The early exercise premium in American put option prices

This study estimates the value of the early exercise premium in American put option prices using Swedish equity options data. The value of the premium is found as the deviation of the American put price from European put-call parity, and in addition a theoretical estimate of the premium is computed. The empirically found premium is also used in a modified version of the control variate approach to value American puts. The results indicate a substantial value of the early exercise premium, where the premium derived from put-call parity is higher than the theoretical premium. The premium also increases with moneyness and time left to expiration, while the effect of interest rate and volatility depends on the moneyness of the option. The modified control variate technique works reasonably well relative to the theoretical models. In particular, for deep in-the-money options, this technique is superior.     

Is there price discovery in equity options?

We use tick-by-tick quote data for 39 liquid US stocks and options on them, and we focus on events when the two markets disagree about the stock price in the sense that the option-implied stock price obtained from the put-call parity relation is inconsistent with the actual stock price. Option market quotes adjust to eliminate the disagreement, while the stock market quotes behave normally, as if there were no disagreement. The disagreement events are typically precipitated by stock price movements and display signed option volume in the direction that tends to eliminate the disagreements. These results show that option price quotes do not contain economically significant information about future stock prices beyond what is already reflected in current stock prices, i.e., no economically significant price discovery occurs in the option market. We also find no option market price discovery using a much larger sample of disagreement events based on a weaker definition of a disagreement, which verifies that the findings for the primary sample are not due to unusual or unrepresentative market behavior during the put-call parity violations.     

FOREIGN-CURRENCY OPTIONS, EX ANTE EXCHANGE-RATE VOLATILITY, AND MARKET EFFICIENCY: AN EMPIRICAL TEST

“The currency option's attraction results from the volatility of foreign-exchange markets, where rates can move as much as 3 percent in a day” (M. Sesit, Wall Street Journal, April 20, 1984, p. 25). This study compares the foreign-exchange rate implicit volatility of call options and put options that are written on a foreign currency. These implicit volatilities should be equal, and equal to the volatility of the proportional change in the exchange rate, given that option prices are efficient and that the foreign-currency option pricing model described by Biger and Hull holds. The foreign-currency options that are examined in this study are the British pound, Canadian dollar, Japanese yen, Swiss franc, and West German mark. The results of this study support the notions of market efficiency and put-call parity.     

Efficiency Tests of the Foreign Currency Options Market

Based on a new options transactions data base from the Philadelphia Stock Exchange Foreign Currency Options Market, this paper examines the importance of the effect of nonsynchronous prices and transaction costs on the usual option market efficiency tests. The tests conducted are based on the transaction cost adjusted early exercise and put-call parity pricing boundaries applicable to the American foreign currency options market. The test results show that the put-call parity boundary tests are sensitive to both nonsynchronous prices and transaction costs. The early exercise boundary tests are sensitive to transaction costs but are not very sensitive to simultaneity of the option price and the underlying spot price. Under the no-transaction costs scenario, a large number of early exercise boundary violations is found even when simultaneous spot and option prices are used. These violations disappear when actual transaction costs are taken into account.     

Do option markets undo restrictions on short sales? Evidence from the 2008 short-sale ban

The effectiveness of any sanction depends on the costs of avoiding its restrictions. We examine whether bearish option strategies were substitutes for short sales during the September 2008 short-sale ban. We find a significant diminution in option volumes and a significant increase in option bid-ask spreads for banned stock relative to unbanned stock during the ban period. Apparent violations of the put-call parity bound became significantly more frequent for banned stocks during the ban period. We conclude that the ban acted as an effective restriction on trading in options.     

The early exercise premia of America put options on stocks

Using the put-call parity, this paper finds that early exercise premia of short-lived American put options on stocks account for a significant portion of put prices. This finding holds even for out-of-the-money put options. The magnitude of the early exercise premia of American put options with no dividend is positvely related to the degree of moneyness, time to maturity of the put option, and the volatility. The magnitude of the early exercise premia of American put options with dividend is positvely related to the degree of moneyness and the risk-free interest rates.     

Option volume,strike distribution,and foreign exchange rate movements

Using Deutschmark currency option data from the Philadelphia Stock Exchange and British pound option data from the Chicago Mercantile Exchange, this article examines the signaling quality of option volume measures on movements in the underlying spot exchange rates. The concept of a volume-weighted strike distribution is proposed. It is demonstrated that measures using the strike distribution are inherently better predictors of both direction and volatility of the exchange rate movements as compared to their more traditional counterparts used in practice, such as the put-call ratio.      

Put-call parity revisited: intradaily tests in the foreign currency options market

We test exchange-traded (PHLX) German mark options for conformance to put-call parity (PCP). Puts and calls are matched to the nearest minute, and the relative impact of competing spot exchange rate sources (Reuters vs. Telerate) is assessed. We find that PCP usually holds (roughly 96% of put-call pairs), with the exception of a notable incident in the European options pits. In those instances in which PCP is violated, we find sharp intradaily and intraweekly seasonalities for American options, with disproportionate PCP violations occurring during the relatively light trading periods in early evening and on Fridays. We also conclude that the Telerate prices as recorded by the PHLX are not as accurate as the Reuters exchange rates provided by Olsen and Associates, probably because of time lags in the Telerate data.     

International tax arbitrage,currency options and put-call parity conditions

Using a finite-horizon general equilibrium model with uncertainty and money, we characterize situations where tax arbitrage opportunities may arise for international portfolio investors in an economy with heterogeneous capital income taxation where foreign currency exposure can be hedged using forward contracts and a set of currency options. We obtain tax-modified option prices similar to the no-tax ones, but augmented by tax-induced “risk-premium” terms; tax-modified put-call parity conditions are derived that revert to their standard (no-tax) format if the respective marginal agents in the bond and option markets are in identical tax brackets.     

Arbitrage tests of the efficiency of the foreign currency options market

In this paper the lower boundary, excercise price, and put-call parity conditions for foreign currency options are subjected to empirical testing. The tests are directed towards the examination of the hypothesis that the foreign currency option market is efficient. The evidence in the ex-post tests is inconsistent with this hypothesis since a large number of violations of theoretical conditions are found in the data.     

Estimating discrete dividends by no-arbitrage

We develop and showcase a simple no-arbitrage methodology for the valuation of discrete dividend payments, based exclusively on market prices of options via the put-call parity. Our approach integrates all available option market data and simultaneously calibrates the market-implied discount curve, thus ensuring consistency across spot and derivative markets. We illustrate our method using stocks of European blue-chip companies.     

The Factors Behind Put-Call Parity Violations of S&P 100 Index Options

This paper examines the determinants of intraday violations of put-call parity of S&P 100 Index options. In particular, tobit regression analysis is used to explain the fraction of daily observations that are apparently mispriced. Compared to a previous study, a much smaller fraction (21 percent) is found of option pairs that violate parity. Dividends are found to be significant, but inversely related to the frequency of violations. The other significant explanatory variable is the options' time to expiration. When the upper bound is violated, the coefficient is positive; i.e., calls are overpriced relative to puts more often for longer term options. The coefficient for the time to expiration is significantly negative for lower bound violations.     

On the multiplicity of option prices under CEV with positive elasticity of variance

The discounted stock price under the Constant Elasticity of Variance model is not a martingale when the elasticity of variance is positive. Two expressions for the European call price then arise, namely the price for which put-call parity holds and the price that represents the lowest cost of replicating the call option’s payoffs. The greeks of European put and call prices are derived and it is shown that the greeks of the risk-neutral call can substantially differ from standard results. For instance, the relation between the call price and variance may become non-monotonic. Such unfamiliar behavior then might yield option-based tests for the potential presence of a bubble in the underlying stock price.     

The Information in Option Volume for Future Stock Prices

We present strong evidence that option trading volume containsinformation about future stock prices. Taking advantage of aunique data set, we construct put-call ratios from option volumeinitiated by buyers to open new positions. Stocks with low put-callratios outperform stocks with high put-call ratios by more than40 basis points on the next day and more than 1% over the nextweek. Partitioning our option signals into components that arepublicly and nonpublicly observable, we find that the economicsource of this predictability is nonpublic information possessedby option traders rather than market inefficiency. We also findgreater predictability for stocks with higher concentrationsof informed traders and from option contracts with greater leverage.     

Banks' option to lend,interest rate sensitivity,and credit availability

Interest rate risk is a major concern for banks because of the nominal nature of their assets and the asset-liability maturity mismatch. This paper proposes a new way to derive a bank's interest rate sensitivity, by examining separately the effects of interest rate changes on existing loans(loans-in-place) and potential loans (loans-in-process). A potential loan is shown to be equivalent to an American option to lend, and is valued using option theory. An increase in interest rates generally has a negative effect on existing loans. However, if both deposit and lending rates rise by the same amount, the value of a potential loan generally increases. Hence a bank's lending slack (or ratio of loans-in-process to loans-in-place) will determine its overall interest rate risk. Empirical evidence indicates that low-slack banks indeed have significantly more interest rate risk than high-slack banks. The model also makes predictions regarding the effect of deposit and lending rate parameters on bank credit availability. Empirical tests with quarterly data are generally supportive of these predictions. This revised version was published online in June 2006 with corrections to the Cover Date.     

What determines interest rates for bitcoin lending?

This study analyses the determinants of interest rates in the cryptocurrency lending market using a unique database from the Decentralised Finance platform. We confirm the existence of both mediation and moderation effects in the cryptocurrency lending market by employing a moderated mediation model. First, the empirical results show that the interest rate is closely related to the loan-to-value ratio, which works as the mediation variable in lending. Second, the interest rate reveals a clear connection with price fluctuations of Bitcoin. This brings up the momentum phenomenon in the lending process and incentives borrowers to acquire more money, leading to pro-cyclical speculation. Third, the lending amount reflects a moderation effect in the lending market, and the net effect of the currency price on the interest rate turns negative when the loan amount exceeds a threshold, resulting in the ‘seesaw’ effect in cryptocurrency lending. The above findings confirm that cryptocurrency lending reflects a certain degree of option characteristics and complies with the risk-debt model, which provides more evidence for understanding the momentum phenomenon and investor behaviour in the cryptocurrency lending market.     

On the hedging of options on exploding exchange rates

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale, modelling for example an exchange rate. The new pricing operator assigns prices to contingent claims according to the minimal cost for superreplication strategies that succeed with probability one for both currencies as numéraire. Within this context, we interpret the lack of the martingale property of an exchange rate as a reflection of the possibility that the numéraire currency may devalue completely against the asset currency (hyperinflation).     

An ex ante analysis of put-call parity

The authors previously had extended the theoretical put-call parity models developed by Stoll (1969) and Merton (1973) to include a dividend term. Ex post tests of the models were generally consistent with market efficiency, but a sufficient number of hedges had high enough returns to warrant analysis of ex ante results. The purpose of this study was to construct hedges 5 and 15 minutes after they were initially identified as having an ex post return in excess of $20 per hedge. The results indicate that mispriced options adjust and that economic profit is sensitive to the level of transaction costs and unlikely even for member firms.     

Distilling private information from plain-vanilla options to predict future underlying stock price volatility: Evidence from the H-shares of Chinese banks

Deviations from put-call parity may arise in response to private information that a select group of investors possess. From a practical perspective, if one possesses private information, using options to speculate or hedge amplifies potential gains given the leverage embedded in options with respect to price changes in the underlying asset. In light of this, and if we assume that the average investor does not possess private information, it is perhaps possible though to infer such information through implied variance spreads and use it to predict future volatility in the underlying asset. In this piece I examine the extent to which such information is economically informative in predicting the intraday return variability of H-shares issued by China's state and joint-stock banks, respectively. Generally speaking, I uncover the following; firstly, call-put implied variance spreads are mean-reverting across time. Secondly, at any given point in time, the magnitude of the deviation from put-call parity is informative in predicting rises in future spot price volatility. Thirdly, straddle/strangle trades predict, at times one week in advance, rises in future spot price volatility. These findings hold after controlling for market-wide implied volatility, the flow and shock in information disseminating to the market, and implicit transactions costs.     

Monetary Policy and Global Banking

When central banks adjust interest rates, the opportunity cost of lending in local currency changes, but—absent frictions—there is no spillover effect to lending in other currencies. However, when equity capital is limited, global banks must benchmark domestic and foreign lending opportunities. We show that, in equilibrium, the marginal return on foreign lending is affected by the interest rate differential, with lower domestic rates leading to an increase in local lending, at the expense of a reduction in foreign lending. We test our prediction in the context of changes in interest rates in six major currency areas.