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## ADNEOM Benelux Training

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**ADNEOM Benelux**Training**FUTURES**Definition : A futures contract is an agreement between two counterparties to exchange a product, called a support or the underlying instrument, at a future date and at a price established at the time of the transaction. Forward contracts This is a non-standard contract concluded freely between two parties according to their specific needs. These "custom" contracts are exchanged on the OTC - Over-The-Counter market. Futures A future is a standard contract exchanged on an organized market. These contracts can be adapted to a large number of situations and are easily traded.**FUTURES**• Future prices • Price isbased on : • The spot priceat the moment • The storagecosts = cost for storing the goods • The carryingcosts = interestpaid for capital immobilization. • To manage counterpartyrisk, the future marketisaffiliatedwith a clearing house.**FUTURES**Arbitrage Cash & Carry Futures price is equal to the cash price, increased by the “base” (storage costs and carrying costs). When the cash price increases, the price of the future increases correspondingly. The further away the contract month, the higher the base. Conversely, it decreases as time passes. The day the contract month is reached, the futures product becomes a "cash" product. There can be differences between the theoretical futures price and the market price of the contract. This is when arbitrage takes place.**FUTURES**Characteristics of futures contracts Future contracts are standardised for liquidity purpose. The standard characteristics of contract futures are as follows: - The Underlying Instrument: the support instrument for a future whose qualities are strictly defined - The Nominal: the size of the futures contract. The nominal value indicates the quantity of the underlying instruments in the contract - The Contract Month: the date at which the underlying instrument will be paid and delivered - The Type of Settlement: the type of settlement defines how the contracts bought or sold on the future will be delivered at the contract month.**FUTURES**In addition, the market management company defines: - An initial deposit or initial margin for the clearing house - Price limits. These limits correspond to the maximum upper and lower price limits permitted for a future before trading is halted. - The tick. This is the smallest amount by which the price of a futures contract is allowed to rise or fall. - Trading unit. This is how prices are expressed (as a percentage of the nominal, as an index point, in dollars per ton, etc.). - The contract month, Contract months are usually quarterly. They are represented by the following letters: H: March M: June U: September Z: December**Options**Definition An option provides the holder with the right (but not the obligation) to buy or sell a specified amount of an underlying instrument at a specified price and within a predetermined time period. There are two types of options: - Buy options, or Calls. Owning a Calls give the right (not the obligation) of buying the underlying - Sell options, or Puts. Owning a Puts give you the right (not the obligation) of selling the underlying**Options**Characteristics - The price of the option is called the Premium. - The exercise or strike price is the price at which the buyer of the option can exercise his rights, that is, buy or sell the underlying instrument. When exercising an option, it is referred to as taking up this option. - The maturity of an option refers to the time remaining until the contract month. By extension, the term maturity often refers to the contract month itself. Depending on the type of option, the right to buy or sell can be exercised: -Throughout the life of the option (American options) - Only at the contract month (European options).**Options**On the options market, four basic positions are possible: - Buyer of a call : buy the right to buy the underlying at the strike price - Seller of a call : sell the right to buy the underlying at strike price, so get the obligation to sell the underlying at the strike price if the buyer exercises the option. - Buyer of a put : buy the right to sell the underlying at the strike price - Seller of a put : sell the right to sell the underlying at the strike price, so he get the obligation to buy the underlying at the strike price if the buyer exercises the option**Options**Depending on the exercise price and the underlying price, options can be:**Options**Option pricing To determine the premium, the parameters are: - The price of the underlying instrument at the time the option was negotiated - The volatility of the underlying (volatility = propensity for a price to fluctuate). Volatility can also be interpreted as incertitude with respect to future changes in the price of the underlying. There are two types of volatility: historical volatility and implicit volatility. Historical volatility is calculated on the amplitude of past variations on an underlying. Implicit volatility translates variation amplitudes expected by the investors in a stock. - The exercise, or strike, price - The contract month - The market interest rate (to determine carrying costs) - The rate of dividends distributed (if the underlying is a stock) - Storage costs (if the underlying represents merchandise).**Options**It is important to note that the price of an option contains two elements: -The intrinsic value of the option The intrinsic value of the option is equal at all times to the difference between the exercise price and the price of the underlying. - The time value The time value must be added to the intrinsic value and represents the price of the uncertainty and is added to the intrinsic value. The time value decreases as the contract month approaches. Premium = Intrinsic value + Time value**Options**Evolution of the premium of a Call according to the following parameters:**Options**The evolution of the premium for a Put option according to the following parameters:**Options**Black & Scholes model The Black–Scholes formula calculates the price of European put and call options. Assumptions : - Stocks are continuously traded - Stock prices follow a Geometric Brownian Motion - Short selling is allowed - No transaction costs or taxes are imposed - Perfectly divisible assets - Riskless arbitrage opportunities are exploited immediately - No dividend during the time to maturity of the derivative - Constant riskless interest rate and flat term structure.**Options**For both, as above: 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**Options**The Greeks Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter. These are the main Greek parameters : - Delta : measures the rate of change of option value with respect to changes in the underlying asset's price. - Vega : measures sensitivity of the option value with respect to the volatility of the underlying asset. - Theta : measures the sensitivity of the value of the derivative to the passage of time : the "time decay." - Rhô : measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term). - Gamma : measures the rate of change in the delta with respect to changes in the underlying price. - Omega : is the percentage change in option value per percentage change in the underlying price, a measure of leverage.**Options**• Clearing house and margin calls • A clearing house reduces the settlement risks by : • netting offsetting transactions between multiple counterparties • requiring collateral deposits • providing independent valuation of trades and collateral • monitoring the credit worthiness of the clearing firms, and in many cases • providing a guarantee fund that can be used to cover losses that exceed a defaulting clearing firm's collateral on deposit.**Options**• Margin requirements • - The premium margin is equal to the premium that they would need to pay to buy back the option and close out their position. It is the value of the option when it has been sell. • The variation margin or maintenance margin is a daily payment of profits and losses. The seller of an option has the obligation to deliver the underlying of the option if it is exercised. To ensure they can fulfill this obligation, they have to deposit collateral. • - Additional margin is intended to cover a potential fall in the value of the position on the following trading day. This is calculated as the potential loss in a worst-case scenario.**Options**• Margin calls • When the margin posted in the margin account is below the minimum margin requirement, the broker or exchange issues a margin call. • The investors now either have to increase the margin that they have deposited or close out their position. • Closing of position in options : • by selling the securities, options or futures if they are long • - by buying them back if they are short.**Strategies**Buying a call is buying the right to buy the underlying at the fixed strike price Buying a call with those values : 15€ is the strike price of the underlying 5€ is the price of the option.**Strategies**Selling a call is being paid to have the obligation to sell the underlying at the fixed strike price. Selling a call with those values : 15€ is the strike price of the underlying 5€ is the price of the option.**Strategies**Buying a put is buying the right to sell the underlying to the fixed strike price. Buying a call with those values : 25€ is the strike price of the underlying 5€ is the price of the option.**Strategies**Selling a call is being paid to have the obligation to buy the underlying at the fixed strike price. Selling a call with those values : 25€ is the strike price of the underlying 5€ is the price of the option.**Strategies**A Long Butterfly Spread needs to take positions on 4 options with 3 different strike prices. It can be build with calls or puts. Here, with calls : - Buy 1 call with a strike price of (X − a) - Sell 2 calls with a strike price of X (double call !!!) - Buy 1 call with a strike price of (X + a)**Strategies**Or the logic can be inverted to have a "sell Butterfly". - Buy 2 puts with a strike price of X - Sell 1 put with a strike price of (X - a) - Sell 1 put with a strike price of (X + a)