Put-Call Parity and the Early Exercise Premium for Currency Options by Geoffrey Poitras,** Chris Veld and Yuri Zabolotnyuk Chris Veld and Yuri Zabolotnyuk (**presenter ) Faculty of Business Administration Simon Fraser University Burnaby, B.C. CANADA

American vs. European Options This paper uses observed American PHLX currency option prices and the European put- call parity condition to estimate the size of the early exercise premium for six currencies This paper uses observed American PHLX currency option prices and the European put- call parity condition to estimate the size of the early exercise premium for six currencies The results provide benchmark information relevant for using the European currency option pricing formula (e.g., Garman-Kohlhagen) to price American options The results provide benchmark information relevant for using the European currency option pricing formula (e.g., Garman-Kohlhagen) to price American options

Previous Studies Zivney (1991, JFQA) provided the basic methodology for using put-call parity to derive the EEP– examined index options Zivney (1991, JFQA) provided the basic methodology for using put-call parity to derive the EEP– examined index options De Roon and Veld (1996, JFM) extended the methodology to options on an index with automatic reinvestment of dividends De Roon and Veld (1996, JFM) extended the methodology to options on an index with automatic reinvestment of dividends Engstrom and Norden (2000) examine the implications of the methodology for equity options Engstrom and Norden (2000) examine the implications of the methodology for equity options

Using European Put-Call Parity The following basic equations are required (where C and P (c and p) are American (European) currency option prices (with the same X and T) The following basic equations are required (where C and P (c and p) are American (European) currency option prices (with the same X and T)

Properties of the EEP The EEP is always non-negative and is defined as the difference between American and European prices The EEP is always non-negative and is defined as the difference between American and European prices Early exercise involves surrender of time value to receive only the intrinsic value at exercise, otherwise the option will be sold and not exercised Early exercise involves surrender of time value to receive only the intrinsic value at exercise, otherwise the option will be sold and not exercised Time value goes to zero as the (deep) in the money American option approaches the S - X Time value goes to zero as the (deep) in the money American option approaches the S - X EEP for at or near the money options is based on the right to exercise the option if it goes deep into the money EEP for at or near the money options is based on the right to exercise the option if it goes deep into the money

Solving for the Dependent Variable The dependent variable is the absolute value of V divided by the relevant call or put option price (depending which option is in-the-money) The dependent variable is the absolute value of V divided by the relevant call or put option price (depending which option is in-the-money)

Properties of the Deviations When S >> X then C – c > 0 and P – p  0 When S >> X then C – c > 0 and P – p  0 When X >> S then P – p > 0 and C – c  0 When X >> S then P – p > 0 and C – c  0 In the call in the money case V  EEP C In the call in the money case V  EEP C In the put in the money case V  EEP P In the put in the money case V  EEP P For options near and at the money, it is not possible to disentangle the EEP because the probability of early exercise is still significant for both the put and call For options near and at the money, it is not possible to disentangle the EEP because the probability of early exercise is still significant for both the put and call

Further Properties of Deviations Distribution free properties for a non-dividend paying security state that call options on a non- dividend paying security will not be exercised early. Distribution free properties for a non-dividend paying security state that call options on a non- dividend paying security will not be exercised early. Extending to currency call options, this result still applies when domestic interest rates are above foreign interest rates. Extending to currency call options, this result still applies when domestic interest rates are above foreign interest rates. Results for calls apply to currency put options as a call on one currency is a put on the other. Results for calls apply to currency put options as a call on one currency is a put on the other.

Examining the Data Set PHLX currency options were actively traded during the early to mid-1990’s. Exchange trading of currency options now shifted to CME/IMM. PHLX currency options were actively traded during the early to mid-1990’s. Exchange trading of currency options now shifted to CME/IMM. PHLX sample covers and uses only the standardized PHLX currency options PHLX sample covers and uses only the standardized PHLX currency options 2389 call/put option pairs with same trade date, symbol, expiration date and strike price call/put option pairs with same trade date, symbol, expiration date and strike price.

Filtering the Data PHLX currency options data set includes only information on the opening and ‘average’ spot price on the transactions data PHLX currency options data set includes only information on the opening and ‘average’ spot price on the transactions data Possibly asynchronous data creates some pricing anomalies where (621) option closing prices violate the arbitrage boundaries (observations eliminated) Possibly asynchronous data creates some pricing anomalies where (621) option closing prices violate the arbitrage boundaries (observations eliminated) Eliminating the (744) near and at the money options is needed because it is not possible to unbundle the EEP’s for this situation Eliminating the (744) near and at the money options is needed because it is not possible to unbundle the EEP’s for this situation

Empirical Results: Table 1 Table 1: Market Valuation of the EEP Table 1: Market Valuation of the EEP Average premium as a % of option price averages 5.71% for puts and 6.88% for puts Average premium as a % of option price averages 5.71% for puts and 6.88% for puts Currencies with on average higher than US interest rates have higher call/lower put prices than currencies with lower than US interest rates Currencies with on average higher than US interest rates have higher call/lower put prices than currencies with lower than US interest rates Not reported: time to maturity varies from a few days to one year, average length is about 3 months Not reported: time to maturity varies from a few days to one year, average length is about 3 months

Empirical Results: Table 2 Table 2: Regression results for REEP Table 2: Regression results for REEP Regression includes interest differential, time to maturity, moneyness and implied volatility Regression includes interest differential, time to maturity, moneyness and implied volatility Results generally confirm the underlying hypotheses Results generally confirm the underlying hypotheses Moneyness coefficient is correct sign but insignificant, this is consistent with non-linearity in the moneyness relationship  once American prices have converged to the exercise boundary, the EEP will be constant as both the European and American boundaries are fixed. Moneyness coefficient is correct sign but insignificant, this is consistent with non-linearity in the moneyness relationship  once American prices have converged to the exercise boundary, the EEP will be constant as both the European and American boundaries are fixed.

Interpreting the results Are the estimated EEP too large? Are the estimated EEP too large? Perfect markets theory indicates actual gains to an early exercise transaction depend on interest rate differences  Table 1 provides information on the size of these differentials (not large) Perfect markets theory indicates actual gains to an early exercise transaction depend on interest rate differences  Table 1 provides information on the size of these differentials (not large) Assuming that market makers are net short, a higher than perfect markets price for an American call may reflect the returns to those making markets in options (bundling a microstructure cost into the EEP Assuming that market makers are net short, a higher than perfect markets price for an American call may reflect the returns to those making markets in options (bundling a microstructure cost into the EEP

Put-Call Parity and Estimation of EEP Two general approaches to estimate EEP Two general approaches to estimate EEP American option pricing model American option pricing model Put-Call Parity condition Put-Call Parity condition Advantage of the Put-Call Parity approach is use of Distribution Free Technique (American price models require distribution assumption) Advantage of the Put-Call Parity approach is use of Distribution Free Technique (American price models require distribution assumption) Disadvantage of Put-Call Parity approach is not a precise estimate (incomplete solution) Disadvantage of Put-Call Parity approach is not a precise estimate (incomplete solution)