3. Empirical approach
3.2 Arbitrage triggers
A mispricing identified in Equation (1)~(3) does not trigger arbitrage unless the magnitude of the price discrepancy is above the total cost for establishing the arbitrage portfolio. In this thesis, the total cost for establishing the arbitrage portfolio consist of the trading cost and opportunity cost of margin deposit. Because of cash is es a ate of the arbitrage cost, especially for non-member market participants.
3.2.1
primarily used for margin deposits, the financing cost for margin deposit provid high estim
Arbitrage triggers based on transaction prices for the Hold-to-Expiration strategy
Profitable arbitrage requires that the pricing error be larger than the cost for executing the portfolio. In this thesis, the trading cost include the transaction cost (
τ
0) and the opportunity cost for margin deposits (M). Since the price where a trade executes may be initiated at a bid, an offer, or a negobid and ask quotes, a spread cost (
tiated price between the initial
ψ
0) must bF ) and the lower (
) arbitrage bounds of the futures can be written as follows:(4) *
ψ τ
(5) e add to transaction costs. The upper( 0+
F
0−For an actual futures price , the magnitude of the short-futures arbitrage profit trage based on transaction prices are, respec
se every TAIEX futures contract is hedged by 4 pairs of call and put options, the total spread cost for the hold-to-expiration strategy is equal to a one-way
F
0and the magnitude of the long-futures arbi tively: The arbitrage profit is otherwise zero.
Becau
spread for the futures contract and 4 times the one-way spread for both the call and option contracts. The total spread cost for the hold-to-expiration strategy can be written as call, and one put option contract, respectively.
The total trading cost for the strategy involves a one-way trading fee for the futures contract and 4 times the one-way ading fee for both options. The options
ement futures contract, and are the opening trading costs for the call and , and is the closing transaction cost fo
strategy
989) if the magnitude of the isp
tr
may be exercised (depending on prices) so that the closing transaction may incur the cost of the call or the put. The maximum total trading cost of the strategy can be written as
3.2.2 Arbitrage triggers based on transaction prices for the Early-Unwinding
An arbitrage position can be unwound profitably upon a reversal of sign of the initial error (Brennan & Schwartz, 1990; Merrick, 1
m ricing exceeds the marginal cost of early unwinding. The marginal cost for early unwinding comprises the incremental trading cost (
τ
1)、spread cost (ψ
1) and the interest savings (m) due to early unwinding by releasing the margin deposits beforeCheng et al. (1998) have found the early unwinding strategy provide incremental profits over the static hold-to-maturity strategy. Unwinding an arbitrage portfol o before expiration involves ta g opposite positions in all the contracts in the initial port
the natural expiration of the initial arbitrage portfolio.
i kin
folio. This incurs extra spread and trading costs. If the marginal spread and trading costs are
ψ
1 and on day (where ), respectively, then an initial short-futures arbitrage position can be unwound profitably if the fair futuresτ
1t
1t
0 <t
1 <T
price ( F ) less the actual futures price ( ) at is greater than the spread and
l profit from unwinding the initial short-futures position will be equal to (8)
ay spread costs for the options pair. That is,
Similarly an initial long-futures arbitrage position can be closed out profitability before T
m F
F
1 − 1* ≥ψ
1+τ
1 −Where,
F
1 >F
1*. The total profit from unwinding the initial long-futures position will be equal to( )
Th nal spread cost for early unwinding is equal to one extra one-way spread cost for one futures contract and 4 times the one-w
)
he marginal trading cost for early unwinding includes the one-way trading costs
y accounted for in setting up the initial portfolio. Hence, the marginal cost equa
hold-to-expiration strategy based on the bid and ask quotation are identical to those based on the transaction cost. But the trade is vai , the spread cost have not been included in the
to expiration, it is potentially profitable if
t
1T
for the arbitrage portfolio but saves the closing cost for futures and options, which was alread
ls )
τ
1 =(τ
1f −ς
1f)+4(τ
1c +τ
1p −ς
1ϕ .3.2.3 Arbitrage triggers based on bid/ask quotes for the Hold-to-Expiration strategy
The financing and trading costs for a
execute at pre ling bid or ask quotes
transaction cost. If the short-futures arbitrage portfolio based on bid/ask quotes is held
) (
)
(
F
0b −F
0U >τ
0 +M
WhereF
0U,τ
0 andM are defined as above.
futures arbitrage strategy based on bid/ask quotes is:
profit is:
(11) re , since they are firm commitments offered by the market makers. However, due
r
The early-unwinding triggers in Cheng et al. (1998) are extended to the context of bid/ask prices. The condition for early unwinding an initial short-futures arbitrage et when the ask pr utures ( ) falls below the lower price bound for the futures ( ) at an intermediate tim
Where
Hence, the profit from the
short-)]
( )
[(
F
0F
0 0M
e
BAS = b − U −τ
+ (10) Likewise, the long-futures strategy is potentially profitable when)
The arbitrage trades, profitable according to the synchronous bid/ask quotes, a exploitable
to stale prices and execution delay, the detected mispricings could be short-lived and non-executable.
3.2.4 Arbitrage triggers based on bid/ask quotes fo the Early-Unwinding strategy
F
aportfolio is m ice of the f 1
L e
t , where
1t
0 <t
1 <T
, by aF
1magnitude no less than the marginal cost of early unwinding. That is,
m
ofit from unwinding the initial sh utures position will be equal to ) Similarly, an initial long-futures arbitrage position
before T if can be closed out profitability
m
The total profit from unwinding the initial long-futures p
1
osition will be equal to
)]
The following regression model is used to test the effects of execution delay and execution risk on the change in e potential arbitrage profit:
t profit derived from transaction prices fol ing a mispricing signal that is inferred from the bid/ask quotes;
e
T,tis the arbitrage profit defined in Equation (6) or (7), and is based on the transaction prices;e
is the arbitrage signal as defined in Equation (10) or (11), and is based on the quoted prices; L denotes the exect BA
t
between detecting a profitable bid/ask signal and executing at transaction price;
σ
t represents the market volatility, and we use it as a proxy for the execution risk. It is measured by average implied volatility of call and put option; t denotes the moneyness of the options used in the arbitrage (MY
t (|X
tF
0,t |/X
t)MY
−
= ). It is used as
a proxy for the liquidity of the option in the arbitrage portfolio.
D represents
t type of arbitrage strategies, with 0the
t =
D
represent a long-futures strategy; and .we expect the coefficient for the delay ) to be negative. That is, on detecting a profitable bid/ask signal, the p
=1
D
t representing the short-futures strategy In a dynamically arbitrage efficient market,(
L
t executionut-call-futures arbitrage profit is enhanced if the prevailing quotes are executed quickly. We expect the coefficient for the degree of moneyness (
MY ) to be negative,
t since the extra misprcing is needed to compensate for a lower level of liquidity. We expect the same negative relation for the execution risk (σ
t). The coefficient for (D
t) shows whether the futures are over price or under price.3.4 Empirical Specification of the model
In this section, the mispricing which is mentioned in Equation (1) will be used to