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Major Theories in Finance

Three major pillars of modern finance.

Capital Asset Pricing Model (CAPM)

Relates the risk of an asset to its required expected return. Dividend and Capital Structure Irrelevance (M and M)

In a perfect world:

i) A firm's share value does not depend on the firm's dividend policy. ii) The firm‟s total value does not depend on the amount of debt it has. Option Pricing Theory

Can find the value of an option.

Shares are a call option on the firm's assets.

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Two concepts

Equilibrium

Equilibrium prices: those at which, on average,

the number of buyers at that price equals the number of sellers. Arbitrage

Two portfolios having identical cashflows (with identical risk) must have identical value.

Otherwise one may arbitrage between them.

CAPM is an equilibrium theory.

Option valuation relies on arbitrage pricing theory.

Construct a hedging portfolio with identical cashflows to the option. Arbitrage concept.

Nick Webber, C++ modelling, introduction

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What is a Financial Asset?

A financial asset is an entitlement to a cashflow.

Factors: Number of payments and when they occur.

Their size and their risk.

Examples

1) An entitlement to receive £100 in one year from

i) a bank,

ii) a tenant.

2) A lottery ticket paying out

i) £100 in one week with probability

ii) £10m in one week with probability

1.

20

1

.

2,000,000

3) An IOU from someone you lent £5 to.

Nick Webber, C++ modelling, introduction

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Examples of Traded Financial Assets:

Shares and bonds

Shares

Bonds,

sovereign

coupons +

Cashflows: dividends

principal

Occurrence: ½ yearly (UK) ½ yearly (UK)

Size:

Risk:

unknown

high

known

less risk

Bonds,

corporate

coupons +

principal

quarterly or

semi-annually

known

intermediate

risk

Dividend size fixed by managers each half-year. Essentially random. Size of (promised) coupons known for sure, but can default.

Can have fixed and floating rates.

Final payment includes the principle.

Nick Webber, C++ modelling, introduction

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Annuities and Perpetuities

Entitlement to receive a fixed sum each year for:

a fixed number of years (annuity),

always (perpetuity).

Forwards and Futures

Obligation to buy (sell) an asset in the future at a price agreed today. Settle at the purchase date (forward contract).

Make partial settlement each day - “Mark to Market” (futures contract). Cashflows for a forward: (long a contract)

Positive at the maturity time T if at maturity

the asset price, ST, is greater than the agreed price, X.

Negative if ST < X.

Cashflow at time T is: C = ST - X.

Nick Webber, C++ modelling, introduction

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Vanilla options: calls and puts

Entitlement to buy (sell) an asset in the future

at a price (the exercise price or strike price) agreed today. No obligation to buy or sell.

An option to buy is called a call, an option to sell is called a put. European option:

Exercisable on the maturity date only.

American option:

Exercisable at any time up to the maturity date.

Bermudan option:

Exercisable at several particular times up to the final maturity date. Nick Webber, C++ modelling, introduction

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Cashflow upon exercise

Cash flow ht for a call option, if exercised at time t:

ht = max(St - X, 0).

Positive if the asset price, St, is greater than the exercise price, X. Zero otherwise.

Cash flow ht for a put option, if exercised at time t:

ht = max(X - St, 0).

Positive if the asset price, St, is less than the exercise price, X. Zero otherwise.

Nick Webber, C++ modelling, introduction

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Basic Ideas of Valuation

Time Value of Money

Riskiness of cashflows

Time Value of Money

Receive £100 with no risk in one year?

Suppose today‟s riskless interest rate is 10%.

Invest £90.91 ( ~ 100/1.1 ) now, get £100 in one year, risklessly. Present value of £100 received in one year is £90.91.

Nick Webber, C++ modelling, introduction

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