Derivatives

Question 1

Forward Contract: Vt(O,T) =

Answer 1

Forward Contract: V_t (0,T)=S_t-F(0,T)/〖(1+r)〗^((T-t)) , value of long, if

Question 2

Equity Forward Contract: F(0,T), F(0,T) continuous, Vt(0,T) continuous

Answer 2

Equity Forward Contract: (0,T)=[S_0-PV(D,0,T)]〖(1+r)〗^T , D-dividends; F(0,T)=(S_0 e^(-δ^c T) ) e^(r^c T); V_t (0,T)=S_t e^(-δ^c (T-t))-F(0,T)e^(-r^c (T-t))

Question 3

Fixed Income Forward Contract: F(0,T)

Answer 3

Fixed Income Forward Contract: (0,T)=[B_0^c (T+Y)-PV(CI,0,T)]〖(1+r)〗^T , CI-coupon interest

Question 4

FRA

Answer 4

FRA: (0,h,m)=(1+L_0 (h+m)((h+m)/360))/(1+L_0 (h)(h/360) )-1 , where h - # days until FRA starts, m – length of FRA (# of days)

Question 5

Forward Contract on Currency: F(0,T), F(0,T) continuous

Answer 5

Forward Contract on Currency: (0,T)=[S_0/(1+r^f )^T ] 〖(1+r)〗^T ; F(0,T)=(S_0 e^(-r^fc T) ) e^(r^c T)

Question 6

Credit risk in a forward contract arises when

Answer 6

Credit risk in a forward contract arises when the counterparty that owes the greater amount is unable to pay at expiration

Question 7

The value of a futures contract just prior to marking to market is

Answer 7

The value of a futures contract just prior to marking to market is the accumulated price change since the last mark to market. The value of a futures contract just after marking to market is zero.

Question 8

Futures Price: fo(T) =

Answer 8

Futures Price: f_0 (T)=S_0 〖(1+r)〗^T

Question 9

Futures Price with storage costs, cash flows, convenience yield:

Answer 9

Futures Price with storage costs, cash flows, convenience yield: f_0 (T)=S_0 〖(1+r)〗^T+FV(storage costs)-FV (cash flows)-FV(convenience yield) [or between each]

Question 10

Futures Price =

Answer 10

Futures Price = Spot Price – Risk Premium

Question 11

Stock Index Futures Price: fo(T) =

Answer 11

Stock Index Futures Price: f_0 (T)=S_0 〖(1+r)〗^T-FV(Dividends)

Question 12

co(T1),co(T2) , po(T1), po(T2)

Answer 12

co(T2) ≥ co(T1) ; earlier expiration T1, later expiration T2; p0(T2) can be either greater or less than p0(T1)

Question 13

Put-Call Parity

Answer 13

Put-Call Parity: c_0+X/(1+r)^T =p_0+S_0

Question 14

Binomial Model (same for put)

Answer 14

Binomial Model (same for put): c=(πc^++(1-π)c^-)/(1+r), π=(1+r-d)/(u-d), c^+=(πc^(++)+(1-π)c^(+-))/(1+r), c_T=Max(0,S_T-X)

Question 15

Black-Scholes-Merton model assumptions (6)

Answer 15

Black-Scholes-Merton model assumptions: the underlying asset follows a lognormal distribution, the risk-free rate is known and constant, the volatility of the underlying asset is known and constant, there are no taxes or transaction costs, there are no cash flows on the underlying, and the options are European

Question 16

↑risk-free rate [effect on call and put prices]

Answer 16

↑risk-free rate ↑call option prices, ↓put option prices

Question 17

Gamma is larger when

Answer 17

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

Question 18

Hedge Ratio, call/put overpriced (underpriced)

Answer 18

Hedge Ratio: =(c^+-c^-)/(S^+-S^- ) , n=(p^+-p^-)/(S^+-S^- ) , call overpriced (underpriced)  sell (buy) call, buy (short) stock  n * # calls = # shares, put overpriced (underpriced)  sell (buy) put, short (buy) stock  n * # puts = # shares

Question 19

Annualized Fixed Rate on a Swap today:

Answer 19

Annualized Fixed Rate on a Swap today:
	Calculate B0(hj) for each interest payment: B_0 (h_j )=1/(1+L_0 (h_j)(h_j/360)) , where hj – interest payment dates, Li(m) – m-day Libor on day i 
	Calculate the fixed swap interest payment rate: FS(0,n,m)=(1.0-B_0 (h_n))/(∑_(j=1)^n▒〖B_0 (h_j)〗) , where n – number of interest payments, m – number of days between each payment, hn-expiration date of swap, $1 hypothetical notional
	Calculate the annualized fixed rate: Annualized = FS(0,n,m) * (360/m) *notional

Question 20

Market Value of the swap x days later:

Answer 20

Market Value of the swap x days later:
	Calculate Bx(hj) for each interest payment: B_x (h_j )=1/(1+L_x (h_j)(h_j/360)) 
	PV remaining fixed payments plus $1 hypothetical notional =FS(0,n,m)*∑_(j=1)^n▒〖B_x (h_j ) 〗+$1(B_x (h_n ))
	PV remaining floating payments plus $1 hypothetical notional =[L_0 (h_1 )*(m/360)+1]*B_x (h_1)
	Market Value (=what you receive – what you pay)

Question 21

Cap Payoff =

Answer 21

Cap Payoff = max (0, reference rate – cap rate)/# periods * notional

Question 22

Floor Payoff =

Answer 22

Floor Payoff = max (0, floor rate – reference rate)/# periods * notional

Question 23

A CDS (credit default swap) is

Answer 23

A CDS (credit default swap) is protection against losses from the default of a borrower