Warrant Scanner

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TAIFEX opt–

US Option Match — How It Works

Same strategy as Direct Match, US option leg

Identical monotonicity arb as Direct Match (same-type warrant vs option), except the option leg is a US ADR option instead of a Taiwan option. The ADR and its Taiwan ordinary share are the same underlying.

Universe (screened for tight ADR parity — persistent/large premium listings like TSM are excluded): 2303 聯電/UMC (1 ADR = 5 shares), 2412 中華電/CHT (1 ADR = 10 shares).

Normalization

The US option is quoted in USD per ADR. It is converted to TWD per Taiwan share so it lives in the same price space as the warrant:

              twd_per_tw_share = usd_per_ADR / adr_ratio × FX  (FX = TWD per USD)
            

1 ADR = adr_ratio Taiwan shares, so one US contract (100 ADR) controls 100 × adr_ratio Taiwan shares (500 for UMC, 1000 for CHT). Warrant units needed = contract_shares / exercise_ratio. Implied vol is scale-free, computed once on the ADR and carried over.

FX assumption

FX is assumed constant over the holding period. A single spot snapshot (TWD=X) is used for every conversion, so all NT$ cash flows and P&L ignore FX drift.

Direct Match — How It Works

What is this finding?

Direct Match pairs a warrant and an option of the same type (both Call or both Put) on the same underlying stock, where the two instruments are priced inconsistently relative to each other.

For calls, a higher-strike call must be cheaper than a lower-strike call — otherwise you could buy the cheaper one and sell the more expensive one for an immediate profit that cannot be erased by any price move at expiry. Direct Match finds pairs where this rule is violated in the market.

Why match to a higher strike (for positive price_diff)?

For a call option, monotonicity says: C(K₁) ≥ C(K₂) whenever K₁ < K₂. The higher the strike, the less valuable the call.

So we compare the warrant (strike K_w) against an option at a higher strike K_o ≥ K_w. If the option is still more expensive despite having the higher strike, that is a direct violation of monotonicity — and the source of the positive price_diff.

Matching to a lower-strike option instead would not be a violation at all — a lower-strike call is expected to cost more.

The math — why is this arbitrage?

Trade: buy warrant at ask (K_w), sell option at bid (K_o ≥ K_w). Net cash at entry:

              Entry credit = opt_bid/share − warrant_ask/share = price_diff > 0
            

At expiry, payoff from the two legs for every possible spot S:

              S < Kw:  both expire worthless → net = price_diff > 0 ✓

              Kw ≤ S < Ko: warrant pays (S−Kw), option expires worthless → net = price_diff + (S−Kw) > 0 ✓

              S ≥ Ko:  warrant pays (S−Kw), option costs (S−Ko) → net = price_diff + (Ko−Kw) > 0 ✓

P&L is non-negative in every scenario. The entry credit is locked in regardless of where the stock ends up — that is what makes it arbitrage.

How does the P&L at expiry (dotted line) work?

The dotted line shows the trade P&L assuming you hold to expiry and both legs settle at intrinsic value (time value = 0):

              P&L at expiry = price_diff + max(0, S−Kw) − max(0, S−Ko)
            

As shown in the math above, this is always ≥ 0 for a valid positive-direction pair (K_o ≥ K_w, price_diff > 0). The dotted line will never go below zero for a correctly-filtered pair.

How does the green line (DTE slider) work?

The green line shows the mark-to-market P&L if you were to close both positions today at their current Black-Scholes theoretical values, using each instrument's implied volatility:

              P&L(S, t) = price_diff + BS(S, Kw, τw, IVw) − BS(S, Ko, τo, IVo)
            

Moving the slider changes τ_o (time remaining on the option). The warrant's remaining time τ_w = τ_o + (warrant_DTE − option_DTE)/365 adjusts accordingly.

The green line can dip below zero mid-life if the option's IV is much higher than the warrant's IV — the option's time value temporarily exceeds the warrant's, creating a mark-to-market loss before expiry. This does not affect the locked-in expiry payoff.

Why is the DTE Diff filter one-sided?

The two expiry dates create a DTE gap. Depending on which leg expires first, the gap works either for or against you:

Favorable side — long leg expires after the short leg: when your short obligation ends, you still hold a position with remaining time value. This is a pure gain. No cap needed.
Unfavorable side — short leg expires after the long leg: after your long leg closes, you are left short a position that still has time value — a liability. Max DTE Diff caps how many days of this unfavorable exposure you are willing to accept.

Setting Max DTE Diff = 0 means you only see pairs where expiry risk is fully in your favor (long leg always outlives the short leg). Higher values allow more DTE mismatch on the risky side.

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Trade Legs (per 1 options contract = 2,000 shares)

Action	Instrument	Qty	Price/unit	Cash flow (NT$)

PCP-Adjusted Comparison (same payoff basis)

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Quantity is board lots (張) for warrants, contracts for options, shares for the underlying. Entry price is per warrant unit / per option point / per share. Warrants are long-only.

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