Options Basics for the CTP Exam
The right without the obligation. What it pays, what it costs, and what the Greeks measure.
An option gives its buyer the right, but not the obligation, to buy (a call) or sell (a put) an asset at a fixed price, the strike, on or before a set date. The buyer pays a premium up front. The seller (writer) keeps the premium and takes on the obligation. That asymmetry is the point: the buyer's loss is capped at the premium, while the gain is open.
A bank treasury meets options two ways: selling them to customers who want to hedge, and running the risk of the options it has sold. The Certified Treasury Professional (CTP) exam covers both sides at a basic level: payoffs, which option hedges which exposure, and what the Greeks measure.
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The Terms
- Call
- Right to buy at the strike. Gains when the underlying rises above the strike.
- Put
- Right to sell at the strike. Gains when the underlying falls below the strike.
- Premium
- The price of the option, paid by the buyer to the seller at the start.
- European and American
- A European option can be exercised only on expiry; an American option at any time up to expiry.
- In, at and out of the money
- A call is in the money when spot is above the strike, at the money when equal, and out of the money when below. The reverse for a put.
- Intrinsic and time value
- Intrinsic value is what the option would pay if exercised now (never below zero). Time value is the rest of the premium.
Worked Example 1: An Importer Buys a USD Call
Illustrative. An importer must pay USD 1 million in three months and fears the rupee will weaken. It buys a USD call, strike ₹84.50, premium ₹0.40 per dollar (₹4,00,000 in total). Payoffs at expiry:
₹83.50
Exercise?
No, buy in the market
Payoff per USD
0
Net of premium per USD
-₹0.40
Net on USD 1 million
-₹4,00,000
₹84.50
Exercise?
Indifferent (at the money)
Payoff per USD
0
Net of premium per USD
-₹0.40
Net on USD 1 million
-₹4,00,000
₹84.90
Exercise?
Yes
Payoff per USD
₹0.40
Net of premium per USD
₹0.00 (break-even)
Net on USD 1 million
₹0
₹85.20
Exercise?
Yes
Payoff per USD
₹0.70
Net of premium per USD
₹0.30
Net on USD 1 million
₹3,00,000
₹86.00
Exercise?
Yes
Payoff per USD
₹1.50
Net of premium per USD
₹1.10
Net on USD 1 million
₹11,00,000
| Spot at expiry | Exercise? | Payoff per USD | Net of premium per USD | Net on USD 1 million |
|---|---|---|---|---|
| ₹83.50 | No, buy in the market | 0 | -₹0.40 | -₹4,00,000 |
| ₹84.50 | Indifferent (at the money) | 0 | -₹0.40 | -₹4,00,000 |
| ₹84.90 | Yes | ₹0.40 | ₹0.00 (break-even) | ₹0 |
| ₹85.20 | Yes | ₹0.70 | ₹0.30 | ₹3,00,000 |
| ₹86.00 | Yes | ₹1.50 | ₹1.10 | ₹11,00,000 |
Break-even for a call buyer is strike plus premium: 84.50 + 0.40 = ₹84.90. The importer's worst-case cost is fixed at ₹84.90 per dollar, however far the rupee falls. If the rupee strengthens to ₹83.50, it simply buys dollars cheaper in the market and its total cost is 83.50 + 0.40 = ₹83.90. A forward at ₹84.50 would have locked the rate both ways; the option keeps the upside for the price of the premium.
Worked Example 2: An Exporter Buys a USD Put
Illustrative. An exporter expects USD receipts and buys a USD put, strike ₹84.00, premium ₹0.35. Break-even is strike minus premium: ₹83.65.
₹82.80
Payoff per USD
₹1.20
Net of premium per USD
₹0.85
₹83.65
Payoff per USD
₹0.35
Net of premium per USD
₹0.00 (break-even)
₹84.00
Payoff per USD
0
Net of premium per USD
-₹0.35
₹85.00
Payoff per USD
0 (sells in the market at ₹85)
Net of premium per USD
-₹0.35
| Spot at expiry | Payoff per USD | Net of premium per USD |
|---|---|---|
| ₹82.80 | ₹1.20 | ₹0.85 |
| ₹83.65 | ₹0.35 | ₹0.00 (break-even) |
| ₹84.00 | 0 | -₹0.35 |
| ₹85.00 | 0 (sells in the market at ₹85) | -₹0.35 |
Certified Treasury Professional format questions. No signup.
Which Option Hedges Which Exposure
Importer paying foreign currency
Risk
Foreign currency rises
Option to buy
Call on the foreign currency
Exporter receiving foreign currency
Risk
Foreign currency falls
Option to buy
Put on the foreign currency
Borrower on a floating rate
Risk
Rates rise
Option to buy
Interest rate cap
Investor or lender on a floating rate
Risk
Rates fall
Option to buy
Interest rate floor
A bid that may or may not be won
Risk
Exposure arises only if the bid succeeds
Option to buy
An option, since the buyer is not forced to deal if the bid fails
| Exposure | Risk | Option to buy |
|---|---|---|
| Importer paying foreign currency | Foreign currency rises | Call on the foreign currency |
| Exporter receiving foreign currency | Foreign currency falls | Put on the foreign currency |
| Borrower on a floating rate | Rates rise | Interest rate cap |
| Investor or lender on a floating rate | Rates fall | Interest rate floor |
| A bid that may or may not be won | Exposure arises only if the bid succeeds | An option, since the buyer is not forced to deal if the bid fails |
The Greeks
Each Greek measures the change in option value for a change in one input, with the others held fixed.
Delta
Measures sensitivity to
Price of the underlying
Key fact
Long calls positive (0 to 1), long puts negative (0 to -1). Portfolio delta is the sum of position deltas.
Gamma
Measures sensitivity to
Change in delta as the underlying moves
Key fact
Gamma is the rate of change of delta. Highest near the money and close to expiry.
Vega
Measures sensitivity to
Volatility
Key fact
Long options gain when volatility rises, calls and puts alike.
Theta
Measures sensitivity to
Passage of time
Key fact
Long options lose value each day, other things equal.
Rho
Measures sensitivity to
Interest rates
Key fact
Usually the smallest of the Greeks for short-dated currency options.
| Greek | Measures sensitivity to | Key fact |
|---|---|---|
| Delta | Price of the underlying | Long calls positive (0 to 1), long puts negative (0 to -1). Portfolio delta is the sum of position deltas. |
| Gamma | Change in delta as the underlying moves | Gamma is the rate of change of delta. Highest near the money and close to expiry. |
| Vega | Volatility | Long options gain when volatility rises, calls and puts alike. |
| Theta | Passage of time | Long options lose value each day, other things equal. |
| Rho | Interest rates | Usually the smallest of the Greeks for short-dated currency options. |
Worked Example 3: Using Delta
Illustrative. A bank has sold the importer the USD 1 million call above. The option's delta is 0.45.
- 1
Bank's exposure
Short a call with delta 0.45 on USD 1 million behaves like a short position of 0.45 x 10,00,000 = USD 4,50,000.
- 2
Effect of a ₹0.10 rise in USD/INR
The option gains about 0.45 x 10,00,000 x 0.10 = ₹45,000 for the buyer, so the bank loses about ₹45,000.
- 3
Delta hedge
The bank buys about USD 4,50,000 in the market. As spot moves, delta changes (that is gamma), so the hedge must be adjusted.
Worked Example 4: An Interest Rate Cap
Illustrative. A borrower has a ₹10 crore floating rate loan and buys a cap at 7%. At a reset, the benchmark is 7.60% for the next 182 days.
- 1
How far above the cap
7.60% minus 7.00% = 0.60%.
- 2
Cap payout
10,00,00,000 x 0.0060 x 182 / 365 = ₹2,99,178, paid to the borrower for that period.
- 3
Net effect
The borrower's cost for the period is capped at 7%, plus the cap premium paid at the start.
FAQs
What is the maximum loss for an option buyer?expand_more
The premium paid. The buyer can always choose not to exercise. The seller's loss on a call is open-ended, which is why banks hedge the options they sell.
How do you calculate break-even on an option?expand_more
For a call, strike plus premium. For a put, strike minus premium. A USD call at strike ₹84.50 with a ₹0.40 premium breaks even at ₹84.90.
Why would a hedger choose an option over a forward?expand_more
A forward locks one rate whether the market moves for or against you. An option protects against the bad move but keeps the gain from a good move, at the cost of the premium. It also suits exposures that may not happen, such as a bid not yet won.
What does a delta of 0.45 mean?expand_more
The option's value changes by about 0.45 of any small change in the underlying price. It also means the option behaves like 45% of the underlying amount for hedging.
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