Currency derivatives

Currency Derivatives

What are Derivatives

• Derivatives are financial contracts whose cash flows and value derives from some underlying financial asset or commodity or indicator. For example, stock options provided to managers.

• Underlying assets may be financial assets, commodities, currencies, etc.

• Counterparties are typically known as buyer (long) and seller (short).

• Forwards and Options are the most contract type

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Currency Forwards

• The exchange of one currency for another at a future date using a pre-determined exchange rate

• At inception, the two parties—long and short—simply agree on the forward price.

• At maturity, the short delivers the contracted units of the base currency and in return the long makes payment using the terms currency.

• Certain currency forwards do not entail actual delivery of the foreign currency and are known as non-deliverable forwards (NDF).



Currency Forwards

• Example 3.2… page 54 – 55



Currency Forwards Terms to remember

• Underlying asset – Units of base currency

• Maturity – Delivery date for the currency

• Forward price – Units of the terms/payment currency per unit of base currency



Currency Forwards Market structure

• Currency forwards are traded in the interbank markets • Outright forwards are different from foreign exchange

swaps (to discuss later) • Forward markets are private and normally parties of

transactions are known to each other • Banks are the key players in such market, MNCs

participate through banks • Most transactions are large, exceeding USD 10 million. • Often, online systems are used to help speedier and

synchronized trades



Currency Forwards Forward price

• Notations – Price of the base currency in the spot market, 𝑆

– Forward price of the base currency, 𝐹

– Domestic interest rate, 𝑟

– Foreign interest rate, 𝑟∗

– Maturity of the forward contract, 𝑡

• Suppose you want to obtain one unit of base currency




• Suppose you want to obtain one unit of base currency at time 𝑡.

• You have two alternatives:

• Alternative A: buy the currency using forward contract – Pay the forward price, 𝐹 , at time 𝑡.

• Alternative B: borrow money to buy the currency today, deposit in bank until time 𝑡. – Borrow 𝑆 at interest rate 𝑟, use it to buy the base currency

– Deposit the base currency and earn at 𝑟∗ until time 𝑡.




• In equilibrium, alternative A and B should cost the same and following relationship must be satisfied:

𝐹 = 𝑆 ×1 + 𝑟

1 + 𝑟∗

𝑡

• Rearranging the equation: 𝐹

𝑆=

1 + 𝑟

1 + 𝑟∗

𝑡

• If 𝑟∗ > 𝑟, then 𝐹

𝑆< 1, and 𝐹 < 𝑆; in this case, forward

premium, 𝐹𝑃 =𝐹

𝑆− 1 =

1+𝑟

1+𝑟∗

𝑡− 1

• Thus, if 𝑟∗ > 𝑟 , forward premium is negative (forward discount) and if 𝑟 > 𝑟∗ , forward premium is positive.




• Example 3.3… page 56 – 57.

• Problem 5… page 77.



Currency Forwards Counterparty risk in forward contracts

• Nonperformance by any of the two parties in the forward contract results in the presence of counterparty risk or default risk.

• MNCs conduct due diligence on their counterparties prior to engaging in forward contracts.

• Despite the presence of such risk, forward contracts are attractive because of its advantage of customization in terms of currency, size, and maturity.



Currency Forwards Counterparty risk in forward contracts

• Example 3.4… page 57

• Problem 2… page 77



Currency Futures

• Participants of forward market is limited to large institutions and MNCs due to the problem of counterparty risk associated with forward contracts.

• Futures markets satisfy the demand for similar derivative contracts of the parties left outside the forward market.

• A futures contract – is an exchange traded version of the forward contract – is standardized with specific maturity and size – allows wider range of players for its relatively small size compared

to forward contracts – offers anonymity



Currency Futures Market structure

• Chicago Mercantile Exchange (CME) is the market leader in currency futures.

• These exchanges provide – infrastructure – clearing functions

• Trading may occur – on the trading floor of the exchange – electronically or virtually around the clock

• Settlement procedure may vary – actual delivery – cash settlement



Currency Futures Daily settlement

• Futures are traded anonymously

• Hence, some sort of collateral, or third party guarantee is necessary for trading to take place

• Consequently, both the long and the short in the futures transaction must set up margin accounts (also called performance bonds) at their brokerages

• Margin accounts are cash accounts to protect concerned parties against default.

• These margin accounts serve as collateral

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• The margin account balances must be more than sufficient to cover any changes in contract value

• It is difficult to cover against default arising out of a large change in the price of underlying currency over a longer period

• However, price changes in any given day would be significantly less compared to that over the contract life

• This is why futures exchanges require accounts to be settled every day.




• Initial deposit in the margin account is called initial margin • At the end of each trading day, change in value of the

futures contract is calculated by (current day’s close – previous day’s close)

• If the contract value increases – fund is transferred from short’s account to long’s account

• If the contract value decreases – fund is transferred from long’s account to short’s account

• The clearing house of the exchange facilitates these transfers • An alternative term used to denote such daily settlement

– mark to market




• If the margin accounts are allowed to contain too low balance, it may fail to provide protection when price declines sharply

• A minimum balance of the account is required to maintain – maintenance margin

• Maintenance margin is lower than the initial margin • If the balance of a margin account falls below the

maintenance margin, it triggers additional funds are requested to deposit – margin call

• If the margin call is ignored, the remaining funds are used to close out the futures position




• Futures are similar to forward contracts

• Cash flows in futures are also quite similar to forward contracts with only one difference – cash flows of futures are settled every day, whereas that of

forward contract is settled only once at maturity

• The sum total of daily settlements in futures should be equal to the final settlement of an equivalent forward contract




• Example 3.5…page 60

• An MNC enters into futures contract to buy CAD @ USD 0.90

• Initial margin is USD 0.60

• Maintenance margin is USD 0.03

• Days remaining before contract maturity, 4 days

• Calculate cash flows per unit of foreign currency.






Day Price

Long Short

Remarks Change Balance CF Change Balance CF

0 0.90 0.06 -0.06 0.06 -0.06 Initial margin

1 0.92 +0.02 0.08 -0.02 0.04

2 0.94 +0.02 0.10 -0.02 0.02 Margin call

0.06 -0.04 Call met

3 0.91 -0.03 0.07 +0.03 0.09

4 0.89 -0.02 0.05 +0.05 +0.02 0.11 +0.11 Close

-0.89 +0.89 Delivery

-0.90 +0.90 Total


• Problem 4… page 77 (assignment)




• Actual futures prices are widely disseminated

• Futures contracts are essentially similar to forward contracts

• We can use currency forward pricing formula to calculate futures price, using annual compounding convention

𝐹 = 𝑆 ×1 + 𝑟

1 + 𝑟∗

𝑡

or using LIBOR convention

𝐹 = 𝑆 ×1 + 𝑟𝑡

1 + 𝑟∗𝑡




• Example 3.6… page 61

• Problem 6… page 77



Futures vs. Forward Prices in the Currency Markets

• Currency markets offer simultaneous trading of forward and futures

• Forwards are traded in interbank market • Futures are traded in exchanges like CME • Difference of forward and futures price of the same

currency often brings the opportunity to exploit such price discrepancy

• Electronic trading systems such as BARX and Globex as well as computerized program trading help many institutions to make profit in this way

• However, in equilibrium, futures price should be equal to forward price



Currency Options

• An instrument that provides the long the right to purchase or sell the underlying/base currency – at a prespecified strike price denominated in the terms currency

– at a future date • only at maturity (European style options)

• at or prior to maturity (American style options)

• Right to purchase is provided by call options

• Right to sell is provided by put options

• Unlike forward/futures, options are more flexible because – future purchase/sale of the underlying asset is optional



Currency Options Options parameters and terminology

• Options give the holder the flexibility of taking one of two actions as appropriate

• Financial options: the underlying asset is any financial asset like a foreign currency

• Real options: business situations that provide flexibility that brings the ability of increasing cash flows by making proper choice

• Underlying asset: commodity, instrument, index, or currency that is bought or sold using the option

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• Strike price/exercise price: contractual price at which the underlying asset is bought or sold using the option

• Maturity is finite, majority expiring in 6 months – option’s value diminishes with each passing day

– this is why options are often called ‘wasting assets’

– ‘American options’ can be exercised at any point in time prior to maturity

– ‘European options’ can be exercised only at maturity




• Option premium: at the time of making the contract, option holder pays a premium to the option seller.

• A rational option holder will exercise the option only if it is profitable

• Hence, option holder cannot lose money from the option

• However, the counterparty or the option seller loses money whenever the option is exercised

• The option premium is the compensation for such loss of the option seller



Currency Options Market structure

• The Philadelphia Stock Exchange (PHLX) pioneered trading in foreign currency options

• At present, PHLX and CME are the main exchanges

• Popularity of exchange traded currency options is less than that of currency futures



Currency Options Option exercise and cash flows

• Payoff equals cash flow at maturity, also called gross profit, or maturity cash flow

• Profit equals payoff net of premium, also called net profit or net cash flow.

• Steps: – Determine the cash flow at inception, based on premium

– Estimate the payoff, which is the difference between spot price and exercise price

– Calculate the profit, by deducting premium from the payoff



Currency Options Option exercise and cash flows: call option

• A purchases a European style currency call option from B by paying a premium of USD0.06. The underlying asset is EUR 1. The option expires in 3 months, and has a strike price of USD1.25.

• Calculate the payoff and profit to the long, if the currency value at maturity is USD 1.34.

• Answer: – payoff is 0.09 to the long

– profit is 0.03 to the long




• Calculate payoff and profit to the long for different values of the currency at maturity.



Call Option: Payoff & Profit to Long (Buyer)

Call Parameters: C = 0.06, X =1.25

All Values in USD

At Contract

Inception Cash Flows At Maturity

Overall

Result

Currency

Value at

Maturity Premium Paid Exercise Price Paid Value Received Payoff Profit

1.16 0.06 No Exercise No Exercise 0 -0.06




1.28 0.06 1.25 1.28 0.03 -0.03

1.31 0.06 1.25 1.31 0.06 0.00

1.34 0.06 1.25 1.34 0.09 0.03

1.37 0.06 1.25 1.37 0.12 0.06

Note: Payoff & Profit to Short (Seller) is the exact opposite (that is, positive values are

negative and negative values are positive)


• Graphically show the payoff and profit to the long for different values of the currency at maturity.



Currency Options Option exercise and cash flows: put option

• P purchases a European style currency put option from Q by paying a premium of USD0.03. The underlying asset is EUR 1. The option expires in 3 months, and has a strike price of USD1.25.

• Calculate the payoff and profit to the long, if the currency value at maturity is USD 1.16.

• Answer: – payoff is 0.09 to the long

– profit is 0.06 to the long




• Calculate payoff and profit to the long for different values of the currency at maturity.



Put Option: Payoff & Profit to Long (Buyer)

Call Parameters: P = 0.03, X =1.25

All Values in USD

At Contract

Inception Cash Flows At Maturity

Overall

Result

Currency

Value at

Maturity Premium Paid

Exercise Price

Received Value Given Up Payoff Profit

1.16 0.03 1.25 1.16 0.09 0.06

1.19 0.03 1.25 1.19 0.06 0.03

1.22 0.03 1.25 1.22 0.03 0.00






Note: Payoff & Profit to Short (Seller) is the exact opposite (that is, positive values

are negative and negative values are positive)


• Graphically show the payoff and profit to the long for different values of the currency at maturity.



Currency Options Option exercise and cash flows: call vs. put option



Currency Options Summary of option payoffs and profits

• Notations: 𝑆𝑡 = price of underlying asset at maturity 𝑋 = option strike or exercise price 𝐶 = call premium 𝑃 = put premium

• Call options are exercised when 𝑆𝑡 > 𝑋 • Put options are exercised when 𝑆𝑡 < 𝑋

































Currency Options Factors affecting call option prices



• Value of underlying asset, (𝑺) • Strike price (𝑿) • Maturity (𝒕)

– Time value – both for call and put

• Volatility (𝝈) – Both for call and put

• Domestic currency interest rate (𝒓) • Foreign currency interest rate (𝒓∗)

Currency Options Pricing call and put options



• Value of underlying asset, (𝑆) • Strike price (𝑋) • Maturity (𝑡) • Volatility (𝜎) • Domestic currency interest rate (𝑟) • Foreign currency interest rate (𝑟∗)

• 𝑒 = 2.7182818283 • 𝑁(. ) is the cumulative distribution

function of the standard normal distribution

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Currency derivatives