PAK Study Manual QF-北美精算师(QFIQF)

Intro-Maths-Fin-1

Financial Derivatives (A Brief Introduction )

Background This chapter deals with the two basic building blocks of financial derivatives:

1. Options

2. Forwards and futures.

We briefly introduce the third class of derivative: swap. We see how a complex swap can be decomposed into a number of forwards and options.

Definitions Derivatives securities are financial contracts that ‘derive’ their value from cash market instruments such as stocks, bonds, currencies and commodities.

At the time of the maturity of the derivative contract, denoted by T , the price F(T) of the derivative asset is completely determined by the market price of the underlying asset (S T ).

For instance, the value at maturity (T ) of a long position in a call option of strike (K) written on an asset (S T ) is:

Max [S T −K ;0]

Also, the value of time T of a long position in a forward contract of forward price (F) written on an underlying asset worth (S(T) at time T is given by:

S (T )−F

Types of derivatives We group derivatives into three general headings:

1. Futures, Forwards, Repos, Reverse Repos and Flexible Repos (Basic building blocks )

2. Options and

3. Swaps

Many of these instruments will be discussed in other parts of the syllabus for the QF Exam.

The underlying asset

: We let (S t ) represent the price of the relevant cash instrument, which we call the underlying asset . The five main groups of underlying asset : We list five main groups of underlying assets:

1.Stocks (These are claims on “real” returns)

2.Currencies

3.Interest rates: Interest rate in not an asset, so we are referring to the direction of interest rates. The assets are Treasuries, bonds.

4.Indexes (S&P 500) and

modities: they are not financial assets either, they are goods in kind. There is another method for classifying the underlying asset:

1.The cash and carry markets and

2.The price discovery markets

Let us discuss these two markets

This new classification is important to us.

In the cash and carry market, one can borrow at risk-free rates, buy and store the product,

and insure it until the expiration date of any derivative contract.

Pure cash and carry market have one property: Information about demand and supplies

of the underlying instrument should not influence the spread between cash and

futures (forward) prices.

In the Pure cash and carry market, any relevant information concerning future supplies and

demands of the underlying instrument is expected to make the cash price and the future price change by the same amount (This is not so, in the price discovery market).

In the price discovery market, it is physically impossible to buy the underlying instrument

for cash and store it until some future expiration date. That strategy (of borrowing, buying and storing) is no longer applicable.

In the price discovery market, any information about the future supply and demand of the

underlying commodity cannot influence the corresponding cash price.

Expiration Date

At the expiration of the forward/futures contract, we expect:

At expiration,tℎe Futures price=F(T)=Tℎe spot price of tℎe underlying asset=S T But, during the life of the futures contract (t