schwartz (GS) model that ignores cointegration. Consistent with the intuition that the cointegration prevents the prices from diverging, the GSC model prices the commodity spread option lower than the GS model which have longer maturity of more than 6 years. In other words, the GS model may overprice the commodity spread options for those with longer maturity without taking account of cointegration. Thus, incorporating cointegration is important for valuation and hedging of long-term commodity spread options such as large scale oil refining plant developments.     

Explaining the volatility smile: non-parametric versus parametric option models

We employ a “non-parametric” pricing approach of European options to explain the volatility smile. In contrast to “parametric” models that assume that the underlying state variable(s) follows a stochastic process that adheres to a strict functional form, “non-parametric” models directly fit the end distribution of the underlying state variable(s) with statistical distributions that are not represented by parametric functions. We derive an approximation formula which prices S&P 500 index options in closed form which corresponds to the lower bound recently proposed by Lin et al. (Rev Quant Financ Account 38(1):109–129, 2012). Our model yields option prices that are more consistent with the data than the option prices that are generated by several widely used models. Although a quantitative comparison with other non-parametric models is more difficult, there are indications that our model is also more consistent with the data than these models.     

Rational early exercise of call options: Australian evidence

Alpert (2010) develops a detailed analysis of the conditions for rational early exercise of call options in the presence of taxes. Using Alpert’s analysis as the theoretical framework, we examine the early exercise of call options in Australia over the period from 1 January 2001 to 30 June 2008. We find that exercises occurring on the last cum‐dividend trading day can be fully explained by non‐tax reasons, whilst taxation is a potential explanation for a large proportion of the early exercises that occur at other times.     

Index Options: The Early Evidence

Index options became the most important traded contracts during their first year of existence. Two contracts, namely those on the S&P100 and the Major Markets Index, have a trading volume which typically surpasses the trading volume in all individual stock option contracts. In this paper, we examine the pricing of the options on the S&P100 and the Major Markets Index. Using intra-day prices, we find the options frequently violate the arbitrage boundary, put/call parity, and are substantially mispriced relative to theoretical values. Our results suggest that tests of option pricing models may be more difficult than previously realized due to nonsynchronous prices, even using “real-time” data from the exchanges.