A binding agreement (obligation) to buy/sell an underlying asset in the future, at a price set today.

Specifies features & quantity of asset, time date and place of deliver, and price buyer will pay at time of deliver

Forwards

What are the pros & cons of forwards?

Pros:

• terms are determined by contracting parties
• may not require collateral
• Customized

Cons:

• Illiquid (due to customization)

• Similar to a forward
• Standardize terms of agreement
• expiration date
• quantity of asset
• Generates homogeneity
• futures require collateral
• futures are traded on exchanges

Payoffs

What is the equation for the payoff of a long forward?

Spot @ expiration - Forward price 

(S_t-F_O,T)

Payoffs

What is the equation for the payoff of a short forward?

Forward Price - Spot Price at expiration

F_O,T - S_T

The right, but not the obligation, to purchase a security at a designated price at a designated time

Preserves upside potential while limiting downside

The seller of a call option is obligated to deliver if asked

Payoff Function for a long call:

Payoff = Max[0, spot price at expiration - strike price]

Payoff = Max[0,S_t-X]

Profit = Payoff - Future Value of option premium

Profit = Max[0,S_t-X] - FV(C_o,t)

Where: FV(C_o,t)=(1+r)*C_o,t

Payoff = -max[0,spot price at expiration - strike]

Payoff = -Max[0, S_t-X]

Profit = Payoff + FV of option premium

Profit = -max[0, S_t-X]+C_o,t

where:  FV(C_o,t) = (1+r)*C_o,t

A Put option gives the right but not the obligationto sell a security at a future time at a specified price

The seller is obligated to buy if asked

Payoff=Max[0,Strike price - Spot price @ expiration]

Payoff = Max[0, X - S_t]

Profit: Payoff - Future Value of premium

=Max[0, X-S_t]-FV(P_o,t)

Where: FV(P_o,t) = (1+r)*P_o,t

Payoff = -Max[0,Strike price - Spot Price  @ Expiration]

Payoff = -Max[0,X-S_t]

Profit = Payoff + FV of option premium

Profit = -Max[0, X-S_t] + FV(P_0,t)

Where: FV(P_0,t) = (1+r)*P_0,t