Warrant

A warrant is essentially an option wrapped as a tradable security. Instead of opening an options account, you buy the warrant like a share through your normal broker; it gives the right to buy (call warrant) or sell (put warrant) an underlying at a set strike until expiry.

Two very different species share the name:

• Covered warrants — issued in huge variety by banks on stocks, indices, currencies and commodities; hugely popular with retail investors in Germany, Hong Kong and elsewhere.
• Company warrants — issued by the company itself (often attached to bonds, IPOs or SPACs as a "sweetener"); exercising them creates new shares.

The appeal is gearing: a small stake controls a large exposure, multiplying percentage gains — and losses, down to zero.

What the term sheet hides

• Ratio: warrants often cover a fraction of a share (ratio 0.1 = ten warrants per share) — headline prices look deceptively cheap.
• Pricing power: the issuer is the market maker; spreads and implied volatility are set by them. Comparing IV across issuers is the informed buyer's defence.
• Credit: a covered warrant is an unsecured claim on the issuing bank (Lehman's warrant holders learned this).

Company warrants dilute

When corporate warrants are exercised the company issues new shares and receives the strike as fresh capital. Existing holders are diluted — so valuing the company's equity must account for the warrant overhang (SPAC investors in 2021 discovered how much this matters).

Gearing measures

Simple gearing = spot / (warrant price ÷ ratio). Effective gearing (elasticity) = gearing × delta — the true % move in the warrant per 1% in the underlying.

Covered warrants: Black–Scholes plus adjustments

Bank-issued warrants are priced as vanilla (sometimes barrier) options with the issuer's marks: \(W = \text{ratio} \times BS(S, K, \sigma_{issuer}, T, r, q)\). The retail-facing margin sits in \(\sigma_{issuer}\) and the spread; empirically, retail-heavy strikes/maturities carry higher IV than the listed-options equivalent.

Company warrants: dilution-adjusted pricing

With \(n\) shares outstanding and \(m\) warrants of strike \(K\), exercising delivers a fraction of the post-money firm. The classic adjustment prices the warrant on the diluted firm value:

where \(V\) is firm equity value including warrant proceeds. In practice, \(V\) itself depends on \(W\), so the equation solves iteratively. For long maturities (5+ years, typical for corporate warrants), inputs shift from trading desks' surfaces to fundamental volatility estimates.

Barrier variants

The retail market's favourite: knock-out warrants ("turbos") die permanently if spot touches a barrier. Their value is nearly intrinsic, \(W \approx (S - K)\times\text{ratio}\), with tiny time value — priced via barrier-option formulas (reflection principle) plus a gap-risk premium for overnight jumps through the barrier.

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.