Equity and FX options

Valuing a European equity or currency option requires spot, carrying costs, a volatility market and a discount curve. These inputs determine the forward, the distribution of the payoff and its present value. QuantSupport provides closed-form pricers for both asset classes and a separate Monte Carlo route for equity options.

FX options

For an option on base currency priced in quote currency, let spot \(S\) mean quote units per base unit. The Garman–Kohlhagen representation used by FxEuropeanOptionPricer is

\[ F=S\frac{P_{\rm base}(0,T)}{P_{\rm quote}(0,T)},\qquad C=P_{\rm quote}(0,T) \left[F\Phi(d_1)-K\Phi(d_2)\right]. \]

The trade contributes notional and side. The call value is expressed in the quote currency. Both policy-resolved discount curves, pair spot and a compatible FX surface are required; an explicit policy is mandatory.

For USD/CLP under USD collateral this can mean SOFR for USD and Collateral(CLP, USD) for CLP. A reciprocal surface is oriented through inverse strike mapping. Curves, active volatility pillars and recorded spot inputs participate in risk. The standalone FX-forward implementation uses a different discount ratio; the book does not assume parity between those implementations.

Equity carry and European valuation

For an equity with spot \(S\), a dividend discount curve \(P_q\) and rate curve \(P_r\), the standard forward is \(F=SP_q/P_r\). A zero-dividend assumption uses \(P_q=1\). The Black expression is

\[ C=P_r(0,T)\left[F\Phi(d_1)-K\Phi(d_2)\right],\qquad d_1=\frac{\log(F/K)+\tfrac12\sigma^2T}{\sigma\sqrt T}, \quad d_2=d_1-\sigma\sqrt T. \]

The instrument supplies expiry, strike, index, currency and call/put type. The closed-form pricer reads the associated surface; its current query uses the resolved strike directly, so arbitrary smile-type metadata does not provide an automatic delta-to-strike conversion.

EquityForwardPricer separately distinguishes forwarding and policy-selected payment discounting. Its spot is the equity fixing on the context evaluation date, not necessarily the trade date. An absent dividend curve means zero dividends; a missing required spot is an error. For the implemented forward,

\[ F=S\frac{P_{\rm dividend}(0,T)}{P_{\rm forward}(0,T)},\qquad V=N\,s\,(F-K)P_{\rm payment}(0,T). \]

This distinguishes carrying costs from the curve used to discount the payment.

Materialized Monte Carlo valuation

BlackMCEuropeanOptionPricer reads a configured path set from the market, selects the stored date closest to expiry and averages intrinsic payoffs:

\[ \widehat V=N P_d(0,T)\frac1n\sum_p \max(S^p_{\text{nearest grid date}}-K,0) \]

for the call form. Relative/ATM strike resolution uses the sample terminal mean as a forward proxy. Grid choice therefore matters independently of sampling error.

The stored paths are generated numerically in f64, with their generation inputs held fixed during pricing. The current sensitivity handler therefore reports discount-curve pillars and omits path-generation delta and vega. Model-backed scripting and exposure use a separate workflow that retains differentiated path construction for supported factors.