Technical publishing · English → Italian

Apparently fluent is not the same as controlled.

This example uses a real 333-word extract from the current print edition of FX Options Volatility Trading, processed through Poliqa.

Real extract. Source: a real extract from Rondanini Publishing’s current print edition of FX Options Volatility Trading. The machine drafts. You edit and sign.

Source

English · 333 source words · one block · delta, gamma, EUR/USD

Step 3 — Rebalancing trade. Buy additional EUR 70,900 (= 599,500 - 528,600) in spot. The desk buys EUR against USD at 1.1100 to increase the spot hedge. Objective To compute the initial delta hedge, establish the hedge position in EUR notional, recompute delta after the 100-pip spot move, and determine the exact rebalancing trade required to restore delta neutrality. Calculation see Steps 1–3 above — initial delta and hedge, recomputed delta at S = 1.1100, and the rebalancing trade. Result Initial delta: 0.5286 →initial hedge EUR 528,600 long. After +100 pips: delta rises to 0.5995. Rebalancing: buy EUR 70,900. Delta is a hedge ratio valid only at the current spot — it must be rebalanced whenever spot moves, which is the practical cost of gamma that the desk pays to remain delta-neutral. Interpretation This example demonstrates why static delta hedging is insufficient. The 100-pip rise in EUR/USD increases the call’s delta from 0.5286 to 0.5995 — the option has moved further into the money and now has a higher unadjusted spot delta 𝐷𝑓Φ(𝑑1). The domestic risk-neutral ITM probability is Φ(𝑑2); the two move in the same direction but are not identical. The EUR 70,900 rebalancing trade is the direct numerical consequence of positive gamma: the option’s delta accelerates as spot moves favourably. For the dealer who is short the call and long the delta hedge, the rebalancing is a cost — buying EUR at the higher price of 1.1100 to maintain neutrality. The premium compensates the seller for assuming contingent risks under the agreed pricing conventions. Realised delta-hedging P&L is path-dependent and may be greater or smaller than the amount embedded in the price: the buyer pays the premium upfront, and the seller incurs cumulative rebalancing costs throughout the option’s life as spot oscillates. The profitability of the short option position depends on whether the cumulative rebalancing costs (driven by realised volatility) are less than the premium received (sized to implied volatility).