Derivatives and Risk Management Review for 118

8/6/2019 Derivatives and Risk Management Review for 118

1/10

5/10/2011

1

Derivatives and RiskManagement

(Adapted from Prof. Dani Salazars Slides)

1

Financial risks

Price risk

Interest rate risk

Credit / Default risk

Foreign currency risk

2

What is a financial derivative?

A derivative is an instrumentwhose value depends on thevalues of other more basic

underlying variables.

3

Uses of derivatives

Hedge

Arbitrage

Speculate

4

Basic forms of derivatives

Commitments

Forwards

Futures

Swaps

Contingents

Options

5

What is a forward contract?

It is an agreement to buy or sell an assetat a certain time in the future for a certainprice

Over the counter securities

Forward contracts are popular oncurrencies and interest rates

6


2/10

5/10/2011

2

Futures contract

An agreement to buy or sell an asset at acertain time in the future for a certain price

Futures are exchange-traded.

Examples of underlyings of futurescontract: commodities, interest rates

7

Swaps

Promise to exchange cash flows atvarious future time periods.

Cash flows maybe based on differentunderlyings such as return on equitymarkets, return on bonds markets, etc.

8

Options

A call option is an option to buy a certainasset by a certain date for a certain price(the strike price)

A put option is an option to sell a certainasset by a certain date for a certain price(the strike price)

9

Commitments versus contingents

A commitment contract gives the holderthe obligation to buy or sell at a certainprice

A contingent gives the holder the right tobuy or sell at a certain price. Such rightsare exercised only when it is beneficial to

the holder of the right.

10

Roadmap

For each of the basic form of derivative,the following subtopics will be discussed:

Nature

Pricing

Pay-off

Valuation

Application

11

FORWARDS AND FUTURES

F

12


3/10

5/10/2011

3

Forwards

A forward contract is an agreement tobuy (long position) or sell (short position)an asset in the future at an agreed price(delivery price) today

The asset could be a stock, a foreigncurrency, another financial instrument(e.g. bond)

13

Difference between Forwards andFutures

Forward Futures

Private contract between twoparties

Traded on an exchange

Not standardized Standardized

Usually one specified deliverydate

Range of delivery dates

Settled at end of contract Settled daily

Delivery or final settlement usual Usually closed out prior tomaturity

Some credit risk Virtually no credit risk

14

Price versus value

For futures or forward, price is the contracted rateof future purchase. It is the future value of the underlying.

Value is similar to profit from the forward orfutures contract. At date of contract, value of forward and futures is zero.

Why?

15

Forward price

f0(T) = S0 (1+r)T

Definition:

f0(T) = Forward price at time 0.

S0 = Spot price of the underlying at time 0.

r = risk-free rate

T = Number of days before expiration

16

Example

The spot price of gold is 600. The one yearinterest rate is 5%. What should be theforward price of a gold forward to bedelivered one year from now.

In our examples, S=600, T=1, and r=0.05so that

F = 600(1+0.05) = 630

17

Forward price of Equity

f0(T) = (S

0 D) (1+r)T

Definition:


S0 = Spot price of the underlying stock attime 0.

D = Present value of dividends to bereceived prior to expiration of forward

r = risk-free rate

T = Number of days before expiration

18


4/10

5/10/2011

4

Forward price of Equity

f0(T) = (S0 D) (1+r)T

Definition:

S0 = Spot price of ABC stock is P10.

D = ABC declared cash dividends of P2 tobe paid 30 days from today. PV of P1.99

r = 30 - 60 days zero-coupon rate is 6% p.a

T = 60 days

f0(T) = (10 1.99) (1+6%)60/360

f0(T) = 8.08819

Forward price of foreign currency

f0(T) = S0 (1+r1)T /(1+r2)

T

Example:

f0(T) = P / $ (1+rP)T /(1+r$)

T

Definition:


S0 = Spot price of the underlying currency attime 0.

r = risk-free rate

T = Number of days before expiration20

Example

f0(T) = P / $ (1+rP)T /(1+r$)

T

Definition:


S0 = Spot price of peso is P 46 = $1.

rP = 30 days peso zero-coupon bond is 3%.

r$ = 30 days peso zero-coupon bond is 1%.T = 30 days

f0(T) = P 46/ $1 (1+3%)30/360 /(1+1%)30/360

f0(T) = 46.07521

Pay-off

On the date of expiration, the long paysthe forward price (F).

And receives delivery of the underlying(Stm).

Mathematically:

Pay-off = Stm F

If S > F, the long is a net receiver.

If S < F, the short is a net payor.

22

23

Profit from aLong Forward Position

Profit

Price of Underlying

at Maturity, STK

24

Profit from aShort Forward Position

Profit

Price of Underlying

at Maturity, STK


5/10

5/10/2011

5

What is the value of a forward?

Vt(T) = St - f0(T)/(1+r1)T-t

Definition


S0 = Spot price of the underlying at t ime t.

r = risk-free rate

t- T= time to expiration

25

Value of forward at time 0

Vt(T) = St - f0(T)/(1+r1)T-t

Vt(T) = 600 - 630/(1+5%)1

Vt(T) = 600 600

Vt(T) = 0

Definition

f0(T) = Forward price at time 0 = 630.

S0 = Spot price of the underlying at time t = 600.

r = risk-free rate = 5%

t- T= time to expiration = 1 year

26

Value of forward 6 months fromnow when spot is 610.

Vt(T) = St - f0(T)/(1+r1)T-t

Vt(T) = 610 - 630/(1+5%)6/12

Vt(T) = 610 614.82

Vt(T) = - 4.82

Definition

f0(T) = Forward price at time 0 = 630.S0 = Spot price of the underlying at time t = 610.

r = risk-free rate = 5%

t- T= time to expiration = 30 days

27

SWAPS

28

Nature

A swap is an agreement to exchange cashflows at specified future times according tocertain specified rules

29

Examples:

Plain vanilla interest rate swap

Foreign currency swap

Equity swap

Equity for bond swaps

30


6/10

5/10/2011

6

Uses of an Interest Rate Swap

Converting a liability from fixed rate to floating rate floating rate to fixed rate

Converting an investment from fixed rate to floating rate floating rate to fixed rate

Valuation of an Interest Rate Swap

Portfolio of bonds = Difference betweenthe Value of a fixed-rate bond and thevalue of a floating-rate bond

Portfolio of forwards = Values ofdifferent cash flows at different periods.

FVTPL - Swaps

A speculator is expecting interest rates to go down. On

January 1, he entered in a 2 year plain-vanilla interest

rate swap to receive a fix interest rate of 6% and pay

floating equivalent to 180-day treasury rate + 3%. The

nominal principal is P5 Million. The counterparties

agreed to swap every June 30 and December 31. The

180-day treasury on January 1 is 3%.

Period 180 day

treasury rates

January 1, 2003 3%

June 30, 2003 4%

December 31, 2003 2%

FVTPL - Swaps

FVTPL - Swaps

Value of Swap

Date of inceptionPoint of view of the speculator.

Value of fixed income investmentcoupon rate: 6%floating rate: 3% + 3%

P 5 Million

Value of floating rate borrowings ( 5 Million)

Value of swaps - 0 -

FVTPL - SwapsSwapJune 30180-day treasury rate= 3%.

No payment on June 30, first swap period

SpeculatorCounter-

Party

6% X P5M [fix]

(3%+3%)X P5M [fl]


7/10

5/10/2011

7

FVTPL - SwapsSwapDecember 31180-day treasury rate= 4%.

Speculator is net payor of P25K

SpeculatorCounter-

Party

6% X P5M X 6/12 [fix]

(4%+3%)X P5M X 6/12[fl]

FVTPL - SwapsValue of SwapOn Balance Sheet Date (December 31)180-day interest rate = 2%Point of view of the speculator.

Value of fixed income investmentcoupon rate: 6%discounting rate: 2% + 3%

P 5.048 Million

Value of floating rate borrowings ( 5 Million)

Value of swaps P 0.048 Million

Therefore, the swap is a derivative assetto the speculator.

Principal 5,000,000.00

market rate 5%

coupon 6%

remaining swap period 2

PV of principal 4,759,071.98

PV of interest 289,113.62PV of fixed income 5,048,185.60

Value of Fixed Income InvestmentValue of Fixed Income InvestmentFVTPL - Swaps

SwapJune 30, Y2180-day treasury rate= 2%.

Speculator is net receiver of P25K

SpeculatorCounter-

Party

6% X P5M X 6/12[fix]

(2%+3%)X P5M X 6/12[fl]

Currency swaps

Counterparties swapped principal at thebeginning of the contract.

Interest are paid periodically based on thecurrency received and agreed uponinterest rate.

Counterparties return the principal at theend of the swap contract.

41

Uses of a Currency Swap

Conversion from a liability in one currencyto a liability in another currency

Conversion from an investment in onecurrency to an investment in anothercurrency


8/10

5/10/2011

8

Valuation of Currency Swaps

Like interest rate swaps, currencyswaps can be valued either as thedifference between 2 bonds or as aportfolio of forward contracts

OPTIONS

44

Options

A call is an option to buy

A put is an option to sell

A European option can be exercised onlyat the end of its life

An American option can be exercised atany time

45

Option Positions

Long Call

Profit from buying one European call option:

option premium = $5, strike price = $100.

30

20

10

0-5

70 80 90 100

110 120 130

Profit ($)

Terminalstock price ($)

Profit = Spot Exercise price premium paid

Profit = premium paid

Short Call

Profit from writing one European call option: option

premium = $5, strike price = $100

-30

-20

-10

05

70 80 90 100

110 120 130

Profit ($)


Profit = Exercise price + premium paid - Spot

Profit = + premium paid


9/10

5/10/2011

9

Long Put

Profit from buying a European put option: optionpremium = $7, strike price = $70

30

20

10

0

-770605040 80 90 100

Profit ($)


Profit = Exercise price - Spot premium paid

Profit = premium paid

Short Put

Profit from writing a European put option: optionprice = $7, strike price = $70

-30

-20

-10

7

070

605040

80 90 100

Profit ($)Terminal

stock price ($)

Profit = Spot + premium paid Exercise price

Profit = + premium paid

Payoffs from Options

K= Strike price, ST = Price of asset atmaturity

Payoff Payoff

ST STK

K

Payoff Payoff

ST STK

K

Terminology: Moneyness :

At-the-money option

In-the-money option

Out-of-the-money option

Simple Option Pricing

53

0or))1(

(

0or))1(

(

0

0

Sr

Xp

r

XSc

t

t

+

=

+

=

Factors affecting option value

Price of underlying

Strike price or exercise price

Time to maturity (life of option)

risk-free interest rate (corresponding tooption maturity; continuouslycompounded)

volatility of asset price

54


10/10

5/10/2011

10

References:

Hull, John. 2007. Fundamentals ofFutures and Options Markets, 6th Edition

Brooks, Robert. Don Chance. 2008.Derivatives and Risk Management Basics

55

Derivatives and Risk Management Review for 118

Documents

Transcript of Derivatives and Risk Management Review for 118