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049

Case 049Options and volatility tradingCore

An importer expects USD/INR to rise from 83.0 to about 84.5 in three months but not beyond 86. Compare a forward, a call struck at 84 and an 84/86 call spread on cost and payoff, and choose a structure.

Goldman SachsLondon · 2025

1The situation

Rupavati Imports, an invented importer of industrial machinery, must pay a supplier USD 5 million in three months. Spot USD/INR is 83.0. Its treasurer expects the rupee to weaken to about 84.5 by the payment date and is confident it will not go beyond 86. Three-month rupee rates are 6.5% and dollar rates 4.5%, and three-month implied volatility is 5%.

The bank offers three structures: a three-month forward; a dollar call, rupee put, struck at 84; and an 84/86 call spread, buying the 84 call and selling the 86 call. All levels in this case are illustrative; confirm live forward points and option prices with the bank before acting on any structure.

2Your task

Price each structure, compare what Rupavati pays per dollar across a range of outcomes, and choose one, saying what the choice depends on.

Quick check

If spot ends at 84.5, exactly as the treasurer expects, which structure gives the lowest rupee cost?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

On this view the forward is the right hedge: it locks about 83.42, below where the treasurer expects spot to be, with no premium and no hole. The 84 call costs 0.57 a dollar and the call spread 0.45; both pay for protection against a fall the view rules out. The spread is the cheaper option, but it stops protecting above 86, the outcome that would hurt an importer most. Options earn their premium only if a rupee rally is a real possibility.

Step 1What does each structure cost, and what does it lock in?

Start with the forward, because it is the benchmark everything else is measured against. Holding rupees for three months earns 6.5% and holding dollars 4.5%, so the forward sits above spot by roughly the 2-point difference for a quarter: 83.0 x e to the 0.02 x 0.25 gives 83.42. The forward is not a forecast of where spot will be; it is simply where the interest differential puts the price for delivery in three months, and here the treasurer's view of 84.5 is above it. The options are priced off that same forward: at 5% volatility the 84 call costs about 0.57 rupees per dollar and the 86 call about 0.11, so the call spread costs 0.45. On USD 5 million that is Rs 28.3 lakh for the call and Rs 22.7 lakh for the spread.

Spot at expiryUnhedgedForward84 call84/86 spread
82.0082.0083.4282.5782.45
83.4283.4283.4283.9883.87
84.5084.5083.4284.5784.45
86.0086.0083.4284.5784.45
88.0088.0083.4284.5786.45
Rupees paid per dollar, premium included. Across the expected outcomes of 84 to 86 the forward's 83.42 is the lowest; the options win only if spot falls below about 82.96, and at 88 the call spread costs 86.45, worse than the forward by 3.04.
Step 2How do the payoffs compare across outcomes?

Draw the rupees paid per dollar against spot at expiry. Unhedged is the diagonal. The forward is flat. The call follows spot up to 84, then goes flat at 84 plus its premium, 84.57. The spread does the same up to 86 at 84.45, then turns up again, because the sold 86 call hands back every rupee above 86. Inside the view, the forward line sits below both option lines: paying a premium buys the right to benefit if the rupee strengthens, and the view says it will not. It is like paying extra for a refundable ticket when you are certain you will travel.

Rupees paid per dollar at expiry: inside the view, the forward is cheapest8182828383848485858686878788888989USD/INR spot at expiry, illustrativeRs paid per USDthe view: 84 to 86unhedgedspread 0.45call 0.57forward83.42
Across the expected range of 84 to 86 the forward at 83.42 is the cheapest line, the 84 call caps the rate at 84.57 and the 84/86 call spread at 84.45, and above 86 the call spread rises again, giving up protection the view says it will not need.
Step 3So when does the call spread make sense?

The spread is the cheaper way to own the view that spot finishes between 84 and 86, and for a trader expressing that view it is a natural choice: it gives up payoff above 86, which the view does not expect, in exchange for a premium 0.11 lower. For a hedger the trade-off runs the other way, because the region it gives up is exactly the outcome that hurts an importer most. At 88 the spread leaves Rupavati paying 86.45, about Rs 1.52 crore more on USD 5 million than the forward would have. And against the forward, the options only win if spot falls below about 82.96 for the spread and 82.85 for the call.

What each option structure costs against the forward, on USD 5 million0-1+1+2-0.43-0.48Spot falls to 82+0.57+0.52Spot 84.5, the view+0.57+1.52Spot 88, outside the viewabove zero: costs more than the forward84 call84/86 call spread
Against the forward on USD 5 million, the options save money only if spot falls to 82; at the expected 84.5 the call costs Rs 0.57 crore more and the spread Rs 0.52 crore more, and at 88 the spread costs Rs 1.52 crore more.

Choose, and attach the condition. For Rupavati, the forward on most or all of the USD 5 million: it matches a view that the rupee weakens, costs nothing upfront and leaves no gap. If the board wants to keep some benefit in case the rupee rallies, the 84 call on a slice does that at a known cost; the call spread belongs with the trading desk, not the treasury. The limits: volatility of 5%, the rates and the forward are illustrative, and a premium paid today costs a little more once funding is counted. Accounting treatment of each structure also differs, so confirm how the company's auditors treat option hedges before choosing on economics alone.

Where candidates lose it

The usual loss is matching the structure to the view without checking the forward. Candidates hear rise to 84.5 but not beyond 86 and reach straight for the 84/86 call spread, without noticing that the forward at about 83.42 already beats every option in the expected range.

The second is forgetting who the client is. A call spread is a fine trade for someone betting on a range, but for an importer the unprotected region above 86 is the disaster scenario, and selling away that protection to save a small premium inverts the purpose of the hedge.

What the interviewer asks next

  • The treasurer now thinks the rupee could strengthen to 81 as easily as weaken to 86. Does your choice change?
  • How would you build a zero-premium structure that caps the rate at 85, and what does it give up?
  • Implied volatility doubles to 10%. Which of the three structures changes in cost, and in which direction?
  • The payment date is uncertain within a two-week window. Which structure handles that best?

Asked at Goldman Sachs, Fixed Income Currency and Commodities, London, 2025 (Wall Street Oasis): I think I was given a scenario and was asked what kind of derivative strategy I would use for that trade.

← Case 048Make a market on the product of two dice. The fair value is 12.25 with a standard deviation near 8.9 and a long right tail. How wide are you for one lot and for ten, and which way do you lean?Case 050 →Three players are each dealt one card from 1 to 10 without repeats, and the contract settles at the highest card. You hold a 7. Price it, then reprice after another player immediately bids 8.5.

Company names and figures are illustrative.

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