Need an all-in-one list with the **Derivatives** formulas included in the CFA Level 1 Exam? We have compiled them for you here. The relevant formulas have been organized and presented by chapter. In this section, we will cover the following topics —** Replication, Forwards, Swaps, Options, and the Binomial Model**.

**1. Replication**

*Long risk-free asset (lending)*

Long~risk–free~asset~(lending) = Long~asset + Short~derivative

*Long derivative*

Long~derivative = Long~asset + Short~risk–free~asset~(borrowing)

*Short asset*

Short~asset = Short~derivative + Short~risk–free~asset~(borrowing)

**2. Forwards**

*FRA settlement to the long*

FRA~settlement~to~the~long= \frac {Notional~principal \times (Floating~rate - Forward~rate) Big( \frac {Days}{360} Big)}{1 + Floating Big( \frac {Days}{360} Big)}

Days = Number of days in floating rate term

Floating = Floating rate

Forward = Forward rate

*Forward rates*

F_0(T) = S_0 (1 + r)^T

F_0(T) = Price of the Forward

S_0 = Spot price of the underlying asset

r = Risk-free interest rate

T = Time of the contract

*Value*

V_T(T) = S_T - F_0(T)

V_T(T) = Value of forward at time T

S_T = Spot price of the underlying at time T

F_0(T) = Price of the Forward

*Net Cost of Carry*

Net~Cost~of~Carry = ϒ - θ

ϒ = Benefits

θ = Costs

*Forward Price with Net Cost of Carry*

F_0(T) = (S_0 - ϒ + θ)(1 + r)^T

F_0(T) = Price of the Forward

S_0 = Spot price of the underlying asset

r = Risk-free interest rate

T = Time of the contract

ϒ = Benefits

θ = Costs

*Value at any point during the contract (time t)*

V_t(T) = S_t - F_0(T)(1 + r)^{-(T - t)}

V_t(T) = Value at time t

S_t = Spot price of the underlying asset at time t

**3. Options**

## Call Options

**In-the-money**: S_T > X**At-the-money**: S_T = X**Out-of-the-money**: S_T < X

Call option Buyer | Call option seller |
---|---|

C_T = Max (0, S_T - X) Pi = C_T - P | C_T = -Max (0, S_T - X) Pi = C_T + P |

C_T = Call option’s value at expiration (T)

S_T = Stock price at expiration (T)

X = Option’s exercise/strike price

Pi = Profit

P = Option’s premium paid

## Put Options

**In-the-money**: S_T < X**At-the-money**: S_T = X**Out-of-the-money**: S_T > X

Put option Buyer | Put option seller |
---|---|

P_T = Max (0, X - S_T) Pi = P_T - P | P_T = -Max (0, X - S_T) Pi = -P_T + P |

P_T = Put option’s value at expiration (T)

S_T = Stock price at expiration (T)

X = Option’s exercise/strike price

Pi = Profit

P = Option’s premium paid

*Put-Call Parity*

S_0 + p_0 = c_0 + \frac {X}{(1 + r)^T}

S_0 = Spot price of the underlying asset at time 0

p_0 = Value of put option at time 0

c_0 = Value of call option at time 0

T = Option’s duration

X = Exercise price of the option

r = Risk-free interest rate

*Put-Call Forward**Parity*

\frac {F_0(T)}{(1 + r)^T} + p_0 = c_0 + \frac {X}{(1 + r)^T}

F_0(T) = Forward price

p_0 = Value of put option at time 0

c_0 = Value of call option at time 0

T = Option’s duration

X = Exercise price of the option

r = Risk-free interest rate

**4. Binomial Model**

*Up-factor*

u = \frac {S_1^+}{S_0}

u = Up-factor

S_1^+ = Upward value of the underlying asset after first period

S_0 = Value of underlying at time 0

*Down-factor*

d = \frac {S_1^-}{S_0}

d = Down-factor

S_1^- = Downward value of the underlying asset after first period

S_0 = Value of underlying at time 0

*Value of option on upward movement*

c_1^+ = Max (0, S_1^+ - X) = S_1^+ - X

X = Exercise price of the option

c_1^+ = Option’s value after upward movement

*Value of option on downward movement*

c_1^- = Max (0, S_1^- - X) = 0

X = Exercise price of the option

c_1^- = Option’s value after downward movement

*Synthetic probabilities*

c_0 = \frac {πc_1^+ + (1 - π)c_1^-}{1 + r}

c_0 = Value of call option

1 - π = Synthetic probability of downward move

**5. Swaps**

*Plain vanilla interest rate swap*

Fixed–rate~payment~(t) = (Swap~FR - LIBOR) \times \frac {T}{360} \times NP

FR = Fixed rate

T = Number of days in the settlement period

NP = Notional principal

**Follow the links to find more formulas on Quantitative Methods, Economics, Corporate Finance, Alternative Investments, Financial Reporting and Analysis, Portfolio Management, Equity Investments, and Fixed-Income Investments, included in the CFA® Level 1 Exam.**