CFA Level 1 - Part 6 Derivatives and Alternative Investment

Forward

Forward contract : constant price, variable value, price is stated in the contract. At initiation, value is zero. Value of long position is (spot price of underlying - forward price)

Forward rate agreement (FRA)
                                                   
                                         (underlying rate at expiration - forward rate) (days/360)
FRA payoff:  notional principal[-------------------------------------------------------]
                                                     1+underlying rate at expiration(days/360)

FRA notation
1 X 3  expires in 1 month , underlying rate 60 day LIBOR

3 X 6  expires in 3 month , underlying rate 90 day LIBOR

Commodity Forward
Convenience yield, storage cost

For consumer of commodity
continuous form: F = S*e^([r+s-c]t)
discrete form: f0(T)  = S0(1+r)T+FV(storage cost,0,T) - FV(convenience yield,0,T)
s- storage cost
c- convenience yield
cost of carry is (funding costs + storage costs - convenience yield)*T

Future

Contango: current spot price < future price
Backwardation: current spot price > future price

The movement of price as future is expiring. For backwardation, future price converge to prevailing spot price.

Commodity
The relationship between risk free rate, storage costs and convenience yield.

Futures price = spot price(1+r) + storage cost - convenience yield

rolled yield: rolling short term contract into a longer term contract, profit from higher spot price

rolled yield: the difference between the spot price of commodity and futures price in contract. It futures price below spot price, the price of futures contract rolls up to the spot price as futures contract near maturity. The price convergence earns the futures contract bearer a positive roll yield. This explanation is called the theory of storage.

Option

Option profit = π
π = Max(0, S_t-X) - C₀ (profit to call buyer)
    X: strike proce, S_t: share price at time T , C₀ : option price

π = -Max(0, S_t-X) + C₀ (profit to call seller)

π = Max(0, X-S_t) - P₀ (profit to put buyer)

π = -Max(0, X-S_t) + P₀ (profit to put seller)

Option intrinsic value
  call option = underlying current share price - strike price
  put option = strike price - underlying current share price

Option price = intrinsic value + time value
  time value depends on underlying's volatility

European option: exercise only on expiration day

Option value
european call option  c_t >= max[0, S_t- X/(1 + r_f)^t]
american call option  C_t >= max[0, S_t- X/(1 + r_f)^t]

european put option p_t >= max[0, X/(1 + r_f)^t - S_t ]

american put option P_t >= max[0, X - S_t ]

Interest Rate Option                    
  value = notional principal [expiry rate - exercise rate] (days/360)
                                           
Put Call parity (European option only)
  fiduciary call = protective put
  c₀ + X/(1 + r_f)^t= p₀ + S₀
   X treasury bond, S₀ stock, c₀ call option

Put Call Forward parity
  p₀  = c₀ +(X - F(0,T))/(1 + r_f)^T
  X-F(0,T)  bond face value, X exercise price of option, F(0,T) forward price


covered call

protective put

Swap
Swap: value of swap at initiation is zero to both parties at initiation
  interest rate swap V_fix = V_floating

Currency swap:
  For example, Target wants to expand in Europe. They borrows $10mil in US from bondholders, go to Deutsche Bank, and change to €9mil.

Interest rate swap:
  value = notional principal [rate] (days/360)
  For example, GE takes floating rate loan from BofA. It can change the floating rate payment to fixed rate payment by entering into a interest rate swap with JPM.

Eurodollar: dollar deposited outside the US