PutCall Parity and the Early Exercise Premium for Currency Options by

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Put-Call Parity and the Early Exercise Premium
for Currency Optionsby

• Geoffrey Poitras,
• Chris Veld and Yuri Zabolotnyuk
• (presenter)
• Faculty of Business Administration
• Simon Fraser University
• Burnaby, B.C.
• CANADA

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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
• The results provide benchmark information
  relevant for using the European currency option
  pricing formula (e.g., Garman-Kohlhagen) to price
  American options

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Previous Studies

• 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
• Engstrom and Norden (2000) examine the
  implications of the methodology for equity options

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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)

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Properties of the EEP

• 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
• 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

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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)

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Properties of the Deviations

• When S gtgt X then C c gt 0 and P p ? 0
• When X gtgt S then P p gt 0 and C c ? 0
• In the call in the money case V ? EEPC
• In the put in the money case V ? EEPP
• 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

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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.
• 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.

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Examining the Data Set

• PHLX currency options were actively traded during
  the early to mid-1990s. Exchange trading of
  currency options now shifted to CME/IMM.
• PHLX sample covers 1992-7 and uses only the
  standardized PHLX currency options
• 2389 call/put option pairs with same trade date,
  symbol, expiration date and strike price.

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Filtering the 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)
• Eliminating the (744) near and at the money
  options is needed because it is not possible to
  unbundle the EEPs for this situation

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Empirical Results Table 1

• Table 1 Market Valuation of the EEP
• 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
• Not reported time to maturity varies from a few
  days to one year, average length is about 3
  months

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Empirical Results Table 2

• Table 2 Regression results for REEP
• Regression includes interest differential, time
  to maturity, moneyness and implied volatility
• 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.

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Interpreting the results

• 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)
• 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

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Put-Call Parity and Estimation of EEP

• Two general approaches to estimate EEP
• American option pricing model
• Put-Call Parity condition
• 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)