Discount Certificate

A discount certificate lets you buy exposure to a stock cheaper than the stock itself. The share trades at €100; the certificate costs €92. That €8 gap is the "discount" — a built-in cushion. The price of the cushion: your gains stop at a cap, say €105. However high the stock flies, €105 is all you get.

This changes who wins in which market. If the stock ends anywhere above €105, you make a solid, known return (€92 → €105 is +14%) — but the direct shareholder does better in a real rally. If the stock goes sideways or slightly down, you win where the shareholder makes nothing: at an unchanged €100, the certificate still returns +8.7%. Only below €92 do you lose — and always less than the shareholder does.

Discount certificates are a German retail invention of the late 1990s and remain a fixture of the Stuttgart and Frankfurt certificate exchanges: a way to express "I think this stock will do roughly nothing" — an opinion plain shares can't monetise.

The construction

Under the wrapper sits the oldest option strategy in the book — the covered call, in its cash-settled form a zero-strike call minus a sold call at the cap \(C\):

Redemption at maturity: \(\min(S_T,\, C)\), converted at the certificate's ratio. The discount you receive up front is precisely the premium of the call you implicitly sold (minus issuer margin, plus a dividend effect — see below).

What sets the discount

• Implied volatility: more vol → richer call premium → deeper discount. Discounters on turbulent stocks look temptingly cheap for a reason.
• Cap distance: a cap at 95% of spot (deep "in the money") gives a large discount and bond-like behaviour; a cap at 120% gives a token discount and near-stock behaviour. The cap choice is the whole trade.
• Dividends: certificate holders receive no dividends — expected payouts are baked into the discount. Part of the advertised cushion is simply your own forgone dividend.

Choosing a cap — the three profiles

• Defensive (cap below spot): maximum return locked in unless the stock falls through the cap; annualised yields resemble a high-coupon bond.
• Neutral (cap at spot): the classic sideways bet.
• Offensive (cap above spot): thin discount, participation in a moderate rally.

Pricing off the skew — the issuer's angle

Fair value is spot minus the cap-strike call, adjusted for dividends \(D\) and funding:

The call is sold at strike \(C\) — typically above spot, on the low side of the equity skew, where implied vol is cheapest. The issuer thus buys back its hedge (it is long the call against you) at depressed vols, while dividend assumptions and a bid–ask around fair value provide further margin. Compare any listed discounter against replicating it yourself with the stock and the exchange-traded call: the spread you find is the wrapper's cost, usually 0.5–1.5% per annum.

Behaviour before maturity

Mark-to-market is not the payoff diagram. A discounter is short vega (you sold a call): rising implied vol cheapens the certificate even with spot unchanged. Theta works for you — the sold call decays — which is why discounters are typically held to maturity, and why their secondary-market prices grind toward the payoff line rather than jumping. Delta sits between 0 and 1, falling as spot rallies through the cap (the certificate becomes a bond) and rising toward 1 in a sell-off (it becomes the stock — at the worst time, the familiar structured-product pattern).

Variants and frictions

• Rolling discount certificates: monthly-resetting caps in an open-ended wrapper — systematic covered-call harvesting, the retail ancestor of today's "covered call ETFs" (JEPI et al.).
• Protect/barrier discounters: add a knock-in barrier below which the cushion vanishes — a discount certificate crossed with a barrier reverse convertible.
• Issuer credit: like all certificates, a senior unsecured note of the issuing bank; the Lehman precedent applies in full.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.