Finance Notes > Corporate Finance Notes

This is an extract of our **4. Derivatives** document, which
we sell as part of our **Corporate Finance Notes** collection written by the top tier of
University Of London (examined By LSE) students.

* The following is a more accessble plain text extract of the PDF sample above, taken from our Corporate Finance Notes.
Due to the challenges of extracting text from PDFs, it will have odd formatting:
*

Derivatives

Derivative Properties and Pricing

Option Payoff and Profit

Option

A right but not an obligation to buy / sell a given asset at a specified price (X) during a specified period of time.

Holder

Call Option

Issuer

Payoff = max [(ST - X), 0]

X Payoff = min [-(ST - X), 0]

STT

S

X Profit (unlimited) = (ST - X) - C

Profit (max) = C

C

X X

X+C

X+C

STT

-C

Put Option

X Loss (max) = Call Premium (C)

Loss (unlimited) = (ST - X) - C

Payoff = max [(X - ST), 0]

Payoff = min [-(X - ST), 0]

X STT

X -X

Profit (max) = (X - ST) - P

P

-P

X-P

X -XP

X-PX

Profit (max) = P

STT

P-X

1 Loss (max) = Put Premium (P)

Loss (max) = (X - ST) - P

Types of Options

European

Features

American

Exercise on the expiration date Exercise on or before the expiration date

(T)

(T - ), where = payoff at exercise date

Arbitrage

Attempt to make costless profits through exploiting price differences of essentially identical assets by buying at a lower price and immediately selling at a higher price in different markets.

Binomial Option Pricing

P(G) = Probability of good state

P(B) = Probability of bad state

S0 = Spot price

S1 = Price at period 1

SG1 = Price in good state at S1

SB1 = Price in bad state at S1

a = Number of units of stock

b = Number of units in the risk free asset

Call premium (Price) = C

Put premium (Price) = P

X = Strike price

R = Risk free rate

Portfolio Replication

Payoff

Portfolio Contents

Call Option Portfolio

Put Option Portfolio

Call option + Risk free asset

Put option + Risk free asset

when P(G) in S1

aSG1 + b(1 + R) = SG1 - X

aSG1 + b(1 + R) = 0

when P(B) in S1

aSB1 + b(1 + R) = 0

aSB1 + b(1 + R) = X - SB1

Cost of Portfolio in S0

aS0 + b = C

aS0 + b = P

Solve the equation to find C and P

Note: Continuous Compounding beR x T

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