4 discusses the methodology. The fifth section presents the empirical results, and section 6 contains some concluding remarks.
2. Put-call parity and the early exercise premium in American options
A long position in a European put can be replicated using a portfolio consisting of a long position in a corresponding call, a short position in the stock and lending
of the present value of the exercise price to the riskless interest rate. This portfolio will have the same payoff as a put on the expiration day, whatever the stock price
might be. In the absence of dividends, taxes and transactions costs, the put price at time t is obtained from the PCP relationship:
p = c − S + Xe
− rT − t
1 where p is the European put price, c is the European call price, X is the common
exercise price, S is the price of the underlying stock, T − t is the time left to expiration, and r is the riskless rate of interest
3
. Since the traded and the replicated put option have the same payoff, their values at time t must be the same in the
absence of arbitrage possibilities. Merton 1973b shows that PCP will not hold if there is a possibility that any of the options will be exercised early. The relationship
between American put P and call C option prices is instead given by the following upper and lower bounds:
S − X B C − P B S − Xe
− rT − t
2 Several studies conduct tests of PCP. Examples are Stoll 1969, Evnine and
Rudd 1985, and Brenner and Galai 1986. In these studies, PCP is tested using American options. Deviations are not uncommon, but the occurrence depends on
the underlying security. An example is Brenner and Galai 1986 who analyse equity options traded on CBOE. They find significant deviations from PCP in cases
where early exercise is likely. Kamara and Miller 1995, who analyse the European SP 500 index options traded on the CBOE, find deviations much less frequent and
smaller than those found in studies using American options. These deviations can not be explained by the early exercise possibility, and should therefore, be inter-
preted as inefficiencies. However, Kamara and Miller find that the violations of PCP mostly reflect the liquidity risk, i.e. the risk of price adjustments from the
placement of the order until execution. In their view, a liquidity risk premium could explain the mispricing of deep-out-of-the money options found in other studies.
Zivney 1991 examines deviations from PCP, using daily data on the American SP 100 index options, to find the value of the early exercise premium. The results
of Zivney show that the value of early exercise is substantial, and that it seems to be larger for puts than for otherwise identical calls. This is in accordance with the
fact that early exercise of a call written on the index is less likely than for a put
3
Testing the PCP relationship itself is not the issue here, and transaction costs and taxes are therefore omitted in the analysis since they will affect the European and American options equally.
option, since the index yields an almost continuous dividend stream. Furthermore, the premium is positively correlated with the riskless interest rate, the time left to
expiration and the moneyness of the option. de Roon and Veld 1996 use deviations from PCP for options written on the
DAX index traded at the Amsterdam Stock Exchange, to infer the value of early exercise. The DAX is a performance index meaning that the dividends are rein-
vested in the index. It is thus similar to a non-dividend paying stock, implying that the calls written on the index never should be exercised early. The problem that the
deviation from PCP actually is an approximation of the difference between the premiums for puts and calls, respectively could thereby be disregarded. Using a
relatively small sample of 175 daily observations, de Roon and Veld find an average early exercise premium equal to 51.3 of the put price. The premium is positively
correlated with the moneyness of the option, the volatility of the index and the riskless interest rate.
The ideal way to establish the early exercise premium would be to calculate the difference between otherwise identical American and European options. Unfortu-
nately, there exist very few markets with both types of options on the same underlying asset. Jorion and Stoughton 1989 exploit the fact that the European
currency options, traded on the CBOE, are virtually identical to the American currency options traded on Philadelphia Stock Exchange PHLX
4
. Using daily data, the authors find an average value of the early exercise premium of around 2
of the option price, but argues that the results could be affected by problems with non-synchronised prices between the two markets. A regression of the premium on
the pricing parameters results in coefficients of the expected sign for call options, while for put options all the coefficients except for the volatility are of the expected
sign, although not significant.
It is also possible to trade both European and American options on the FTSE-100 stock index on the options market in the UK. McMurray and Yadav
1996 as well as Unni and Yadav 1998 utilise this feature to estimate the early exercise premium directly
5
. McMurray and Yadav find evidence, using hourly data, of significant early exercise premiums for both call and put options. The premiums
are higher than both the deviations from PCP according to Zivney 1991 and the premiums predicted by the theoretical binomial model when the overall sample is
analysed. Though, when only in-the-money puts are analysed, the average premium is higher for the binomial model. The early exercise premium is positively related to
moneyness and time left to expiration. However, some cases of negative premiums are found, especially for out-of-the-money options, suggesting that European
4
The CBOE European options were only traded for a few years, and they never attracted much volume.
5
Unfortunately, for pairs of European and American options on the FTSE 100 index, with the same time left to expiration, there is never a common exercise price. In other words, the analysis of McMurray
and Yadav 1996 as well as Unni and Yadav 1998 is not made entirely in a ceteris paribus sense with respect to the early exercise premium.
options sometimes could be overvalued relative American options. Unni and Yadav 1998 extend the analysis by using transactions data for a longer time period.
Regression results show that the early exercise premium and the pricing parameters correspond as predicted by theory. Finally, using transactions data, Dawson 1994
compares the prices of American and European FTSE-100 index options by constructing butterfly spreads. The results suggest that both American and Eu-
ropean options are frequently overpriced, depending on how the spreads are constructed. The conclusion is that this could be explained by an imperfect linkage
between the prices of the two option types, rather than by a systematic overvalua- tion of the early exercise premium.
3. Institutional setting and data
