Derivative Securities - lecture set 1-4

Derivative Securities - lecture set 1-4

1. Purposes for derivatives securities

   • Hedging
   • Speculating
   • Arbitrage

2. Futures/Forwards

   • Contract specifications
     • The asset
     • Contract size
       • The number of units of the underlying (asset) per contract
     • Delivery arrangement
       • Where? How?  Always determined by the short party.
     • Delivery month
     • Delivery price
     • Position limit
   • Closing out a futures contract
     • Take delivery
       • Often not an option - expensive and difficult to have 100ML of oil on hand 
     • Take an equal but opposite position
       • The payoff is the price change between when you initially enter and when you closed out the contract
   • Payoffs
     • Long
       • Graphically
         • Long contract payoff
     • Short
       • Graphically
     • Margins
       • Comprised of your initial and maintenance margin
       • Marking to market
         • The difference between today and yesterdays settlement price 
         • If the difference is positive, the long positions account is credited .  If the difference is negative, the long position account is debited and the short is credited. 
     • Convergence
   • Hedging
     • Minimizing or eliminating the variance of a portfolio return (i.e., a set of positions) at a particular date in the future. 
     • Questions when deciding to hedge
     • Short Hedge
       • It is appropriate when the hedger owns the underlying asset, expects to sell it in the future and wants to lock in the selling price.                       
       • NATURALLY LONG 
       • Payoffs
     • Long Hedge
       • It is appropriate when the hedger has (or, expects) to purchase the asset in the future and wants to lock in the buying price.    
       • NATURALLY SHORT 
       • Payoffs
     • Perfect hedge (conditions)
     • Basis & Basis risk
       • The Hedge Ratio
         • Create a hedge (two portfolios) that minimise the variance. 
         • Definition
           • The ratio of the size of the position taken in the futures contract to the size of the exposure (natural position)    
         • The equation
           • h*
             • The slope coefficient of the linear regression of the change in s on the change in f 
       • Hedging
         • Stock index futures
           • Relevant conditions
             • Portfolio matches the index exactly
             • Maturity of available futures exactly matches the hedging horizon
             • Daily settlements ignored
           • Optimal contract position (w exact match)
             • Optimal if the match is not exact
               • Changing betas
     • Issues with the perfect hedge
       • Asset mismatch - cross hedging
       • Maturity mismatch
         • Rolling the hedge forward
           • Steps:
             • 1. Close out the initial futures contract
             • 2. Take the same position in the same contracts (but with the later delivery date)
             • 3. Repeat - if necessasary

3. Pricing

   • Forwards and futures
     • No arbitrage forward price
       • Arbitrage decision rules
     • Forwards and futures (w income etc)
       • No arbitrage forward price (w income)
         • I represents the present value of all cashflows from the asset. 
       • No arbitrage forward price (w known yield)
       • No arbitrage (currency forward)
       • Commodity Forwards and futures
         • Investment
           • U
             • U is the present value of storage costs  U = PV(SC)
         • Consumption
           • Presumed (theory) decision rule
           • The convenience Yield
             • This is the benefit someone gets from holding the consumption asset. 
             • General idea:
               • The present value of the future contract taking into consideration the convenience of holding the consumption asset will be equal to the present value of the contract accounting for the storage costs.  This makes sense as if the two sides of the equation were not equal then either someone can purchase the asset for less than they value it or they would have paid more than they value for the asset which also does not make sense. 
               • Future price accounting for all factors
             • Cost of Carry
               • COST OF CARRY = Storage costs + interest paid to finance asset - any income earned on the asset 
               • Dividend paying stock
               • Non-dividend paying stock
               • For a currency
               • For a commodity
   • Options
     • Types of options
       • Long Call
       • Long put
       • Short call
       • Short put
       • Value of options
         • Call options
         • Put options
         • Factors affecting option value
           • Stock price & Strike price
             • Call options
               • More valuable when  1. Stock prices increase 2. The Strike price is lower 
             • Put options
               • Put options are more valuable when 1. Stock prices increase  2. The strike price is higher
           • Time to expiration (T-t)
             • American calls & puts
               • More valuable as time to maturity increases
             • European calls & puts
           • Interest rate
           • Dividends
             • Increases the value of puts, decreases the value of calls. 
           • Volatility
             • As volatility increases, both puts and calls increase in value. This is bc the chance of positive movement increases (more likely to increase and decrease) while the maximum loss remains constant. 
     • Margins

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