L2 flash cards derivatives - ss 17

Study Session 17, Reading 50

Synthetic Call

fiduciary call - consists of a European call and a risk free bond. protective put - consists of a put and underlying asset.

Formula:


Synthetic Put

Formula:

It says that a put is equal to a long call. A short position in the underlying. Long position in the bond.


Synthetic Stock

Formula:

Buy a European call. Sell a European put. Invest the present value of exercise price in a riskless pure discount bond.


Synthetic Bond

synthetic bond - a portfolio of financial instruments designed to mimic the cash flow and risk profile of a bond.

A synthetic bond may contain financial instruments such as bond puts, bond calls, bond futures, Treasuries, money market securities, and CDS'.


Binomial Model for Options on AssetsA binomial tree is built depicting different prices under

different probabilities. If there is no risk involved, all assets will be priced to provide a

riskless rate of return.

Value:P=1+r-d/u-d


Binomial Interest Rate Option Pricing

Formula(s): Expiration value of a caplet = max 0,{(1-yr-cap rate)×notional ⦋

principal} /1+one year rate⦌

Expiration value of a floorlet = max 0,{(floor rate-one year ⦋rate)×notional principal} /1+one year rate⦌


Assumptions Underlying the Black-Scholes-Merton Model

Price of the underlying follows a lognormal distribution.Lognormal variable has values which are normally distributed. The value of the option has a minimum of zero. The risk free rate is constant and known. Interest rate volatility is important for determining the value

of bonds.


Effect of Changes in Input Values on Call Option Prices

Higher for higher underlying priceHigher for longer time to expirationHigher for higher volatilityHigher for higher risk free rateHigher for lower exercise price


Effect of Changes in Input Values on Put Option Prices

Higher prices for lower underlying pricesHigher prices for higher volatilityHigher prices for lower risk free rateHigher prices for higher exercise price


Delta of an Option in Dynamic Hedging

Delta estimates the change in price for a one unit change in the price of the underlying.

Formula(s):

Delta Call =change in call price/change in stock price.

Change in call price ≈ N(d1)× change in stock price

Change in put price ≈ N(d1)-1× change in stock priceWhere: N(d1) - call options delta

N(d1)-1 - put option’s delta


Delta of an Option in Dynamic Hedging (cont.)

Dynamic hedging (also called delta neutral hedge) involves creating a delta neutral portfolio with a combination of short call options and the underlying stock.

Formula:

number of call options needed to delta hedge=number of shares hedged/delta of call option


Gamma Effects on a Delta HedgeGamma measures the rate of change in delta as the price of

the underlying changesGamma can be used as a measure of the effectiveness of a

delta hedge.Hedges with at the money options will have higher gammas.Small changes in the stock prices will cause large changes in

deltas and frequent rebalancing


Effect of Underlying Asset's Cash Flows on the Price of an Option

Some assets have cash flows attached to them Option prices need to be adjusted for these cash flowsAll else equal, cash flows on the underlying will decrease the

value of a call option. All else equal, cash flows on the underlying will increase the

value of a put option.


Historical Volatility for Estimatingthe Future Volatility of the Underlying Asset

Volatility - measures the day to day price changes in the market. Historical volatility - a measure of price changes during a specific time

period in the past

Factors to calculate volatility:1. Calculate the continuously compounded return at each interval. 2. Calculate the daily price changes. 3. Calculate the average daily price change.4. Calculate the standard deviation of returns. 5. Annualise historical volatility.


Implied Volatility for Estimatingthe Future Volatility of the Underlying Asset

Implied volatility looks into the future. It can be inferred by working backward by setting the BSM price equal to the market price.


Put-Call Parity for Options on Forwards

Two portfolios will be created to make the put call parity.

Formula(s):

Co+

Co+


American and European Options on Forwards and Futures

The Black model can be used to price the European options on futures:

c = e − rcT[FN(d1) − XN(d2)]p = e − rcT[X(1-N( − d2)) – F(1-N( − d1))]


Pricing and Valuation of SwapsA swap rate (fixed rate) is determined at the time of initiation

of the swap.The value of the swap at the time of the initiation is zero to

both the parties. The swap rate makes the present value of the fixed rate

component equal to the floating rate component of the swap.


Interest Rate Swaps to Off-Market FRAs

Swaps are also referred to as a series of off- market FRAs.Each FRA fixed rate differs but the swap fixed rates are known

for the life of the swap.The swap fixed rate is equal to “average” rate of on-market

FRAs. The FRA payment is determined at the end of the period.


Plain Vanilla Swap to Interest Rate Call and Put

Swaps can also be equal to interest rate calls and puts.A fixed rate paying swap is equal to long interest rate call and

short interest rate put. A fixed rate receiver swap is equal to long interest rate put

and short interest rate call.


Fixed Rate and Market Value of the Swap

The fixed rate is determined at the time of initiation.

Formula(s):

Where: Zn - the n period zero coupon bond


Fixed Rate and Market Value of the Swap (cont.)

Formula(s) to calculate Market Value:

Market value is also sometimes called the replacement value


Four types of currency swaps1. Fixed for fixed2. Fixed for floating3. Floating for floating 4. Floating for fixed


Fixed Rate on Currency Swap

Formula(s):


Three types of equity swaps1. Pay fixed and receive return on the equity2. Pay floating rate and receive the return on the equity3. Pay the return on one equity and receive the return on another equity


Fixed Rate on an Equity Swap and Market Value

The equity side can be valued by multiplying the notional principal with the one percent change in the equity side since the last payment date

Formula:


Swaptions

swaption - an option on a swap. It gives the holder a right to enter into an interest rate swap in the future.

strike rate - the fixed rate in the Swaption is predetermined


Payoffs and Cash Flows of an Interest Rate Swaption

If the swap rates rise, a payer Swaption is in the money. A receiver swaption is in the money if the interest rates fall.Annuity payments will be achieved by the holder of the option by

exercising an in the money swaption.Payoff comes in the form of interest savings.


The Value of an Interest Rate Swaption at Expiration

payoff of a payer swaption = max×∑(discount factor)

payoff of a receiver swaption = ×∑(discount factor)

The value of the receiver swaption at expiration is the maximum of zero and the present value of a stream of payments.


Credit Risk

swap credit risk - the risk that one party will be unable to make the payments owed to the other party

current credit risk - the risk pertaining to the current payment due

potential credit risk - the risk of a party being unable to make a future payment is called the


Swap Spread and its Relation to Credit Risk

The swap spread indicates the average credit risk in the global economy.

The swap spread is the quality or default risk spread between a default free security and LIBOR.

Swap Spread = Fixed-rate on Swap - yield on default free security of the same maturity as the swap


Interest Rate Caps

interest rate cap or ceiling - an agreement where one party agrees to pay when the reference rate is greater than predetermined rate

caplets - individual interest rate call options

long cap - equal to a portfolio of long put options on fixed income security prices.


Interest Rate Floors

interest rate floor - an agreement in which one party agrees to pay when the reference rate is less than the predetermined rate

floorlet - separate put option

long floor - is equal to a portfolio of long call options on fixed income security prices


Payoff for a Cap and Floor

Formula(s):

Payoff to cap buyer= Max (0, Notional Principal×(Reference rate-Cap rate)×(actual days/360))

Payoff to floor buyer = Max (0, Notional Principal×(Floor rate-reference rate)×(actual days/360))


Interest Rate Collar

interest rate collar - a combination of a long interest rate cap and a short interest rate floor.

zero-cost collar - a collar is structured such that the premium paid for a cap is equal to the premium received from the floor


Credit Default Swapsand Corporate Bonds

CDS is just like an insurance contract. It provides the buyer protection against the default risk, bankruptcy or credit ratings downgrade.

CDS are usually written on fixed income securities, a bond, or a loan.


Advantages of Credit Default Swaps

Credit Default Swaps (CDS) provide a hedge against event risk. CDS allow for the management of credit risk separately. Default risk and interest rate risk can be managed separately.


Uses of Credit Default SwapsTo hedge the credit risk exposure Easy liquidity and access to the rest of the participants in the

market To satisfy regulatory capital requirements For hedging and enhancing income


Credit Derivative Trading Strategies

Basis TradeCurve TradeIndex TradeOptions TradesCapital Structure TradesCorrelation Trades


Basis Trade

Value:cash-default swap = CDS spread (premium)- asset (bond) swap

spread

negative basis - the bond is cheaper than the CDS and a positive annuity can be built by buying bond and the CDS

positive basis trade - involves shorting the bond which makes it complicated to execute

Economy & Finance

L2 flash cards derivatives - ss 17