The pricing of callable preferred stock

The Pricing of Callable Preferred Stock

Clifford F. Thies and Steven C. Isberg

ABSTRACT

In this study, the authors use both the Black/Scholes European option model and the Barone-Adesi/Whaley American option model to estimate call option values implicit in seasoned callable preferred stock issues. Consistent with the finding that call features increase bond yields, a significant relationship is found between estimated option values and discounts of these securities' market prices from their estimated income values. However, the size of the discount is only a fraction of what would be predicted by the American option model. Specifically, the market does not appear to take the "early exercise premium" into account. Furthermore, this discount seems to be isolated to in-the-money call features that have evolved to their final call price. Thus, incorporation of a call feature into a security's indentures, with a deferment period and an initial premium call price, appears to represent a pure gain for the issuing corporation.

Introduction

The value of the call feature in callable debt and preferred stock has usually been modelled as a zero-sum game. The gain to the issuing firm which, by reason of the call feature, retains the right to retire the issue at a specified price, is presumed equal to the discount of the value of the callable security from what its value would be if it were not callable (see, for example, Elton and Gruber 1971). If the call feature is, indeed, a zero-sum game, it is natural to ask why call features are so common in corporate bonds and preferred stocks. As Myers (1971, 539) states, either financial markets are not efficient in pricing callable securities, or the function of the call feature is not solely to reduce interest costs.

According to Pye (1966, 203), the popularity of the call feature results from risk aversion. If "the price differential between non-callables and callables is equal to the

Clifford F. 77ffes is Associate Professor of Finance, University of Bahimore. Baltimore, MD 21201. Steven C. lsberg is Assistant Professor of Finance, University of Bahirnore, Bahimore, MD 21201.

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JOURNAL OF ECONOMICS AND FINANCE

expected value of the option," all corporations will want to issue callable debt in order to reduce risk associated with refinancing. However, because investors would be symmetrically averse to bearing this refinancing risk, they will not want to hold fairly priced callable securities. Accordingly, an equilibrium would be achieved when the call feature becomes sufficiently overpriced in order to induce enough lenders to hold them.

Bodie and Taggart (1978, 1987) argue that firms almost always issue debt that is callable because they value the flexibility offered by callable securities by more than their pure option values. If, for example, certain assets are used to secure a callable debt issue, the lien on these assets can be lifted--allowing the firm to sell or otherwise re-employ the assets--through exercise of the call feature.

These two theories both imply that corporations are willing to pay, through discount in the price of the bond (or higher yield), at least as much as and possibly

more than the option value for the inclusion of a call feature in the indentures of a bond or preferred stock issue. On the other hand, if financial markets are not efficient in pricing callable securities, and in fact underdiscount them, then corporations would tend to include call features in order to capture that part of their value not taken into account by the market. ~ The authors address the question of whether corporations issue callable securities for reasons of preferences, in which case the securities would be discounted by at least as much as the option value of their call features, or because call features are consistently undervalued by the market.

The classic work on the actual value of call features was conducted by Hess and Winn (1962). They examined 1250 high grade corporate bonds issued during the period 1926-1959. A survey of investors--including life insurance companies , banks and trust companies--found that, in their opinion, noncallable and deferred callable issues required lower yields relative to freely callable issues. In addition, during the second half of 1959, but not before then, deferred callable bonds were found to carry lower yields than similarly-rated freely callable bonds.

In contemporary work, Spivey (1989) finds that the call feature costs 15-20 basis points on municipal bonds, more if interest rates are expected to fall. Kish and Livingston (1990) further find that the call feature adds approximately 60 basis points to the offering yield of corporate bonds.

While prior researchers demonstrate that the call feature raises bond yields, by focusing on yield as opposed to price, they do not address the important question: are financial markets efficient in pricing callable securities? That is, are the discounts of the prices of callable securities from their income values equal to the option values of their call features? In this study the foregoing question is addressed by using option pricing models to estimate the value of call options implicit in seasoned callable preferred stock, and comparing these to the discounts of these securities' market prices from their income values.

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The Pricing o f Callable Preferred Stock

Modeling the Option Value of Call Features

A European call option is the right, but not the obligation, to purchase an asset at a specified future date ("expiration"), at a specified price ("exercise price"). An American call option is a similar right, but can be exercised at any time up to and including expiration. It is obvious that the value of an American call option is at least equal to that of an otherwise similar European call option. Any value of an American option in excess of the value of an otherwise similar European option is referred to as the "early exercise premium."

Call features usually found in bonds and preferred stocks are in some ways similar to European call options and in other ways similar to American call options. Like both kinds of call options, these confer to the issuer the right, but not the obligation, to purchase--or retire--securities at an exercise price referred to as the call price. 2

The way in which call features in bonds and preferred stock resemble European call options is "call deferment." Virtually all corporate bond and preferred stock call indentures defer or disallow call for ten years in the case of industrial issues or five years in the case of utility issues (Goldberg 1984). The way in which these call features resemble American call options is that, once the deferment period is over, call can be exercised at any time as long as the issue remains outstanding. Therefore, until the deferment period is over, it is not clear whether the American, European or some hybrid model should be used to value such call features. Once this deferment period is over, it is clear that the American option model should be used. In this study the authors use both the European and American option pricing models to value the call features imbedded in callable preferred stock. Caveats regarding interpretation o f the results are discussed below.

To model the option value of the call feature, first let S, X, t, a, r and b be a preferred stock's market price, its call price, effective term to expiration, 3 the volatility of its market price, the risk-free interest rate, and cost of carry. Assuming perfect markets, in particular that transactions costs are zero, and additionally that the stochastic process governing the prices of preferred stocks is a geometric Brownian motion and that a, r, and b are constant, the value of a European call option (CE) is given by:

C r = S e - " N C d l ) - X e - ~ N ( d : ) (1)

where

d 1 = [ In (S /X ) + (r - b + . r a 2 ) t ] l ( a t "5) Oa)

d 2 = [ In (S IX) + (r - b - . r o 2 ) t ] / ( a t -~) ( lb)

and N(.) is the cumulative normal distribution (Black and Scholes 1973 and Merton 1973). While this, the Black/Scholes option pricing model, is now common in the finance literature, it may be helpful to motivate its use. The two terms N(d~) and N(d2) can be viewed as the cumulative probability of an upmove and/or a downmove, respectively, in a preferred stock's market price. The market value of

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the call option as determined by Equation (1) can be interpreted as its intrinsic value (i.e., S-X), adjusted by the probabilities of stock price movements and the opportunity cost of money.

An American option, on the other hand, can be exercised at any time up to and including its expiration date. Its value can therefore be viewed as that of a similar European option plus an amount referred to as the early exercise premium:

Determining the value of the early exercise premium, demands the use of either extensive simulation analysis or some other approximation methodology. A recently developed approximation by Barone-Adesi and Whaley (1987) is particularly useful in modeling the call feature of a preferred stock. In the Barone-Adesi/Whaley model, the optimal early exercise price, S*, is first solved as an implicit function of the variables X, t, r, b, a. Given S*, the value of an American call option (CA)is given as

where

C a = Cg + a ( S I S * ) * (2)

n = - ( S * / q ) [1 - e(b-') 'N(dl(S*))] (2a)

q = [_(2b/o2_I) _ {(2blo2_I)2 + 8r/(o~(l _e-n)) }-s]12 (2b)

when S < S*, and is equal to S - X when S > S*. Although the term representing the early exercise premium is difficult to interpret, it does indicate that as the option's term-to-expiration decreases, the early exercise premium falls.

If the market values callable preferred stocks efficiently, the market price should equal the difference between its income value and the option value of its call feature. Observation of a deviation between the market price and this theoretical value may indicate the presence of a pricing inefficiency that may yield a benefit to the buyer or issuer of such a stock, depending upon the sign of the deviation.

Data and Methodology

The sample data for this study are composed of all non-convertible, fixed-rate, utility corporation preferred stocks, rated Aa, A and Baa, as reported in the December issues of Moody's Bond Record for each of the odd numbered years between 1981 and 1989. This sampling procedure provides a total of 768 observations (ranging from 129 to 163 per year). Utility preferred stocks are used because they constitute a large assortment of relatively standardized instruments. Moody's also provides information on each issue's credit rating, annual dividend, dividend payment dates, par value, current call price, date until which the current call price is effective (unless the issue has evolved to its final call price), and whether or not the issue's indentures provide for a mandatory sinking fund. For each issue, corresponding end-of-month price data are obtained NYSE Daily Stock Price Record.

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For each observation, the data are operationally defined as follows:

S = market price: the average of the high and low sales price, or of the bid and ask price as reported by the Price Record.

X = exercise price: current call price, or average of current call price and par value if the current call price is not the final call price.

r = the risk-free interest rate: Moody's Aa-utility preferred stock dividend rate.

b = cost-of-carry: presumed to be zero on the basis that a utility corporation's opportunity cost of funds would be the yield on its outstanding securities.

t = term-to-expiration: presumed to be 20 years for preferred stocks without a mandatory sinking fund, and to be 10 years for preferred stocks with one. 5

a = volatility: presumed to be 0.25. 6

The above data are employed to calculate the option values of each bond using the European and American call option valuation methods given by Equations (1) and (2) respectively. Income value is calculated as the annual dividend divided by Moody's utility preferred dividend rate for its credit rating.

TABLE 1

SELECTED MEAN CHARACTERISTICS SEASONED UTILITY PREFERRED STOCKS, 1981-1989

American Income European Option Option

Market Price/Par Valuel/Par ValueZ/Par ValueZ/Par

1981 0.513 0.487 0.013 0.068

1983 0.649 0.632 0.032 0.131

1985 0.774 0.786 0.054 0.204

1987 0.755 0.748 0.0503 0.202

1989 0.791 0.792 0.057 0.230

i Estimated as a preferred stock issue's annual dividend divided by the Moody's preferred stock dividend rate for the issue's credit rating.

Estimated using the Black/Scholes European call option model and the Barone- Adesi/Whaley American call option model in the manner described in the text.

Selected characteristics o f the five samples are presented in Table 1. Note that, in 1981, when interest rates were historically high, market prices as well as income values of seasoned preferred stocks were low. Not surprisingly, the option values in

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the call features of these preferred stocks were especially low. By 1985, with the fall in interest rates, market prices, income and option values had considerably increased. It is also interesting to note just how large the American option values are relative to the European. This reflects the long durations of preferred stocks.

It may be considered strange for the estimated income values of these preferred stocks to approximate their market prices given that these are callable securities and should, therefore, sell at discounts from their income values. However, the fact that Moody's rates represent the average yields of samples of seasoned utility corporation preferred stock issues, which themselves are callable, implies that the dividend rates used to estimate income values are biased. That the present estimates of income value on average approximate market price indicates that the bias in Moody's sample is reflective of the bias in the universe of seasoned utility preferreds. This bias is revisited below.

To test hypotheses relating to price efficiency, several regressions of the following form are estimated:

price = 130 + [~1 income value + 132 option value + e (3)

where, for each preferred stock issue, price is the average of the high and low sales price, or of the bid and ask price as reported by NYSE Daily Stock Price Record, and income and option values are as defined above.

In an efficient market, the/30 would equal zero, /3~ one, and /32 negative one, meaning that the market would increment price for the present value of future dividends, and decrement price for the option value retained by the issuer through the call feature. On the other hand, if the market is not efficient, and underdiscounts securities for the value of their call features, then the coefficient /32 would be negative but less than one in absolute value.

To test hypotheses regarding the pricing of the call feature, the coefficient/~1 is constrained to equal one, and the sign and significance of the coefficient /3~ is analyzed. The model is also estimated by differentiating call features between those that are in-the-money (S _ X) or out-of-the-money (S < X), and those having evolved their final call price as opposed to still featuring a transitional call price. 7

Before proceeding to the next section, a word is in order regarding the imposition of the constraint that /31 equal one. As is discussed above, Moody's rates are upwardly biased. This bias would be minimal when interest rates are high, and the risk of call low. However, where interest rates are low, and the risk of call significant, this bias could affect estimation, s Fortunately, within any particular sample, this bias is roughly constant across securities, a function of the average option value implicit in the securities in Moody's samples. Critically, within each sample, mismeasurement due to this bias is not necessarily correlated with the estimate of option value.

This bias problem can be overcome by imposing the constraint that the coefficient on the income variable be one (which is equivalent to transferring it to the left-hand side of the equation, making the dependent variable into the difference between price and income value), and allowing the intercept to vary from zero. In this case, the systematic portion of the mismeasurement of income value would be captured by the

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intercept term (so that the expected value of/3o no longer equals zero), and the unsystematic portion would be incorporated into the regression error term (so that R2s will be lower than what they would be with perfectly measured data).

Results and Interpre ta t ion

Pooled regressions, based on all 738 observations in the five cross-sectional samples, are reported in Table 2. Regressions [1] and [2] contain the results for the simplest model using the European and the American call option models. (Recall that in these and all other reported results, the coefficient/31 is constrained to equal one.) Of interest, the coefficient/32 is found to be negative and significant. Consistent with research focusing on yields as opposed to price, the call feature is found to have a negative impact on price. However, the magnitude of the coefficient/3~ is found to be quite small. While the market appears to discount preferred stocks, it does not appear to discount them sufficiently for the option value of their call features.

TABLE 2

POOLED ESTIMATES

Market Price/Par = /30 + /31 Income Value/Par + Option Value/Par + e

Regression Ill [21 [31 [41 [5] [6l Option Model Euro Amer Euro Amer Euro Amer

B0 0.018 0.022 0.003 0.005 0.016 0.017 (5.61) (5.42) (0.77) (1.34) (7.28) (7.74)

B~ 1.0 1.0 1.0 1.0 1.0 1.0 in-the-money -0.170 -0.050 transitional call price (0.71) (0.78)

/3z out-of-the-money 0.395 0.068 transitional call price (2.83) (2.14) in-the-money -0.519 - 0 . 2 0 4 -0.'622 -0.236 final call price (9.11) (9.75) (11.38) (12.42) out-of-the-money 0.444 0.090 final call price (5.79) 0.83)

/~2 0.947 0.947 0.956 0.956 0.954 0.954

The sample consists of all seasoned, fixed rate, callable, utility preferred stocks reported in NYSE Daily Price Record for 1981, 1983, 1985, 1987 and 1989, a total of 768 observations. The Income Values, and European CEuro) and American (Amer) Option Values of these preferred stocks are described in Table 1 and the text.

Regressions [3] and [4] provide results in which four types of call features are differentiated (i.e., in-the-money, out-of-the-money, final call price, and transitional call price). The coefficients on the option values of the in-the-money, final call features are very significant and large in value, arguably near one in the case based

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on the European call option model. 9 Even so, this indicates that the market may not be taking into account the "early exercise premium" insofar as, once past the initial call deferment period, these are American call options.

The coefficients on out-of-the-money and transitional call features are either wrong-signed or insignificant. Accordingly, regressions [5] and [6] constrain these coefficients to zero. The subsequent results reinforce the above finding that the market discounts the price of preferred stocks for call features that are in-the-money and have evolved to their final call price.

TABLE 3

ESTIMATES OF/~, SAMPLE PARTITIONED BY YEARS Market Price/Par = /3o + fll Income Value/Par + /32 Option Value/Par + e

Regression [ 11 [21 [3 ] [41 [5] [6 ] Option Model Euro Amer Euro Amer Euro Amer

in-the-money in-the-money Year Obs final call price final call price 1981 139 1.13o 0.292 NA NA NA NA

(4.87) (4.32) ::: 6 3 : i :0!03~ ~::ii : : iiiiiiiii

1985 158 -0.458 -0.221 -0.409 -0.220 -0.609 -0.263 (4.03) (5.09) (3.78) (5.48) (6.67) (8.92)

1989 149 -0.625 -0.104 -0.722 -0.209 -0.738 -0.223 (6.13) (2.60) (7.43) (5.15) (9.41) (7.22)

Selected results for each of the five annual cross-sectional samples are reported in Table 3. Results for 1981 and 1983 are counter-intuitive, perhaps reflective of the high level of interest rates that made the contribution of call features to the value o f seasoned preferreds insignificant. Note that the "NAs" reported in the case of the 1981 sample indicate there were no preferred stock issues with in-the-money, final call features. Results for 1985, 1987 and 1989 confirm the findings, discussed above, based on analysis o f the pooled sample, and demonstrate that the regression model is reasonably robust over the sample period.

Table 4 is analogous to Table 3 except that in it the sample is partitioned by rating instead of by year. The insignificant results obtained for regressions [1] and [2] using Aa- and A-rated preferred stocks might be considered disappointing. Otherwise, the results are similar to those reported in Table 2, and demonstrate that the regression model is reasonably robust over rating classifications.

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TABLE 4

ESTIMATES OF ~ , SAMPLE PARTITIONED BY RATING Market Price/Par = /30 + fl~ Income Value/Par + B2 Option Value/Par +

Regression [ 1 ] [21 [3] [4] [5] [6]

Option Model Euro Amer Euro Amer Euro Amer

in-the-money in-the-money Rating Obs final call price final call prlee

Aa 108 0.100 -0.031 -0.277 -0.133 -0.403 -0.151 (0.90) (0.94) (1.99) (3.05) (2.68) (3.52)

: : : : : : : : : : : : : : : : : : : : : : : : . : : : : : : : : : : : : : ::::::: : : : : : : : : : : : : : : : : : : : : :::: : : : : : ' : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : . : : : :5 : : : : :::: :::::: :::: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ::::: :: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ::: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

Baa 432 -0.380 -0.109 -0.642 -0.220 -0.712 -0.250 (5.02) (3.83) (8.31) (7.50) (9.77) (9.53)

TABLE 5

ESTIMATES OF f12, SAMPLE PARTITIONED BY HIGH-LOW OR BID-ASK SPREAD

Market Price/Par =/30 +/3~ Income Value/Par + 132 Option Value/Par +/3~ Spread/Par +

Regression [ 11 [2] [31 [41 [51 [61

Option Model Euro Amer Euro Amer Euro Amer

in-the-money in-the-money Spread Obs final call price final call price

<2% 641 -0.170 -0.040 -0.443 -0.167 -0.545 -0.203 (2.85) (1.99) (7.20) (7.30) (9.11) (9.55)

>2% 127 -0.578 -0.277 -0.811 -0.337 -0.867 -0.332

(3.79) (4.88) (5.40) (6.39) (6.60) (7.81)

Tab le 5 is also analogous to Table 3 except that in it the data a re par t i t ioned by spread , as an indica tor o f l iquidi ty. Here , d i f ferences between the high and low sales

pr ice , o r the b id -ask quotes re la t ive to pa r value dis t inguish the subsamples . Those

with d i f fe rences less than o r equal to two percent , which would be o n e - h a l f po in t on

a $25 pa r va lue issue, might be regarded as " l iquid"; and those with a g rea te r

d i f fe rence , as " i l l iquid ." W h i l e the pr ices o f i l l i qu id securit ies appear to be s o m e w h a t

more sens i t ive to the i r opt ion values , the s imi lar i ty o f results across this pa r t i t ion ing o f the da ta is fur ther conf i rmat ion o f the model . l~

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Conclusions

Using both the Black/Scholes and the Barone-Adesi/Whaley option models, the authors have estimated the option values implicit in the call features of seasoned callable preferred stock issues. These estimated option values were then compared to the differences between the market prices and income values of these issues. A significant relationship is found between the estimated option values and discounts of market prices from income values. However, the size of the effect of the call feature on market price is significantly less than would be predicted by either the Black/Scholes European option model or the Barone-Adesi/Whaley American option model. Furthermore, this effect is isolated to in-the-money call features having evolved to their final call price and does not at all appear to be factored into the prices of out-of-the-money callable preferreds or the prices of callable preferreds with transitional call prices. Additionally, the market does not appear to take the "early exercise premium" of call features into account.

Pye (1966), Bodie and Taggart (1978), and others have argued that the near universal incorporation of call features into industrial and utility bonds and preferred stocks is based on the willingness of these corporations to pay at least a fair price for the right to retire outstanding securities. This would imply a market discount at least equal to the option value of the call feature. Nevertheless, this study indicates that, at least with respect to utility preferreds, price is not fully discounted by the option value of the call feature.

The finding of less than a complete discount implies that it is market inefficiency, and not corporate preferences, that puts the call feature into preferred stock. Indeed, this study's specific findings support this conclusion. Preferred stocks are underdiscounted, if they are discounted at all, for the option value of out-of-the- money options and options which have not yet evolved to their final call price. Therefore, it would be, for the issuing corporation, a pure gain to include an out-of- the-money (by specifying a premium call price) deferred call feature into the indentures of a preferred stock issue.

NOTES

~That arbitragers do not take advantage of such mispricing indicates that the market in hybrid securities such as callable preferred stock would not be perfect. That is, it is costly to short overpriced callable preferreds and simultaneously hold long a replicating portfolio of noncallable (or substantially out-of-the-money callable) preferreds and either sell puts or buy calls.

ZTypically, the call price equals the security's par value plus a premium of one year's interest or dividend. Also typically, the premium fails over time, eventually to par value.

3Although preferred stocks are nominally perpetuities, many of them feature mandatory sinking funds that effectively give them an expected term to redemption. In addition, other contingencies, such as the acquisition of one firm by another, may mandate redemption of preferred stock issues.

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4In the case of non-dividend paying stocks, and whenever b > r, it is never optimal to exercise an American call option early; therefore, the early exercise premium is zero and the value of an American call option is the same as that of an otherwise similar European call option.

5Constraining the term for sinking fund preferreds to be one half that of non-sinking fund preferreds, this presumption roughly maximizes the goodness-of-fit of the regressions to be discussed below.

~I'he volatility of preferred stock prices, as implied by changes in Moody's utility preferred stock dividend rates over various 30-month periods, ranged from about 0.15 to about 0.35 during the period from 1979 to 1989. Presuming volatility to be 0.15 or 0.35 does not affect the results.

7Preferreds still in their deferment period are included in the later category. This may account for the perverse significant wrong-signed coefficients reported in Table 2.

SThus, an estimate of Equation (3) using the data of 1981 and 1983 delivered intercepts insignificantly different from zero and slopes insignificantly different from one. However, using the data of 1985, 1987 and 1989, intercepts significantly positive and slopes significantly less than one were obtained.

9To be sure, this coefficient is significantly less than one; but given model uncertainty, it would not be unreasonable to say that this is not sufficient evidence to show market inefficiency in the case of in-the-money call options that have evolved to their final call price.

1~ an equation like Equation (3) is estimated with a spread variable added, its coefficient is found to be positive and significant. This might indicate that large spreads are due to unrepresentatively high ask quotes.

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REFERENCES

Barone-Adesi, Giovani, and Robert E. Whaley. "Efficient Analytic Approximation of American Option Values." Journal of Finance 42 (June 1987): 301-320.

Black, Fischer, and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy 81 (May-June 1973): 637-654.

Bodie, Zvi, and Robert A. Taggart. "Future Investment Opportunities and the Value of the Call Provision." Journal of Finance 33 (September 1978): 1187-2000.

Elton, Edwin J., and Martin J. Gruber. "Dynamic Programming Applications in Finance." Journal of Finance 26 (May 1971): 473-506.

Goldberg, Michael A. "The Determinants of Interest Rates." In Dennis E. Logue, ed., Handbook of Modern Finance. New York: Warren, Gorham and Lamont, 1984.

Hess, Jr . , Arleigh P., and Willis Winn. The Value of the Call Privilege. Philadelphia: University of Pennsylvania, 1962.

Kish, Richard J., and Miles Livingston. "The Value of the Call Option on Corporate Bonds." Paper presented at the 1990 Eastern Finance Association meeting.

Merton, Robert C. "A Rational Theory of Option Pricing." Bell Journal of Econorrdcs and Management Science 4 (Spring 1973): 141-183.

Moody's Bond Record. Various issues.

Myers, Stewart C. "Discussion." Journal of Finance 26 (May 1971): 538-539.

NYSE Daily Price Record. Various issues.

Pye, Gordon. "The Value of the Call Option on a Bond." Journal of Political Economy 74 (April 1966): 200-205.

Spivey, Michael F. "The Cost of Including a Call Provision in Municipal Debt Contracts." Journal of Financial Research 12 (Fall 1989): 203-216.

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Documents

The pricing of callable preferred stock