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**Currency and Foreign Exchange Derivatives**

Jeff Capasso and Scott Bruckner

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**Overview Currency on an International Level Limitations and Risks**

Forwards and Futures Foreign Exchange (FX) options

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What is an FX Market?

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**Characteristics of Foreign Exchange**

Spot Transaction vs. Forward US Dollar usually involved in transactions European convention American convention Use of options on derivatives Barrier options

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**Forward and Futures Markets**

Forward Contract A private agreement between two parties to buy or sell an asset at a specified point in time in the future for the forward price prevailing at the time the contract is initiated The forward price of a contract is contrasted with the spot price at the time of maturity, T The difference between the spot and the forward price would result in a forward premium or forward discount

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Futures Contract Margined daily to the spot price of that day with a forward contract which has the same agreed-upon delivery price Eliminates the much of the credit risk with the required daily payments Frees the contract from vulnerability to large movements in the price of the underlying asset Maintained by an agency or separate corporation known as a clearing house Settles trading accounts, clearing trades, collecting and maintaining margin costs, regulating delivery Guarantees the transactions, which drastically lowers the probability of default

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**Spot and Forward Exchange Rates**

Spot and forward exchanges are traded in an over the counter market where money center banks are the dealers Spot exchange rate is a quote for the exchange of two currencies in two business days Example: Dollar-Yen exchange of 99.00/99.10 Dealer is willing to buy dollars for yen at yen per dollar or sell dollars for yen at the rate of yen per dollar Forward Exchange rate is a quote for settlement at a more distant date in the future

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**Interest Parity Theorem (IPT)**

Expressed as a basic algebraic identity that relates interest rates and exchange rates The market sets the forward or futures rate in relation to the spot to absorb the interest rate differential between the two currencies, which is known as the interest rate spread Cost of carry model: (F = forward price, S = spot price, r = risk free interest rate, s = storage price, c is the foreign exchange rate, t = time of delivery) If the returns are different, an arbitrage transaction could produce a risk-free return

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**Currency Forward Contract**

Agreement between two counterparties to exchange currencies at a fixed rate on a settlement day in the future. The value of the contract assumes positive or negative values as a function of exchange rates, the domestic and foreign interest rates, and the remaining time to settlement To exit a forward contract one must establish a closing contract where you sell the same quantity of currency in your foreign exchange. Forms a basis on how to value a forward contract On settlement day, positive or negative residual will exist and must be settled.

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**Valuing a Forward Contract**

Suppose on day (t) the time, T, which remains before settlement is as follows: T =(T-t) A Forward Contract pays for F0 in dollars and receives one unit of foreign currency at time T: F0 *e-RdT The value of one unit of foreign currency in dollars at time T: St*e-RfT Value of the contract is established by subtracting the forward contract price and the price of the currency at time, T: Vt = St*e-RfT - F0*e-RdT

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**Trading Mechanisms in Foreign Exchange**

Forward position must contact a bank to request a quote The contract will specify the cost of a foreign exchange, date of delivery and the price Example: An agent contacts Citibank Desires to form a contract to buy 1,000,000 Swiss Franks Receives quote of .6201/.6205 Accepts to purchase one million Swiss Franks at with an expiration date of 6 months In order to close his contract, one must request to cover his position shortly before the time of maturity, T. Receives a quote of .6250/.6255 in order to sell the forward Francs. This results in the bank netting out his position and pays him the difference in price: ( )*1,000,000 = $4,500

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**Trading Mechanisms in Foreign Exchange (Cont.)**

Futures market deals with standardized contracts Trading in these standardized contracts is conducted by open auction on the floor of the exchange Example: An agent purchases a contract on the open floor of the exchange The standardized Swiss Franc contract calls for delivery of 125,000 francs, for delivery in March, June, September or December for up to two years An order to buy 1,000,000 francs calls for the purchase of 8 long contracts Order was filled at $.6200 If price falls to the next day the agent would report a loss: ( )*125,000*8)=$1000 Profit or Loss is to be paid to the clearing house each day

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**What about uncertainty?**

Ex) Say a company in the United Kingdom is to receive a payment in 90 days of 1,000,000 US Dollars. How do they hedge that risk? Is there any uncertainty? Options: UK Pound as a call, USD as a put

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**Four Assumptions for FX Options**

Geometric Brownian Motion determines the Spot Price Option prices are a function of one variable, the Spot Price Markets are frictionless Interest rates, domestic and foreign, are constant

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**FX Derivatives α = expected rate of return on a security**

δ = standard deviation of the security rate of return rd = the domestic (riskless) interest rate rf = riskless foreign interest rate σ = volatility of the current spot price S = spot price C(S,T) = price of FX call option (domestic units per foreign units)

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**Ito’s Lemma Useful to find differential of a stochastic process**

Source: wikipedia.org (search term: Ito’s lemma) Useful to find differential of a stochastic process Also utilized in Black-Scholes

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European vs. American? American must be more than the cost of the option itself. Super Derivatives

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