CFA Level 2 - Derivatives

Forward

Pricing and Valuation of Forward Contracts

Generic Forward Contract
  Vt = St - Ft/(1+r)^(T-t)

Equity Forward

  F_t = S_te^-Dte^r_ct
  F(0,T) = S₀(1 + r)^T - FV(D,0,T)
  F(0,T) = [S₀ - PV(D,0,T)](1 + r)^T

  V_t = S_te^-Dt - F_te^-r_ct
  Vt = St - PV(D,t, T) - Ft/(1+r)^(T-t)

Equity forward holders are not entitled to receive dividends

continuously compounded rate and discrete rate conversion:
  r_fc = ln(1+r_f)

Currency Forward

  Ft = St (1+rd)^t / (1 + rf)^t

  Vt = St/(1 + rf)^(T-t) - Ft/(1+rd)^(T-t)

Put Call Parity
  C + PV(x) = P + (S - PV of dividends)

Fixed Income Forward
conversion factor is used when there are a number of eligible bonds to  deliver, the conv factor adjustment is not precise, the seller will select the cheapest to deliver bonds

Future
Future and spot prices must converge at expiration.

Options
Binomial option pricing model

 π = (1 + r - d ) / (u - d)
 p⁺ = (πp⁺⁺ + (1 - π) p^+- ) /  (1 + r)
 p^- = (πp^+- + (1 - π) p^-- ) /  (1 + r)

High rf => higher call option price, lower put option price

gamma is larger when more uncertainty about whether option will expire in or out of the money

Interest Rate Derivatives
Interest Rate swap is combination of purchase interest rate call option, and sale of interest rate put option

Credit Default Swaps 
A credit derivative is a derivative where the underlying is a measure of borrow's credit quality. CDS, one party makes payment to another party, and receives a promise of compensation if third party defaults.

CDS are similar to put options.

credit events: bankruptcy, failure to pay, involuntary restructuring

CDS pricing: expected loss =  loss given default X probability of default

Trading strategy: company will undergo LBO
  buy the CDS, because of higher prob. of default
  buy the stock, because of stock price rises

Swaps
Fixed rate swap
Swaption: pay floating, receive fixed - receiver swaption
     receive floating, pay fixed - payer swaption
Currency Swap: exchange of principal amounts in different currencies at swap initiation that is reversed at swap maturity
FX Swap - same as currency swap, but no payment of interim interest