 Derivatives are products whose values are derived from one or more, basic underlying variables.  Types of derivatives are many- 1. Forwards 2. Futures 3. Options 4. Warrants 5. Swaps The markets for derivatives exchange:  Exchange Market  Over the counter market

 A forward contract is a customized contract between two entities, where settlement takes place on a specific date in the future at a certain price agreed upon.  Can be contrasted with the spot contract which deals with buying or selling an asset today.  Is traded in the over-the-counter market-not standardized  Long position and short position  Used to hedge foreign exchange risk.

 A standardized forward contract.  Two types of futures :  Commodity futures  Financial futures  Key differences between forward and futures contract would be :  Forward contract is tailor made; Futures is a standardized contract  No collateral required for forward contracts; margin required for futures  Forwards are settled on the maturity date; futures are marked to market on a daily basis

 Clearing margin are financial safeguards to ensure that companies or corporations perform on their customers' open futures and options contracts.  Customer margin Within the futures industry, financial guarantees required of both buyers and sellers of futures contracts and sellers of options contracts to ensure fulfillment of contract obligations.  Initial margin is the equity required to initiate a futures position.  Maintenance margin A set minimum margin per outstanding futures contract that a customer must maintain in his margin account.

CASE 1:  S 0 :Spot price today  F 0 :Futures or forward price today  T:Time until delivery date  R:Risk-free interest rate for maturity T The formula for calculation is:

Example  IBM stock is selling for $68 per share. The zero coupon interest rate is 4.5%. What is the likely price of the 6 month futures contract?

CASE 2:The price of a non interest bearing asset futures contract. The price is merely the future value of the spot price of the asset, less dividends paid. I = present value of dividends CASE 3: If an asset provides a known % yield, instead of a specific cash yield, the formula can be modified to remove the yield. q = the known continuous compounded yield

 Hedgers  Speculators  Arbitrageurs

 An option establishes a contract between two parties concerning the buying or selling of an asset at a reference price.  The buyer of the option gains the right, but not the obligation, to engage in some specific transaction on the asset, while the seller incurs the obligation to fulfil the transaction if so requested by the buyer.  Is traded on both the exchange market and over the counter market.  Option to buy is a call option  Option to sell is the put option  Types:  European Option: exercised only on the expiration date  American Option: on or before the expiration date

Options maybe : (for call option)  ATM (At the money):  Exercise price = Market price  ITM (In the money):  Exercise price <Market price  OTM (Out of the money):  Exercise price > Market price

LONG CALL  A trader who believes that a stock's price will increase might buy the right to purchase the stock (a call option) rather than just purchase the stock itself. He would have no obligation to buy the stock, only the right to do so until the expiration date. If the stock price at expiration is above the exercise price by more than the premium (price) paid, he will profit. If the stock price at expiration is lower than the exercise price, he will let the call contract expire worthless, and only lose the amount of the premium. call option

LONG PUT  A trader who believes that a stock's price will decrease can buy the right to sell the stock at a fixed price (a put option). He will be under no obligation to sell the stock, but has the right to do so until the expiration date. If the stock price at expiration is below the exercise price by more than the premium paid, he will profit. If the stock price at expiration is above the exercise price, he will let the put contract expire worthless and only lose the premium paid.put option

SHORT CALL  A trader who believes that a stock price will decrease, can sell the stock short or instead sell, or "write," a call. The trader selling a call has an obligation to sell the stock to the call buyer at the buyer's option. If the stock price decreases, the short call position will make a profit in the amount of the premium. If the stock price increases over the exercise price by more than the amount of the premium, the short will lose money, with the potential loss unlimited.

SHORT PUT  A trader who believes that a stock price will increase can buy the stock or instead sell, or "write", a put. The trader selling a put has an obligation to buy the stock from the put buyer at the put buyer's option. If the stock price at expiration is above the exercise price, the short put position will make a profit in the amount of the premium. If the stock price at expiration is below the exercise price by more than the amount of the premium, the trader will lose money, with the potential loss being up to the full value of the stock.

 The Black-Scholes formula calculates the price of European put and call options.  The value of a call option for a non-dividend paying underlying stock in terms of the Black–Scholes parameters is:  Also,

 The price of a corresponding put option based on put-call parity is:  N() is the cumulative distribution function of the standard normal distribution  T − t is the time to maturity  S is the spot price of the underlying asset  K is the strike price  r is the risk free rate (annual rate, expressed in terms of continuous compounding)  σ is the volatility of returns of the underlying asset

 Swaps are private agreements between two parties to exchange cash flows in the future according to a prearranged formula. They can be regarded as portfolios of forward contracts.  The two commonly used swaps are : Interest rate swaps: These entail swapping only the interest related cash flows between the parties in the same currency. Currency swaps: These entail swapping both principal and interest between the parties, with the cash flows in one direction being in a different currency than those in the opposite direction.

 A is currently paying floating, but wants to pay fixed. B is currently paying fixed but wants to pay floating. By entering into an interest rate swap, the net result is that each party can 'swap' their existing obligation for their desired obligation. Normally the parties do not swap payments directly, but rather, each sets up a separate swap with a financial intermediary such as a bank.

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